V106 3 S 2015 S IN INSI I NINS 107 ISSN 1991-1696 …...2016/12/15 · V106 3 S 2015 S IN INSI I NINS 107 September 2015 Volume 106 No. 3 Africa Research JournalISSN 1991-1696 Research

Vol.106 (3) September 2015 SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS 107

September 2015Volume 106 No. 3www.saiee.org.za

Africa Research JournalISSN 1991-1696

Research Journal of the South African Institute of Electrical EngineersIncorporating the SAIEE Transactions

Vol.106 (3) September 2015SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS108

(SAIEE FOUNDED JUNE 1909 INCORPORATED DECEMBER 1909)AN OFFICIAL JOURNAL OF THE INSTITUTE

ISSN 1991-1696

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SAIEE AFRICA RESEARCH JOURNAL

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SPECIALIST EDITORSCommunications and Signal Processing:Prof. L.P. Linde, Dept. of Electrical, Electronic & Computer Engineering, University of Pretoria, SA Prof. S. Maharaj, Dept. of Electrical, Electronic & Computer Engineering, University of Pretoria, SADr O. Holland, Centre for Telecommunications Research, London, UKProf. F. Takawira, School of Electrical and Information Engineering, University of the Witwatersrand, Johannesburg, SAProf. A.J. Han Vinck, University of Duisburg-Essen, GermanyDr E. Golovins, DCLF Laboratory, National Metrology Institute of South Africa (NMISA), Pretoria, SAComputer, Information Systems and Software Engineering:Dr M. Weststrate, Newco Holdings, Pretoria, SAProf. A. van der Merwe, Department of Infomatics, University of Pretoria, SA Dr C. van der Walt, Modelling and Digital Science, Council for Scientific and Industrial Research, Pretoria, SA.Prof. B. Dwolatzky, Joburg Centre for Software Engineering, University of the Witwatersrand, Johannesburg, SAControl and Automation:Dr B. Yuksel, Advanced Technology R&D Centre, Mitsubishi Electric Corporation, Japan Prof. T. van Niekerk, Dept. of Mechatronics,Nelson Mandela Metropolitan University, Port Elizabeth, SAElectromagnetics and Antennas:Prof. J.H. Cloete, Dept. of Electrical and Electronic Engineering, Stellenbosch University, SA Prof. T.J.O. Afullo, School of Electrical, Electronic and Computer Engineering, University of KwaZulu-Natal, Durban, SA Prof. R. Geschke, Dept. of Electrical and Electronic Engineering, University of Cape Town, SADr B. Jokanović, Institute of Physics, Belgrade, SerbiaElectron Devices and Circuits:Dr M. Božanić, Azoteq (Pty) Ltd, Pretoria, SAProf. M. du Plessis, Dept. of Electrical, Electronic & Computer Engineering, University of Pretoria, SADr D. Foty, Gilgamesh Associates, LLC, Vermont, USAEnergy and Power Systems:Prof. M. Delimar, Faculty of Electrical Engineering and Computing, University of Zagreb, CroatiaDr A.J. Grobler, School of Electrical, Electronic and Computer Engineering, North-West University, SA Engineering and Technology Management:Prof. J-H. Pretorius, Faculty of Engineering and the Built Environment, University of Johannesburg, SA

Prof. L. Pretorius, Dept. of Engineering and Technology Management, University of Pretoria, SA

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INTERNATIONAL PANEL OF REVIEWERSW. Boeck, Technical University of Munich, GermanyW.A. Brading, New ZealandProf. G. De Jager, Dept. of Electrical Engineering, University of Cape Town, SAProf. B. Downing, Dept. of Electrical Engineering, University of Cape Town, SADr W. Drury, Control Techniques Ltd, UKP.D. Evans, Dept. of Electrical, Electronic & Computer Engineering, The University of Birmingham, UKProf. J.A. Ferreira, Electrical Power Processing Unit, Delft University of Technology, The NetherlandsO. Flower, University of Warwick, UKProf. H.L. Hartnagel, Dept. of Electrical Engineering and Information Technology, Technical University of Darmstadt, GermanyC.F. Landy, Engineering Systems Inc., USAD.A. Marshall, ALSTOM T&D, FranceDr M.D. McCulloch, Dept. of Engineering Science, Oxford, UKProf. D.A. McNamara, University of Ottawa, CanadaM. Milner, Hugh MacMillan Rehabilitation Centre, CanadaProf. A. Petroianu, Dept. of Electrical Engineering, University of Cape Town, SAProf. K.F. Poole, Holcombe Dept. of Electrical and Computer Engineering, Clemson University, USAProf. J.P. Reynders, Dept. of Electrical & Information Engineering, University of the Witwatersrand, Johannesburg, SAI.S. Shaw, University of Johannesburg, SAH.W. van der Broeck, Phillips Forschungslabor Aachen, GermanyProf. P.W. van der Walt, Stellenbosch University, SAProf. J.D. van Wyk, Dept. of Electrical and Computer Engineering, Virginia Tech, USAR.T. Waters, UKT.J. Williams, Purdue University, USA

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VOL 106 No 3September 2015

SAIEE Africa Research Journal


September 2015Volume 106 No. 3www.saiee.org.za

Africa Research JournalISSN 1991-1696

Research Journal of the South African Institute of Electrical EngineersIncorporating the SAIEE Transactions Teletraffic Analysis of a Call Admission Control Scheme

with TCP Protocol Induced T Walingo .................................................................................. 110

A Study on Impulse Noise and Its ModelsT. Shongwe, A.J. Han Vinck and H.C. Ferreira ........................ 119

Development of a Maintenance Strategy for Power Generation PlantsL. Ndjenja and J.K. Visser ............................... ........................ 132

Model Predictive Control of an Active Magnetic Bearing Suspended Flywheel Energy K.R. Uren, G. van Schoor and C.D. Aucamp ........................... 141

Incentives and South Africa’s Automotive IndustryPerformance: A System Dynamics M. Kaggwa and J.L. Steyn ........................................................ 152

Analysis and Optimization of Auto-Correlation BasedFrequency Offset EstimationI.M. Ngebeni, J.M. Chuma and S. Masupe .............................. 162

SAIEE AFRICA RESEARCH JOURNAL EDITORIAL STAFF ...................... IFC


TELETRAFFIC ANALYSIS OF A CALL ADMISSION CONTROL SCHEME WITH TCP PROTOCOL INDUCED FACTORS T. Walingo* * Centre of Radio Access and Rural Technologies, University of KwaZulu-Natal, Private Bag X54001, Durban, South Africa E-mail: [email protected] Abstract: Future networks face tremendous challenges towards providing guaranteed Quality of Service (QoS) for the multiple traffic types employing numerous protocols. This work presents an expanded parameter Call Admission Control (CAC) scheme and intelligent scheduling to provide QoS on modern networks. The expanded parameter CAC scheme features the lower layers Signal to Interference Ratio (SIR) and network delay as admission parameters. The SIR is due to the transmission on the code division multiple access network and delay is due to the operation of the Transmission Control Protocol (TCP). TCP delay is a good representative of the aggregated delays of the entire network; both access and core network as it is at a higher layer. TCP was ideally designed for wired networks. TCP performance is degraded and leads to substantial delay while operating on wireless lossy links as it reduces the sending rate and resends lost packets. This work presents an analytical framework for evaluating the performance of a wireless TCP based CAC model which features Batch Markovian Arrival Process (BMAP) traffic, a better representative of the future traffic characteristics than the traditional Poisson traffic. A teletraffic analysis of a network with TCP is done and the impact of TCP induced delays on the network is investigated for a future generation CAC scheme. Keywords: BMAP, Call admission control, CDMA, Multimedia traffic, TCP.

1. INTRODUCTION Future networks design needs to overcome the numerous network and traffic challenges. The network challenges include those associated with increasing the network capacity, accommodating diverse heterogeneous networks, mobility management and dealing with diverse network protocols e.g. Code Division Multiple Access (CDMA) and TCP with their own inherent problems [1][2][3]. They also handle diverse ever growing applications over cellular networks with their own challenges. The traffic challenges include; diversity in QoS requirements, multimedia traffic types, real time or non-real time with different QoS metrics (BER and delay). Furthermore, the traffic may exhibit other properties such as burstiness, correlation and self-similarity. An efficient CAC scheme is one of the methods employed to guarantee QoS on a CDMA based network. This heterogeneous mix of services with varying QoS metrics and characteristics must be supported and provided with their guaranteed QoS. Each traffic type has got key QoS defining metric(s). These key metric(s) for a traffic type must be identified and made the principal admission parameter(s). The most common QoS parameters for most traffic on a CDMA network are the SIR and delay. SIR has traditionally been the de facto parameter for CAC on CDMA based networks [4][5]. A combination of several admission parameters has been encountered in seldom [6][7]. In this work, the employed CAC considers both SIR and delay. The SIR is on the CDMA wireless link while the delay can be due to scheduling on the wireless link or in the core network. In a realistic network, delay is a result of

the effects of the numerous factors; scheduling, processing, transmission and routing. Access network delays and core network delays that arise due to transmission, scheduling and routing protocols have been widely explored as compared to other protocol induced delays [8][9]. Some network protocols like TCP, the transport layer protocol, Automatic Repeat request (ARQ), the link layer protocol, several Media Access Control (MAC) protocols like CDMA introduce delays in networks due to their operation. CDMA and ARQ protocol induced delays have received sufficient attention unlike the TCP induced delays [7][8][10]. TCP is one of the de facto transport protocols on the internet today. There are many TCP variants [11][12]; Tahoe, Reno, New Reno, SACK, Vegas, Fast TCP etc. However, their basic core functionality is the same. TCP was ideally designed for wired networks where the losses are not so great [3]. However, for an anything anytime anywhere network, TCP will operate on wireless networks with higher packet losses than expected. This leads to a degradation of the TCP’s performance as it was not meant to perform on very lossy links. TCP affects the whole network in the following ways; firstly, during congestion it reduces the sending rate on the network and secondly, when a packet is lost it resends the packet. These factors introduce latency in the whole network. They cause delays and greatly impact on the teletraffic performance of the network. TCP delay is an aggregation of delays at various layers of the protocol stack. It is a comprehensive summary of the user’s end to end delay including the access and core network delays. It is therefore imperative that a CAC scheme should feature the delay introduced by TCP. An analytical framework


for investigating a CAC for a future Next Generation Networks (NGN) with TCP protocol induced delay is presented in this work. Modern network models need to be used to effectively evaluate the performance of current and future CAC schemes. The analytical traffic models need to evolve with the evolving traffic characteristics. Traditionally, simple traffic models like the Poisson model have been used. However, they have been shown to be unsuitable for current and future IP based traffic [13]. BMAP traffic models have been favored to evaluate the performance of the CAC scheme. This is because BMAP is a generalization of a wide variety of traffic types and can effectively represent modern traffic than the Poisson model. The BMAP model suffers from drawbacks of complexity and fuels the matrix state space explosion of Markovian analytical models. It can easily render the analysis intractable. An approximate Markovian model to evaluate the BMAP based traffic models without too much error margins is developed and used in the teletraffic analysis. Closely related works [14][15][16], have addressed in parts the various sections of this work and not as a complete unit. A TCP-aware CAC scheme to regulate the packet-level dynamics of TCP flows is proposed and analyzed in [14]. A TCP call is admitted to the system and TCP call adjustment is done by reducing the transmission rate to fit in the available bandwidth. The work does not employ modern traffic models and the wireless link is not modeled. The work in [15] models the TCP window and addresses the inefficiencies that arise due to the peculiar window evolution. It introduces TCP feedback into the CAC procedures in different non terrestrial wireless architectures. The work is simulation based and no analytical model is developed. A more recent work in [16] develops an analytical model to investigate the performance experienced by TCP sessions sharing a wireless channel by a fixed point approach; two models for different packet loss scenarios, imperfect error correction and buffer overflow. Different analytical queuing models are investigated and compared. The paper justifies the use of simple queuing models, M/M/1/K or Geo/Geo/1/K as compared to the BMAP/G/1/K. Though debatable, there is no call admission control employed and the wireless link is not explicitly modeled. The main contribution of this work is to provide a unified analytical model of a multiclass heterogeneous TCP based wireless network featuring; modern BMAP traffic and a CAC based on the wireless SIR and TCP feedback delay. Performance evaluation for the various TCP protocols over different wireless channel models is done. This paper is organized as follows; Section 2 presents the system model; network model, CAC model and the wireless channel model. The analytical evaluation of SIR capacity and TCP based delay capacity is done in the section. The teletraffic queuing based analytical model is

developed in Section 3 where the following is presented; non-homogeneous BMAP arrival process and the Markovian model. The performance measures for evaluating the developed models are presented in Section 4. The obtained results are presented and discussed in Section 5 and the conclusions drawn in Section 6.

2. SYSTEM MODEL

2.1 Network Model The network consists of mobile stations of different classes; high priority traffic sensitive to both delay and packet loss, medium priority traffic that can tolerate some delay and packet loss violations and low priority best effort traffic. The traffic classes are grouped into the three groups depending on their desired BER (SIR) and delay thresholds. The CDMA based access network is employed. A call admitted in the network starts a TCP session for transmission of its traffic. TCP operates with independent sessions for each source and class. The different sessions affect each other by increasing interference on the wireless link and congestion in the core network. A particular call i of class k arrives according to a BMAPk distribution. The call requires SIR threshold

TkSIR and delay threshold Tkd . If admitted, the call generates traffic that is scheduled for transmission on the wireless queues as shown in the complete network system model of Fig. 1.

CAC(SIR/Delay)

Admitted callsDropped calls

BMAP2(SIR2, d2)

BMAP3(SIR3, d3)

BMAP1(SIR1, d1)

TCPSESSIONS

TCPSESSIONS

TCP DELAY

TCP DELAY

TCPSESSIONS

Fig. 1: System model

2.2 Call Admission Control Algorithm The call admission control employed is as follows. An arriving call requests admission from the base station. To admit a new call i of class k , the guaranteed QoS (SIR and delay bounds), for the particular call should be provided and the QoS of the existing calls should not be severely affected by admitting the call. The SIR capacity is determined, if there is no capacity, the call is dropped; the delay capacity is determined, if available, the call is


admitted. The analytical capacities represented by (2) and (16) are calculated in the sections that follow. 2.2.1 Capacity Based on interference The received signal to noise ratio ikob NE of user i kMi ,..2,1 of class k Nk ,...1 is given by:

k ijoikjkjk

ikikikikob

Wphf

phGNE1

, (1)

where ikG is the processing gain, ikh the path gain, ikp the transmitted power, jk the source activity factor, o the noise factor, W the bandwidth, f the ratio of the external to internal interference. The probability of accepting a call based on SIR under the minimum power requirement [17][18], S

Ap , is the given by [19]:

10 ),( ZPPSA . (2)

where tCtfttCZ (3)

and ikg is the power index, ik the power constraint and tC are respectively given by:

ikikTob

ikTobik GNE

NEg

,

, , (4)

ikikiki

oik ghp

W/min

, (5)

k i

ikik gttC , (6)

The mean and variances of Z can easily be derived [19]. If (2) is satisfied, then there is capacity based on SIR. 2.2.2 CAC capacity based on TCP Protocol Delay To determine TCP delay capacity, the TCP window evolution needs to be modeled. The behavior of various TCP protocols; window evolution, slow start, congestion avoidance, fast recovery and timeout has extensively been presented in literature [3][20][21]. Though there are many variants [11][12], the basic TCP protocols are used. TCP Window evolves in cycles which can be divided into rounds. After packet loss detection, a TCP cycle begins with either slow start or congestion avoidance and ends with the successful conclusion of fast recovery mechanism or on the basis of a timeout. A round starts with the transmission of w packets where w is the current size of the congestion window. To model the evolution, an analytical loss window model [22] is employed. Let

iW denote the maximum window size reached in the i th cycle.

mrecdd

dmreci WWWifW

WWWW

,,,min

(7)

where mW is the maximum window size allowed on the wireless link due to the constraint of the sum of wireless

link and the buffers in the system, recW is the maximum receiver buffer size that the receiver advertises at the beginning of TCP flow establishment. Finally, dW is the window where a packet drops due to congestion or the wireless channel losses. The sequences of window sizes at which packets are dropped in successive cycles iW form a Markov chain with transition matrix dii wWwWP 1 . The steady state loss window

probability dwP , dw = 1, 2… mW can be found from the transition matrix. The transition probability matrix is characterized by [22]

1

for 1 1

for

for

d

d

d

ssw s s s

ci i d sw s c s

ccw c c s

P D P S w P L w w w

P W w W w P D P S w P L w w w

P D P S w P L w w w

(8)

The terms of the equation are defined by the following events with sw as the slow start threshold: The event that the next cycle starts in congestion

avoidance given a packet loss at congestion window of dw is

dcwD . Its probability is dcwDP .

The event that the next cycle starts in slow start given a packet loss at congestion window of dw is

dswD . Its probability is dd cwsw DPDP 1 .

The event that packets successfully reach the receiver to attain a window size w belonging in slow start given that it started from slow start is

wS ss . Its probability is wSP s

s . The event that packets successfully reach the

receiver to attain a window size w belonging in congestion avoidance given that it started from slow start is wSc

s . Its probability is wSP cs .

The event that packets successfully reach the receiver to attain a window size w belonging in congestion avoidance given that it started from congestion avoidance is wS c

c . Its probability is

wSP cc

The event that a packet loss in a cycle results in a loss window w belonging in slow start is wLs . Its probability is wLP s .

The event that a packet loss in a cycle results in a loss window w belonging in congestion avoidance is wLc . Its probability is wLP c .

The probabilities are calculated in the sections that follow.

a) Calculation of wS ss , wS c

s and wS cc

Let dw , the drop window size in round d , be in slow start. To obtain a loss window size of dw the following


events must occur; 1 ds wx packets have to be successful and the dw ’th packet has to be dropped. The probability that enough packets successfully reach the receiver to attain a window size w belonging in slow start given that it started from slow start wSP s

s is given by:

1 dwss wTwSP

d , (9) where 1dw wT

d is defined in (23) of the wireless

section and noting that a packet is transmitted in a slot. Let dw , the drop window size in round d , be in congestion avoidance. To obtain a loss window size of

dw in congestion avoidance starting from congestion avoidance the following events must occur; cax packets have to succeed in the congestion avoidance

21 caca

cascarrrwx

(10)

where sdca wwr is the number of successful congestion avoidance rounds and sw is the slow start window threshold at which TCP enters congestion avoidance. The probability that enough packets successfully reach the receiver to attain a window size w belonging in congestion avoidance given that it started from congestion avoidance wSP c

c is given by

cawcc xTwSP

d , (11)

where caw xTd

is defined in (23). Let dw , the drop window size in round d , be in congestion avoidance. To obtain a loss window size of

dw in congestion avoidance starting from slow start the following events must occur; cast xxx packets must succeed. sx is the number of the successful slow start packets while cax are the successful congestion avoidance packets. The probability that enough packets successfully reach the receiver to attain a window size w belonging in congestion avoidance given that it started from slow start wSP c

s is given by:

twcs xTwSP

d

, (12) where tw xT

dis defined in (23).

b) Calculation of dswD and

dcwD The next cycle starts in slow start if the previous cycle ended in a timeout. Therefore,

dswDP is equal to the

timeout probability toP at the loss window of dw .

dcwDP is found from dd cwsw DPDP 1 , since the

next cycle either begins in slow start or congestion avoidance. For TCP Tahoe and Old Tahoe, 1

dswDP ,

therefore 0dcwDP . For the other TCP protocols the

probabilities are computed from the timeout probability toP discussed in the section below.

c) Timeout probability Calculation

When all the means of recovering from a packet by the TCP protocol fails, timeout occurs where the window reinitializes itself and restarts. Timeouts can be classified as direct or indirect. A direct timeout occurs if the number of duplicate Ack’s that arrive at the sender is less than a certain threshold (normally 3). For a small window 3dw , the number of duplicate Ack’s will not arrive at the sender and therefore, 1toP . For a larger loss window, the number of packets successfully delivered in the loss window dw , ,dx should be less than . The probability of a direct timeout toP is given by:

1dd

xdwto xTP

(13) An indirect timeout occurs if the TCP algorithm goes to fast retransmit and then the first recovery fails and a timeout occurs. This is given by the probability that the algorithm goes to fast retransmit and less packets go through for a first recovery to succeed and a timeout occurs. The probability of indirect timeout toP is given by

111

d

d

d

dx

dwx

dwto xTxTP . (14)

d) Calculation of wLs and wLc The probability of a packet loss in a cycle resulting in a loss window w belonging in slow start, wLP s , and the probability of a packet loss in a cycle resulting in a loss window w belonging in congestion avoidance,

wLP c , are identical and reduce to the probability of a packet loss after successful delivery of several packets. This is the probability of failure to deliver a packet in one slot. It is given by:

11TwLP s . (15) The values of

dswDP and dcwDP distinguish between

various TCP protocols. The probabilities depend on the wireless channels packet loss probabilities.

e) The TCP based delay capacity The TCP window evolves according to the network dynamics. Its growth is dependent on packet loss due to congestion or the wireless channel and the time of sensing the losses. The TCP window is therefore a good representative of the whole network delay due to the Round Trip Time (RTT) of sending a packet and receiving the acknowledgement. The TCP induced delay

Tkd can be translated into minimum packets to be transmitted per RTT kRttn . This directly translates to the TCP’s window size kRttw noting that each window/round is transmitted in one RTT. A call will satisfy admission criteria if the number of packets transmitted per RTT is above kRttn (window above kRttw ). Therefore the delay


bound of a particular traffic can be estimated from the average window size. The delay based probability of admitting a user of class k is given by:

m

kRtt

W

www

DAP

(16) where w is the probability of a TCP window size of w ,

mWw 0 . For the TCP model the loss window characterizes the maximum throughput of a TCP session. Together with the round trip time, this determines the least delay that can be guaranteed for a particular TCP session. 2.3 Wireless Model and packet error probability The wireless channel is modelled as a Finite State Markov Chain (FSMC). The FSMC Model represents the channel with multiple states with each state corresponding to a transmission mode [23]. It can be reduced to a Two State Markov Chain (TSMC) if the number of states reduces to two. In the FSMC the range of the received SNR is partitioned into a finite number of intervals. Let L100 0 be the thresholds of the received SNR. Then the channel is in state 1,,1,0 , LlSl , if the received SNR is in the interval ),[ 1 LL . An L-State FSMC Channel Model is depicted in Fig. 2.

0 1 2 L

P00

P01

P10

P11 P12 P22

P21 PLL

PL-1,L

PL,L-1

. . .

Fig. 2 2 L-State FSMC Channel Model The steady state distribution of the FSMC is , where

110 ,,, L and i is the probability that the underlying Markov chain is in state i given the chain is stable, and L is the number of states. In a typical multipath propagation environment, the received signal envelope has a Rayleigh distribution. With additive Gaussian noise, the received instantaneous SNR is distributed exponentially with Probability Density Function (PDF) [23]

0 ,1exp1

00

p (17)

where 0 is the average SNR. In this case, the steady-state probabilities of the channel states are given by

010 expexp

1,,1,0 ,1

ll

l

l

l

Lldp (18)

while satisfying

11

L

ll (19)

The packet error probability is a function of a given modulation scheme and a Forward Error Correction (FEC) code. Let eip be the channel bit error probability in the i -th state. The BER performance of uncoded BPSK scheme is given by,

i

iiiei Z

GgQQp (20)

where i represents the average value of SIR of a BPSK in the i -th state and Q is the Gaussian cumulative distribution function, ig the power index and iG the processing gain. Assuming ir is the service bit rate and taking into account that the transmission time of each packet is specified to tT . The number of bits per frame

nF is given by itn rTF . The packet loss probability per state lip is obtained as:

nFeili pp 11 (21)

The packet loss probability in a slot is given by:

L

iilil pP

0 (22)

Considering a transmission scheme where a packet is transmitted per slot and assuming there is no state transition within a slot, the probability of x packets transmitted successfully in n slots is:

xnl

xln PP

xn

xT

1 . (23)

This is used in calculating the packet loss probabilities for the TCP window evolution. 3 TELETRAFFIC ANALYTICAL EVALUATIONS 3.1 The BMAP Arrival Processes of the Model BMAP traffic models are used in the modeling of the network traffic as opposed to the simple Poisson models. The traffic arrival process is according to a non-homogeneous BMAP process due to the call admission control. The process is a 2-dimesional non homogeneous level dependent Markov process 0:, ttJtN pp on the state space mwwv 1 0, v:, for each 0p .

tN p is the number of arrivals and tJ p is the phase of

the process with an infinitesimal generator pQ of the structure;

30

21

20

12

11

10

03

02

01

00

DDDDDDDDDD

Q p, (24)


where the properties of the non-homogenous infinitesimal generator are dependent on the level p due to the effects of the CAC algorithm, a function of the number in the system. The stationary probability vector of the underlying Markov chain with generator D , denoted by , satisfies;

,0D 1e , (25) where e is a column vector of 1’s. The fundamental arrival rate, gives the expected number of arrivals per unit time, is thus given by;

1q

qeqD. (26)

The sBMAP can be considered as a superposition of several identical Markov Modulated Poisson Processes (MMPP’s). The arrival rate matrix and the infinitesimal generator matrix R, for the MMPP are given by:

1

0

00

, (27)

1010

0101

rrrr

R , (28)

where 1 ,0 , iP pAii and p

AP is an admission probability dependent on the level and is a product of (2) and (16). The elements of the generator matrix pD0 and

pD1 are functions of and R [24] and incorporates CAC parameters. 3.2 The Markovian Analytical Model

The teletraffic analysis is done by a Markovian model. A full Markovian model suffers from an explosion on the matrix state space [24] and can’t be used for complex networks. An approximate model has been used whose performance was tested and found to be close to the exact model [25]. The model used involves decomposition of the various classes into different priority queues at different stages with combined traffic. Consider three traffic classes with Class 1 as the highest priority and Class 3 the lowest. The arrival of traffic class k is governed by a kBMAP , which is itself a combination of several processes from the sources that constitute the traffic class. An illustration of the approximate analytical model is as presented in Fig. 3. For Stage 1, the traffic arrival into the high priority queue is a combination of the two high priority classes,

211 BMAPBMAPBMAPHP . The traffic arrival into the low priority queue is simply the lowest priority traffic class, 31 BMAPBMAPLP . The low priority traffic does not differentiate between the two traffic types of higher priority. The total arrival into the system is

3211 BMAPBMAPBMAPBMAPG . Let the total number of calls in the system be 1T , the total number of class one calls be X , the total number of class two calls

be Y and the total number of class three calls be Z . The average number of calls at stage one can be represented by YXEZETE 1 (29)

BMAPHP1

BMAPLP1

BMAPG1

BMAPHP2

BMAPLP2

BMAPG2

STAGE 1 STAGE 2

C1 C2

Fig. 3 Approximate Analytical Model The expected number of calls in the high priority queue YXE is calculated directly as a level dependent

1//GBMAP queue with arrival BMAPHP1. The expected number of calls in the whole system 1TE is also calculated directly as a level dependent 1//GBMAP with arrival BMAPG1. The expected number of low priority calls ZE can be approximated by (29). For Stage 2, the traffic arrival into the high priority queue

2HPBMAP is 1BMAP . The traffic arrival into the low priority queue 2LPBMAP is simply 2BMAP . The total arrival into the system is 2GBMAP and is given by

212 BMAPBMAPBMAPG . Let the total number of Class 1 and Class 2 calls in the system be 2T . The following expression holds for the expected number of calls at Stage 2: YEXETE 2 (30)

The expected number of calls in the high priority queue XE is calculated directly as a level dependent

1//GBMAP queue with arrival BMAPHP2. The expected number of calls in the whole system YXETE 2 as calculated at Stage 1. The expected number of low priority calls YE can thus be deduced from (30). It should be noted that 2TE can also be calculated as a level dependent 1//GBMAP for accuracy comparisons. This is numerically tested and the results for the second stage normalized. The approximations are made possible by the fact that the lowest priority traffic does not differentiate between the higher priority ones. The higher priority traffic utilizes the complete network capacity. The model can be extended to several stages as an approximate model for evaluating more complex networks.


3.2 Analytical Evaluation of the Level Dependent 1//GBMAP Queue

The 1//GBMAP queuing system with level dependent arrivals is described by a stochastic process

0:, ttJtX [24], where tX and tJ are defined as the number of calls in the system referred to as the level and the phase of the arrival process at time t , respectively. Let be the epoch of the th departure from the queue, with 00 . Then 1,, JX is a semi-Markov process on the state space mjiji 1,0:, . The state transition probability

matrix of the semi-Markov is xP GBMAP 1//ˆ where

01 x . The stationary vector of the Markov chain 1//1// GBMAPGBMAP PP and its steady state transitional probability matrix is given by

.....

F

31

30

22

21

20

13

12

11

10

3210

1//

HHHHHHHHHFFF

P GBMAP

, (31) where, the elements of the matrices q

nH and nF are

defined as follows: ijqnH PrGiven a departure at time

0 , which left q customers in the system and the arrival process in phase i , the next departure occurs in a finite time x with the arrival process in phase j , and during

that service there were n arrivals, ijnF PrGiven a departure at time 0, which left no customer in the system and the arrival process in phase i , the next departure occurs in a finite time x with the arrival process in phase j , leaving n customers in the system. The matrices are

xiJqXjJnqX

PHqq

ijqn

1

11

,,|,

, (32)

xiJXjJnX

PF ijn

1

10

10

,,0|,

. (33) The derivation of the state transition matrix and the steady state distribution from the state transitional matrix of (31) is done by the level dependent Markovian means [24][25][26]. 4 PERFORMANCE MEASURES

The call blocking probability is used as the performance measure for the developed model. The steady state probability of the number in the system s is computed first. Let k be the blocking probability of call i of class k . The blocking probabilities are given by

Ss

sa

k iSP .,1 , (34)

where DA

SA

a PPiSP , , determined by (2) and (16) of the CAC algorithm. 5 DISCUSSION AND RESULTS

The performance of the analytical CAC algorithms is validated by simulations using a developed C++ discrete event simulator. Typical CDMA parameters are used in the simulation; processing gain of 128, chip rate 1.25MHz, AWGN of 10-18 with maximum power of 1watt is used. The call parameters were; call duration of 200 seconds, with on and off time of 0.5 seconds and 1 second respectively with an exponentially distributed service time. For the numerical results the BMAP considered is a superposition of several identical MMPPs alternating between two states. The values are chosen as follows: 01 2 . The value of 01r and 10r used are 0.01 and 0.04, respectively. The traffic classes were selected as follows: Class 1 SNR/Delay in dB/seconds as 13/0.2, Class 2 as 8/0.3 and Class 3 as 5/0.5. For the TCP protocol; a fine timeout of 100 ms and a coarse timeout granularity of 500 ms were used. The first retransmit threshold of 3 was used and a fixed packet size of 500 bytes was used on the network. The round trip time of 200 ms was chosen and a maximum window of 20 packets was allowed. The results of the teletraffic performance of the different TCP protocols, Tahoe and Reno, in terms of blocking probability are shown in Fig. 4. From the results, the following can be deduced; firstly, the dropping probabilities increase with an increase in the offered load as expected. Secondly, TCP Reno performs better that TCP Tahoe in terms of the call blocking probabilities as it achieves less blocking than TCP Tahoe. Finally the Poisson model achieves less blocking probabilities than the BMAP model. This can be disadvantageous in terms of overestimating the theoretical performance of the system resulting in poor network dimensioning. The analytical and simulation results tally well.

Fig. 4 Comparisons of Different Traffic Models

0

0.1

0.2

0.3

0.4

0.5

0.6

0 2 4 6 8

Bloc

king

Prob

abilit

y

Offered Load

Tahoe_Sim_BMAPTahoe_Ana_BMAPTahoe_Sim_PsnTahoe_Ana_PsnReno_Sim_BMAPReno_Ana_BMAPReno_Sim_PsnReno_Ana_Psn


The analytical model was engaged to determine the behavior of TCP with different traffic classes. The results are as shown in Fig. 5. From the results, it is evident that the different traffic classes were differentiated in performance. Class 1 achieves better performance than Class 2 which performs better than Class 3. Their blocking probabilities increase with an increase in the offered load.

Fig. 5 Teletraffic Analysis of Different Traffic The next test is the performance of TCP for the different wireless network protocols namely the Two State Markov Chain (TSMC) model and the Finite State Markov Chain (FSMC) model. The results are shown in Fig. 6. From the results we can deduce the following; as has been the case TCP Reno performs better than TCP Tahoe with any type of wireless model. The most important deduction is that for all the cases of TCP the TSMC wireless channel incurs less blocking than the FSMC model. This is feasible since the TSMC is an approximation of the FSMC. It could easily overestimate the losses on the network and lead to network dimensioning problems.

Fig. 6 Analysis for different wireless models.

The TCP window is the most significant aspect in its performance. In the next network test, the results of average window size of TCP Reno at various loads with or without CAC and for different values of timeouts of

2001_ TO and 1502_ TO are shown in Fig. 7. The following can be deduced: The window sizes decreases with an increase in the offered load. As the load

increases, though regulated by the CAC scheme, the network traffic increases. However, the window size of TCP with CAC reduces very gradually as compared to the one without CAC. The CAC blocks incoming calls and maintains the QoS of the calls already in the system. A higher load increases the probability of packet error in the network. More timeouts occur and thus inhibit the growth of the window. TCP with a long timeout granularity performs better than that with a short time granularity.

Fig. 7 TCP Reno’s window for different timeout values 6 CONCLUSION

Telecommunication network protocols have found themselves being used on environments of which they were not meant to be used. Their effects need to be quantified on the new environments. CAC schemes and intelligent scheduling on the links has always been employed to alleviate the tremendous challenges of networks. These CAC schemes need to incorporate the effect of network protocols and features of future traffic. In this work, a CAC scheme featuring the following is developed, multiple traffic types, multiple admission parametersand TCP protocol issues with BMAP traffic. TCP delays are a good representative of the whole systems delay. To assess their effectiveness, the performance analysis of the solutions to alleviate network challenges (CAC) has been done. With the developed model, the effects of TCP protocol induced delays have been investigated for different TCP protocols. The results indicate that a CAC algorithm maintains the QoS for various TCP traffic in the network.

7 REFERENCES [1] R. Prasad and T. Ojanpera, “An overview of CDMA evolution toward wideband CDMA,” IEEE Communication Surveys & Tutorials, vol. 1, no. 1, pp. 2–29, 1998. [2] Ka-Cheong Leung, V. O. K. Li, “Transmission control protocol (TCP) in wireless networks: issues, approaches, and challenges” IEEE Communication Surveys & Tutorials, vol. 8, no. 4. pp. 64-79, 2006.

0

0.2

0.4

0.6

0.8

1

0 5 10

Bloc

king

Pro

babi

lity

Offered Load

Reno_C1

Reno_C2

Reno_C3

0

0.2

0.4

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0 2 4 6 8 10

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ckin

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roba

bilit

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Reno_FSMCReno_TSMCTahoe_TSMCTahoe_FSMC

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dow

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Offered Load

Reno_To_1

Reno_To_2

Reno_To_1_CAC

Reno_To_2_CAC


[3] Y. Tian, K. Xu, and N. Ansari,”TCP in Wireless Environments: Problems and Solutions,” IEEE Communications Magazine, vol. 43, no. 3, pp. 27–32, March 2005. [4] Z. Liu and M. Zarki: “SIR-Based Call Admission Control for DS-CDMA Cellular Systems”, IEEE Journal on Selected Areas in Communications, vol. 12, pp. 638-644, May 1994. [5] W Jeon and D. Jeong: “Call Admission Control for CDMA Mobile Communications Systems Supporting Multimedia Services”, IEEE Transactions on Wireless Communications, vol. 1, no. 4, October 2002. [6] W. Yue and Y. Matsumoto: “Output and Delay Process Analysis for Slotted CDMA Wirelesss Communication Networks with Integrated Voice/Data Transmission,” IEEE Journal on Selected Areas in Communications, vol. 18, no. 7, pp. 1245-1253, July 2000. [7] C. Chang and K. “Medium Access Protocol Design for Delay-Guaranteed Multicode CDMA Multimedia Networks” IEEE Transactions on Wireless Communications, vol. 2, no. 6, November 2003. [8] N. Tadayon, H. Wang, D. Kasilingam and L. Xing, “Analytical Modeling of Medium-Access Delay for Cooperative Wireless Networks Over Rayleigh Fading Channels” IEEE Transactions on Vehicular Technology, vol. 62, no. 1, January 2013. [9] T. Spyropoulos, T. Turletti and K. Obraczka, “Routing in Delay-Tolerant Networks Comprising Heterogeneous Node Populations” IEEE Transactions on Mobile Computing, vol. 8, no. 8, August 2009. [10] I. Cerutti, A. Fumagalli and P. Gupta, “Delay Models of Single-Source Single-Relay Cooperative ARQ Protocols in Slotted Radio Networks with Poisson Frame Arrivals” IEEE/ACM Transactions on Networking, vol. 16, vo. 2, April 2008. [11]Qureshi, B. , Othman, M., Hamid, N.A.W. “Progress in various TCP variants” 2nd International Conference on Computer, Control and Communication, 2009, pp 1-6. [12] Balakrishan H. et. al. “A Comparison of mechanisms for improving TCP performance over wireless links,” Proceedings of ACM SIGCOMM’96, August 1996. [13] A. Klemm, C. Lindemann, M. Lohmann, “Traffic modeling of IP networks using the batch Markovian arrival process” Performance Evaluation, vol. 54, no. 22, pp. 149–173, 2003. [14] X. Wang, D. Eun, and W. Wang, “A Dynamic TCP-Aware Call Admission Control Scheme for Generic Next Generation Packet-Switched Wireless Networks,” IEEE

Transactions on Wireless Communications, vol. 6, no. 8, August 2007. [15] Georgios Theodoridis, Cesare Roseti, Niovi Pavlidou, and Michele Luglio, “TCP-Call Admission Control Interaction in Multiplatform Space Architectures,” EURASIP Journal on Wireless Communications and Networking, 2007. [16] Dmitri Moltchanov, “A study of TCP performance in wireless environment using fixed-point approximation,” Computer Networks, vol. 56, pp. 1263–1285, 2012. [17] L. Yun and D. Messerschmitt: “Power Control for variable QoS on a CDMA channel”, In Proceeding of IEEE MILCOM conference, fort Monmouth, NJ, pp. 178-182, October 1994. [18] A. Sampath, P.S. Kumar and J.M. Holtzman: “Power control and resource management for a multimedia CDMA wireless system”, Proceedings of PIMRC’95, Toronto, Canada, pp. 21-25, September 1995. [19] T. Walingo and F. Takawira, “Cross Layer Extended Parameter Call Admission Control or Future Networks” SAIEE African Research Journal, vol. 104, no.1, March 2013. [20] J. B. Postel, “Transmission Control Protocol”, RFC 793, September 1981. [21] Stevens, W, ‘TCP Slow Start, Congestion Avoidance, Fast Retransmit, and Fast Recovery Algorithms”, RFC 2001, 1997. [22] T. Walingo and F. Takawira, “TCP Over Wireless With Differentiated Services’ IEEE Transactions on Vehicular Technology, vol. 53, no 6, pp. 1914-1926, November 2004. [23] Hong Shen Wang and Nader Moayeri, “Finite-State Markov Channel—A Useful Model for Radio Communication Channels,” IEEE Transactions on Vehicular Technology, vol. 44, no. 1, pp. 163-172, February 1995. [24] D. M. Lucantoni, "New results on the single server queue with a batch Markovian arrival process", Communication Statistics– Stochastic Models, vol. 7, pp. 1-46, 1991. [25] Tom Walingo, “Teletraffic analysis of Next Generation Networks” PhD dissertation, School of EECE, UKZN, Durban, South Africa, 2010. [26] Hofmann J., “The BMAP/G/1 queue with Level-Dependent Arrivals - An Overview," Telecommunication Systems, vol. 16, pp. 347-360, 2001.


A STUDY ON IMPULSE NOISE AND ITS MODELS

Thokozani Shongwe ∗ and A. J. Han Vinck † and Hendrik C. Ferreira ‡

∗ Department of Electrical and Electronic Engineering Science, University of Johannesburg, P.O. Box524, Auckland Park, 2006, Johannesburg, South Africa E-mail: [email protected]† University of Duisburg-Essen, Institute for Experimental Mathematics, Ellernstr. 29, 45326 Essen,Germany E-mail: [email protected]‡ Department of Electrical and Electronic Engineering Science, University of Johannesburg, P.O. Box524, Auckland Park, 2006, Johannesburg, South Africa E-mail: [email protected]

Abstract: This article gives an overview of impulse noise and its models, and points out some importantand interesting facts about the study of impulse noise which are sometimes overlooked or not wellunderstood. We discuss the different impulse noise models in the literature, focusing on their similaritiesand differences when applied in communications systems. The impulse noise models discussed arememoryless (Middleton Class A, Bernoulli-Gaussian and Symmetric alpha-stable), and with memory(Markov-Middleton and Markov-Gaussian). We then go further to give performance comparisons interms of bit error rates for some of the variants of impulse noise models. We also compare the biterror rate performance of single-carrier (SC) and multi-carrier (MC) communications systems operatingunder impulse noise. It can be seen that MC is not always better than SC under impulse noise. Lastly,the known impulse noise mitigation schemes (clipping/nulling using thresholds, iterative based anderror control coding methods) are discussed.

Key words: Impulse noise models, Multi-carrier modulation, Single-carrier modulation,Bernoulli-Gaussian, Middleton Class A, Symmetric alpha-stable distribution.

1. INTRODUCTION

The effects of impulse noise are experienced by mostcommunications systems. There has been a lot of researchpertaining to impulse noise, which involve modelling ofthe impulse noise phenomena and combating impulsenoise in communications systems. Research articlesaddressing impulse noise and its effects are found acrossdifferent fields in communications, some of which areelectromagnetic interference, wireless communication,and recently powerline communication. We thereforesee it necessary to bring a contribution which gives ageneral view of impulse noise in communications systems,from the different research fields. The purpose of thisarticle is to give an overview of impulse noise, and pointout some important and interesting facts about the studyof impulse noise which are sometimes overlooked. Webegin by looking at the earliest work on impulse noisemodelling by Middleton [1, Chapter 11], in Section 2..Then we go on to discuss the common impulse noisemodels in the literature, in Section 3., dividing them intothose with memory and without memory. We also lookat the application of these models with single-carrier andmulti-carrier systems. Lastly, we give an overview of thecurrently known methods of combating impulse noise, inSection 4.. This article follows from the preliminary workin [2].

2. AN INTRODUCTION TO MIDDLETON NOISEMODEL

The phenomenon of impulse noise was first described indetail by Middleton [1, Chapter 11] in the 1960s, wherehe gave a model for impulse noise in communications

systems. To obtain the model, Middleton [1, Chapter 11]described impulsive noise in a system as consisting ofsequences of pulses (or impulses), of varying duration andintensity, and with the individual pulses occurring more orless random in time. He went further to divide the origin ofimpulse noise into two categories: (a) Man-made, which isinduced by other devices connected in a communicationsnetwork and (b) naturally occurring, due to atmosphericphenomena and solar static which is due to thunder storms,sun spots etc. The man-made impulse noise was describedas trains of non-overlapping pulses, such as those inpulse time modulation. The impulse noise due to naturalphenomena was described as the random superpositionof the effects of the individual natural phenomena [1,Chapter 11]. A model for such noise is given in [3], [4]and [5] as

n(t) =L

∑i=1

aiδ(t − ti), (1)

where

• δ(t − ti) - is the ith unit (ideal) impulse, described as adelta function.

• ai - are statistically independent with identicalprobability density functions (PDFs),

• ti - are independent random variables uniformlydistributed in the time period T0,

• L - the number of impulses in any observation periodT0, assumed to obey a Poisson distribution


PT0(L) =(ηT0)

Le−(ηT0)

L!. (2)

In (2), η is the average number of impulses per second, andT0 is the observation period of the impulses. Therefore,ηT0 is the average number of impulses in the period T0. Itcan be seen that the noise model described by (1) is idealbecause the impulses are assumed to be delta functions,where aiδ(t − ti) describes the ith impulse of amplitude ai.

The noise model described by (1) and (2) was originallyreferred to as the Poisson noise model in [1, Chapter 11],and was widely studied and applied in many systems [3]–[6]. Ziemer [3], utilised the Poisson impulse noise modelto calculate error probability characteristics of a matchedfilter receiver operating in an additive combination ofimpulsive and Gaussian noise. In [5], the Poissonnoise model was used to evaluate the performance ofnoncoherent M-ary digital systems, ASK, PSK and FSK.

In his later work, Middleton [1] developed statistical noisemodels which catered for noise due to both man-made andnatural phenomena [7]– [9]. In [7] Middleton classifiedthe noise models into the following three categories: ClassA – the noise has narrower bandwidth than that of thereceiver; Class B – the noise has larger bandwidth thanthat of the receiver; Class C – the sum of Class A andClass B noise. The most famous of these noise modelsis the so-called Middleton Class A noise model, which hasbeen widely accepted to model the effects of impulse noisein communications systems. We will, in short, refer to theMiddleton Class A model as Class A model.

3. IMPULSE NOISE MODELS

Following Middleton’s noise models [1, Chapter 11], manyauthors studied impulse noise modelling. In this section,we discuss some impulse noise models found in theliterature. In our discussion of the other impulse noisemodels we will occasionally mention the Middleton ClassA model for reference or comparison purposes as it isa very important model in the study of impulse noise.To date, the following names appear in the literature fordifferent impulse noise models:

1. Impulse noise models without memory

• Middleton Class A

• Bernoulli-Gaussian

• Symmetric Alpha-Stable distribution

2. Impulse noise models with memory

• Markov-Middleton

• Markov-Gaussian.

Impulse noise models without memory

3.1 Middleton Class A

The Class A noise model is still a form of the Poison noisemodel, but with the impulse width taken into account in(2). We dedicate space to describing the Class A noisemodel because it has become the cornerstone of impulsenoise modelling and has been extensively studied andutilised in the literature (see [10]– [17].) The Class A noisemodel gives the probability density function (PDF) of anoise sample, say nk as follows:

FM(nk) =∞

∑m=0

PmN (nk;0,σ2m), (3)

where

N (xk;µ,σ2) represents a Gaussian PDF with mean µ andvariance σ2, from which the kth sample xk is taken.

Pm =Ame−A

m!(4)

and

σ2m = σ2

ImA+σ2

g = σ2g

( mAΓ

+1), (5)

where σ2I is the variance of the impulse noise and σ2

g is thevariance of the background noise (AWGN). The parameterΓ = σ2

g/σ2I gives the Gaussian to impulse noise power

ratio. We can see that (2) and (4) are Poisson PDFs. Thedifference in (4) is that the term (ηT0) has been replacedby the parameter A. The parameter A here represents thedensity of impulses (of a certain width) in an observationperiod. Therefore, A = ητ/T0, where η is the averagenumber of impulses per second (as in (2)) and T0 = 1,which is unit time. The new parameter τ, is the averageduration of each impulse, where all impulses are taken tohave the same duration. We now talk of density of impulsesinstead of number of impulses as done in (2). In (4) wetherefore have the densities of impulse noise occurringaccording to a Poisson distribution.

The density is what has become accepted as “impulsiveindex”, A. The impulsive index is a parameter that isnot well explained in the literature. We therefore givesome details about the impulsive index, to enhance itsunderstanding. It is worth stating that A ≤ 1, this followsfrom the definition of impulsive index being a fraction ofimpulses in a given observation period T0. Therefore, forητ > T0, the impulsive index is capped at 1 no matter howlarge ητ is, in the observation period T0.

Fig. 1 shows a pictorial view of the impulsive index, A,and what it means. Fig. 1 (a) shows η impulses eachof duration τ, where the impulses occur in bursts (nextto each other). In Fig. 1 (b) we show η = 3 impulseseach of duration τ, where the impulses do not necessarily


1 2 η

A = ητT0ητ

T0

. . .τ

(a)

T0 = 1

ττ τ

1 2 3

A = 3τ

(b)

Figure 1: Example of Impulsive index: (a) Impulsive index(density) of η impulses, each with width (duration) τ, occupying

a given time period T0 and (b) impulsive index (density) of 3impulses, each with width (duration) τ, occupying a given time

period T0 = 1.

occur in bursts. We also specify the period of observationas T0 = 1 in Fig. 1 (b), which is usually the case in thecalculation of the impulsive index. The conclusion drawnfrom Fig. 1 is that whether impulses occur in bursts ornot, the calculation of the impulsive index follows the sameprocedure.

3.2 Bernoulli-Gaussian

The Middleton Class A noise model has already beenexplained. It can be seen that the PDF of the ClassA noise model in (3) is a sum of different zero meanGaussian PDFs with different variances σ2

m, where thePDFs are weighted by the Poisson PDF Pm. This summingof weighted Gaussian PDFs is generally referred to as aGaussian mixture. Another popular impulse noise model,which is a Gaussian mixture according to the Bernoullidistribution, exists in the literature and is called theBernoulli-Gaussian noise model (can be found in [18]–[21].) This noise model is described by the following PDF:

FBG(nk) = (1− p)N (nk;0,σ2g)+ pN (nk;0,σ2

g+σ2I ). (6)

The Bernoulli-Gaussian noise model has similarities to theClass A noise model. To show the similarities, we usethe channel models in Fig. 2. Fig. 2 (a) is a two-staterepresentation of the Class A noise model, and Fig. 2 (b) isa representation the Bernoulli-Gaussian noise model. Themodels in Fig. 2 look very similar, with the only differencebeing that in Fig. 2 (b) it is explicitly stated that the noisesample added to the data symbol Dk, in either of the two

states, is Gaussian distributed. Whereas in Fig. 2 (a), onlythe state with variance σ2

g can have a Gaussian distribution.However, the state with impulse noise does not necessarilyhave a Gaussian distribution.

Dk Dk

σ2g

σ2g + σ2

I/A

A

1− A

(a)

Dk Dk

N (0, σ2g)

N (0, σ2g + σ2

I/p)p

1− p

(b)

Figure 2: (a) Two-state Class A noise model and (b)Bernoulli-Gaussian noise model.

It should be noted that in the impulse noise model in Fig.2, for the states with impulse noise, the impulse noisevariance σ2

I is divided by the probability of entering intothat state (A or p), such that the impulse noise variance inthe system (total number of time samples) becomes σ2

I . Toexplain this, let us use the Class A noise model as follows:in the Class A noise model which is defined by (3)–(5), itcan be seen that the impulse noise variance of the state m is(σ2

I m)/A as shown in (5). This variance of state m occurswith probability Pm (see (4)), hence the average impulsenoise variance of the Class A noise model is

∞

∑m=0

Pmσ2

I mA

=σ2

IA

∞

∑m=0

mPm =σ2

IA

×A = σ2I . (7)

From a simulation point of view, we explain the divisionof σ2

I by A as follows: let us assume a transmission of Nsymbols. For the impulse noise variance, in the vectorof length N, to be approximately σ2

I , each symbol hasto be affected by impulse noise variance σ2

I /A. It caneasily be shown that this situation will result in the impulsenoise of σ2

I over the N symbols, as follows: we knowthat impulse noise occurs with probability A, and for Nsymbols (assuming very large N) we have approximatelyAN symbols affected by impulse noise of variance σ2

I /A.This gives the impulse noise variance in N samples asσ2

N = AN ×σ2I /A = Nσ2

I . Then the average impulse noise


variance is σ2N/N = σ2

I , which is the result in (7). For thetwo models in Fig. 2 to be more similar, set A = p.

The Bernoulli-Gaussian noise model has been widelyadopted in the literature, and some researchers prefer toemploy it over the Class A noise model because it is moretractable than the Class A noise model. The Class A modelhas the advantage of having its parameters directly relatedto the physical channel. If so desired the Class A model canbe adjusted to approximate the Bernoulli-Gaussian, hencegiving the Bernoulli-Gaussian model the advantages of theClass A model as well.

The Class A model can also be simplified, and be mademore manageable. It was shown in [11] that the PDF ofthe Class A noise model in (3) can be approximated by thefirst few terms of the summation and still be sufficientlyaccurate. Truncating (3) to the first K terms results in theapproximation PDF (normalised), which is

FM,K(nk) =K−1

∑m=0

P′mN (nk;0,σ2

m), (8)

whereP′

m =Pm

∑K−1m=0 Pm

.

The model in (8) allowed Vastola [11] to design a thresholddetector with a simpler structure, which would not havebeen the case if he was using the model in (3) which hasinfinite terms. It was also shown in [11] that the firsttwo or three terms are good enough in (8) to approximatethe PDF in (3). In [17], the first four terms were usedto approximate the PDF of the Class A model. In oursimulations, we shall use up to the first five terms of (8),and such a model is shown in Fig. 3.

We now give some results showing the bit error rate (BER)versus SNR when using the model in (8) for different Kvalues. Such results are shown in Figs. 4 and 5, whereBPSK modulation is used and K = 2, 3 and 5. In eachfigure, we use a theoretical BER curve for BPSK (given by(9) for M = 2, where M is the order of the PSK modulationand Eb is the signal’s bit energy) as a reference curveagainst which all curves are compared. Figs. 4 and 5 showthe effect of different values of A and Γ on the model.

Pe,MPSK = (1−A)M−1

MQ

(√Eb

σ2g

)

+ AM−1

MQ

(√Eb

σ2g(1+1/AT )

). (9)

Note that the expression in (9) is normally written withoutthe term (M − 1)/M. However, for accuracy, the (M −1)/M term needs to be included in the expression toindicate that a symbol affected by noise only gets to bein error with probability (M − 1)/M. This is important

Dk

P ′4

2σ2I

A + σ2g

P ′0

P ′3

Dk

σ2g

σ2I

A + σ2g

4σ2I

A + σ2g

3σ2I

A + σ2g

P ′1

P ′2

Figure 3: Five-term, K = 5, approximation of the Class A model.

for low order modulation, but can be neglected for higherorder modulation because the term approaches one as Mgets larger.

It can be observed in Figs. 4 and 5 that the model in (8)approximates the Class A model in (3) better for low valuesof A (see Fig. 4), such that even for two terms, K = 2,we get a very good approximation of the theoretical BERcurve. For high values of A (see Fig. 5), however, werequire more terms in (8) to approximate the results of themodel in (3), at least for the part of the curve influenced byA (the error floor).

Fig. 5 shows that the results of the K = 5 channel modelclosely approximate the effect of A on the BER curvebetter than when K = 2. This is obviously due to thefact that the more terms (higher K values), the better theapproximation of the Class A PDF. However, the K = 2channel model results show a better approximation of theimpulse noise power (1/(AΓ), which is observed around aBER of 10−5) compared to when K = 5. This is becauseof the m parameter in the term σ2

I m/A in (5), whichinfluences the impulse noise power. Using more terms in(8) to approximate the results of the model in (3) is moreeffective in estimating the effect of A in the BERs, but notthe impulse noise power.

3.3 Symmetric alpha(α)-stable distribution for impulsenoise modelling

The impulse noise models discussed so far (the MiddletonClass A and the Bernoulli-Gaussian) are by far the mostwidely used in the literature to model impulse noise.There is another impulse noise model that is becomingmore common in the literature, and that is the symmetricα-stable (SαS) distribution. This section is therefore ashort note on symmetric α-stable distributions used tomodel impulse noise.

SαS distributions are used in modelling phenomenaencountered in practice. These phenomena do notfollow the Gaussian distribution, instead their probabilitydistributions may exhibit fat tails when compared to theGaussian distribution tails [22, Chapter 1]. While stabledistributions date back to the 1920s (see [23]), their usage


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ate

A/2

−10log10 (AΓ)

AWGN + Impulse noise, K=2

AWGN, theory

AWGN + Impulse noise, theory



(a) A = 0.01, Γ = 0.1.

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100

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Bit

Err

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ate

A/2

AWGN, theory



AWGN + Impulse noise, theory


−10log10 (AΓ)

(b) A = 0.01, Γ = 0.01.

Figure 4: Bit error rate results using the impulse noise modelshown in Fig. 3, with K = 2, 3 and 5. BPSK was used for the

modulation.

in practical applications had been limited until recentlybecause of their lack of closed-form expressions exceptfor a few (Levy, Cauchy and Gaussian distributions) [22,Chapter 1]. Nowadays powerful computer processorshave made it possible to compute stable distributionsdespite the lack of closed form expressions. This hasled to the increasing usage of stable distributions inmodelling. Impulse noise is one phenomenon encounteredin communication systems which has a probabilitydistribution with fat tails [24]. SαS distributions aretherefore considered appropriate for modelling impulsenoise [24]– [27].

In this section we give examples of the PDFs of theSαS model for impulse noise, the Class A model and theBernoulli-Gaussian model. This is meant to show how theSαS model compares, in terms of the PDFs, with the otherimpulse noise models already discussed.

The SαS distributions are characterised by the followingparameters:

• α: is the characteristic exponent, and describes the

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AWGN, theoryAWGN + Impulse noise, theoryAWGN + Impulse noise, K=5AWGN + Impulse noise, K=2AWGN + Impulse noise, K=3

(a) A = 0.3, Γ = 0.1.

0 5 10 15 20 25 30 35 4010−5

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100

Eb/2σ2g, dB (SNR)

Bit

Err

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ate

AWGN, theoryAWGN + Impulse noise, theoryAWGN + Impulse noise, K=5AWGN + Impulse noise, K=2AWGN + Impulse noise, K=3

(b) A = 0.3, Γ = 0.01.

Figure 5: Bit error rate results using the impulse noise modelshown in Fig. 3, with K = 2, 3 and 5. BPSK was used for the

modulation.

tail of the distribution (1 < α ≤ 2).

• β: describes the skewness of the distribution (−1 ≤β ≤ 1); if the distribution is right-skewed (β > 0) orleft-skewed (β < 0).

• γ: is the scaling parameter (γ > 0).

• δ: is a real number that gives the location ofthe distribution. This number tells us where thedistribution is located on the x-axis (when the x-axisis used to represent the value of the random variableas per the norm).

The parameters α and β describe the shape of thedistribution; while γ and δ can be thought of as similarto the variance and the mean in a Gaussian distribution,respectively, care should be taken when using theseparameters as variance and mean.

When modelling impulse noise using the SαS distribution,the noise is thought of as broadband noise, i.e, the


bandwidth of the noise is larger than that of the receiver[28]. Hence, the SαS distribution can be used in theplace of the Middleton Class B noise model which requiresmore (six) parameters to be defined compared to the fourparameters required to describe the SαS distribution.

Fig. 6 shows PDFs of the SαS models for different valuesof α while the other parameters are kept fixed (β = 0 andδ = 0). The parameter γ is set at γ = 1 for all PDFsexcept for the α = 2 PDF where γ = 1/

√2. This case of

α = 2, γ = 1/√

2, β = 0 and δ = 0 results in the normaldistribution as seen in Fig. 6. It should be noted thatthe SαS distribution of α = 2, β = 0, δ = 0 and γ > 0 isgenerally the Gaussian distribution; making the Gaussiandistribution a special case of the SαS distributions. Ourmain aim of presenting Fig. 6 is to show the change ofthe tails of the SαS PDFs with change in the parameter αand show that the tails are fatter than that of the Gaussiandistribution for α < 2.

−5 −4 −3 −2 −1 0 1 2 3 4 50

0.1

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nctio

n

α=0.5α=2, γ=1/sqrt(2) − Gaussian

α=1.5

α=1

(a) SαS distributions

2.5 3 3.5 4 4.5

0

0.01

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Noise amplitude

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dens

ity fu

nctio

n

Gaussian, α=2, γ=1/sqrt(2)

α=0.5

α=1.5

α=1

(b) Tails of the distributions

Figure 6: SαS distributions of different values of α while β = 0,γ = 1 and δ = 0. The normal distribution is also included as a

SαS distribution of α = 2, β = 0, γ = 1/√

2 and δ = 0.

It can be seen in Figs. 6 and 7 that the PDFs of the impulsenoise models (Bernoulli-Gaussian, Middleton Class A andSαS) have fat tails. For the Bernoulli-Gaussian andMiddleton Class A PDFs, the tails are controlled by theprobabilities of impulse noise p and A, respectively; when

1.5 2 2.5 3 3.5 4 4.5 5−0.02

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n

Class A: Γ=0.1, A=0.3

Class A: Γ=0.01, A=0.3

Class A: Γ=0.01, A=0.1

Class A: Γ=0.01, A=0.01

Class A: Γ=0.1, A=0.01

Class A: Γ=0.1, A=0.1

(a) Tails of the PDFs of the Class A model

2.5 3 3.5 4 4.5 5

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n

Bernoulli−Gaussian: Γ=0.01, A=0.01

Bernoulli−Gaussian: Γ=0.1, p=0.3





(b) Tails of the PDFs of the Bernoulli-Gaussian model

Figure 7: Tails of the PDFs of the Class model for differentvalues of A and Γ; tails of the PDFs of the Bernoulli-Gaussian

model for different values of p and Γ.

the probability of impulse noise (p or A) increases, thePDFs tails get fatter. For the SαS PDF, the tails arecontrolled by the parameter α; with low values of α (α< 2)giving PDFs with fatter tails.

Impulse noise models with memory

Through measurements in a practical communicationschannel, Zimmermann and Dostert [29] showed thatimpulse noise samples sometimes occur in bursts, hencepresenting a channel with memory. They further proposeda statistical impulse noise model, based on a partitionedMarkov chain, that takes into account the memory natureof impulse noise. Following the work in [29], other authorsstudied impulse noise with memory as seen in [30], [31],[17] and [32]. In [30], a two-layer two-state Markovmodel is used to describe bursty impulse noise. Thefirst layer uses a two-state Markov chain to describe theoccurrence of impulses and the second layer uses anothertwo-state Markov chain to describe the behaviour of asingle impulse. To model impulse noise with memory,Markov chains are invariably used by most authors in theliterature. The two models, Markov-Middleton [17] andMarkov-Gaussian [31] are modifications of the Class Aand Bernoulli-Gaussian models, respectively, by including


Markov chains. Having discussed the impulse noisemodels without memory, there is no need for a lengthydiscussion about the impulse noise models with memory.This is because the impulse noise models with memoryare founded on those models without memory. In Fig. 8we show Markov-Middleton models, which means ClassA model with memory. These models in Fig. 8 are anadaptation of the model shown in Fig. 3. The model inFig. 8 (a) is a “direct” adaptation of the one in Fig. 3, withall the parameters unchanged except for the introduction ofmemory. However, the model in Fig. 8 (b) [17] allows forall states to be connected such that it is possible to movefrom one bad state (state with impulse noise) to anotherbad state, which was not possible with the models in Fig. 3and Fig. 8 (a). With this modification, in Fig. 8 (b), comesa new parameter x, which is independent of the Class Amodel parameters A, Γ and σ2

I . The parameter x describesthe time correlation between noise samples. The transitionstate in Fig. 8 (b) has no time duration, it facilitates theconnection of the other states. It was shown in [17] thatthe PDF of their model in Fig. 8 (b) is equivalent to that ofClass A model shown in (8).

2

3

4

0

1

P ′0

1− P ′0

2σ2I

A

σ2I

A

4σ2I

A

3σ2I

A

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P ′4

P ′3

P ′2

1− P ′0

1− P ′0

1− P ′0

(a)

P ′0

2σ2I

Aσ2I

A

4σ2I

A3σ2

I

A

P ′1P ′

4P ′3 P ′

2

xxx xx

234 1 0

Transition state

(b)

Figure 8: Markov-Middleton impulse noise models with fiveterms: (a) is adapted from [33] and (b) is adapted from [17]

A Note on Multi-carrier and Single-carrier modulationwith Impulse noise

Many authors may correctly argue that the short fall ofthe Class A and Bernoulli-Gaussian noise models is thatthey do not take into account the bursty nature of impulsenoise. However, for MC modulation it does not matterwhether the noise model employed has memory or ismemoryless. This is because in MC modulation, thetransform (DFT) spreads the time domain impulse noiseon all the subcarriers in the frequency domain such thatit becomes irrelevant how the noise occurred (in burstsor randomly). This is well explained by Suraweera andArmstrong [34], who showed that the degradation causedby impulse noise in OFDM systems depends only on thetotal noise energy within one OFDM symbol period, noton the detailed distribution of the noise energy within thesymbol. When it comes to SC modulation, however, it maybe important to distinguish impulse noise with and withoutmemory.

Here we employ the two-state Class A memoryless modelin Fig. 2 (a), with the PDF of the state with impulsenoise and AWGN being Gaussian. This makes the modelmore similar to the Bernoulli-Gaussian in Fig. 2 (b). Inthis two-state Class A model, ignoring the effect of thebackground noise for a moment, we know that the averageimpulse noise power is σ2

I = σ2g/Γ. The impulse noise

power affecting a symbol is σ2I = σ2

I /A = σ2g/AΓ. For

discussions and analysis, we will be using the impulsenoise power σ2

I = σ2g/AΓ.

Given a fixed impulse noise power σ2I = σ2

g/AΓ, we varyimpulse noise probability A and the impulse noise strengthΓ such that σ2

I remains the same. This means that if welower A by a certain amount, we have to increase Γ bythe same amount such that the product AΓ is unchanged.This we do in order to keep σ2

I the same, while observingthe effect of changing the probability of impulse noise Aon the performance of Single-Carrier and Multi-CarrierModulation. It is interesting to note that for very lowA, SC modulation performs better in the low SNR regioncompared to MC modulation. However, SC modulationgives an error floor, while MC modulation does not. Thisbehaviour is seen in Fig. 9.

Two important conclusions can be drawn from thebehaviour observed in Fig. 9:

• For very low A, very few symbols are affected inSC modulation, hence the low probability of error inSC no matter the strength (or average variance) ofthe impulse noise. However, with MC modulation,what matters is the average impulse noise variance inthe system because the noise power is spread on allsubcarriers causing every symbol to be affected by theimpulse noise.

• MC modulation has the benefit of eventuallyoutperforming SC modulation as the SNR increases.


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128−OFDM, A=0.01, Γ=0.01SC, A=0.1, Γ=0.001SC, A=0.01, Γ=0.01SC, A=0.001, Γ=0.1SC, A=0.0001, Γ=1

Figure 9: Comparison of MC and SC modulation in a channelwith AWGN and impulse noise of variance

σ2I = σ2

g/AΓ = 1/(0.01×0.01) = 104. σ2I is fixed at 104 while

different values of A (10−1, 10−2, 10−3 and 10−4) are seen toinfluence the performance of SC modulation.

This is because with MC modulation, the factor 1/Adoes not not affect the SNR requirement like in SCmodulation. We show this independence on A in MCmodulation in Fig. 10.

From the two points above, we can say that MC mod-ulation’s performance is independent on the probabilityof impulse noise occurrence A, while SC modulation’sperformance shows a strong dependence on A. Therefore,one has to carefully choose between MC and SCmodulation depending on the probability of impulse noisethat can be tolerated in the communication. By this wemean that if, for example in Fig. 9, A = 10−4 andcommunication is acceptable at probability of error of10−4, then SC modulation will be the best choice overMC modulation because it will only give an error floorjust below A, at A(M −1)/M. Ghosh [18] also mentionedthat there are conditions where SC modulation performsbetter than MC modulation. It was also shown in [19],using the Bernoulli-Gaussian noise model, that the impactof impulse noise on the information rate of SC schemes isnegligible as long as the occurrence of an impulse noiseevent is sufficiently small (i.e. very low p in (6).)

4. COMBATING IMPULSE NOISE

Several techniques for combating impulse noise havebeen presented in the literature. We shall discuss thesetechniques in light of MC modulation, OFDM. Thesetechniques fall into the following three broad categories:

1. Clipping and Nulling (or Blanking):With clipping or nulling, a threshold Th is used todetect impulse noise in the received signal vector rbefore demodulation. Clipping and nulling differ inthe action taken when impulse noise is detected inr. If a sample of r, rk is detected to be corrupted

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A=0.001, Γ=0.1

A=0.01, Γ=0.1A=0.01, Γ=0.01

A=0.001, Γ=0.01 A=0.1, Γ=0.001

AWGN, theory

−10log10(0.01)

−10log10(0.1)

−10log10(0.001)

Figure 10: Shows that with MC modulation the SNRrequirement is σ2

I = 1/Γ instead of 1/AΓ, even though a symbolis affected by impulse noise of variance σ2

I /A . BPSK OFDMwas used, with a DFT size of 10000.

with impulse noise, its magnitude is clipped/limitedaccording to Th = Tclip (Clipping), or set to zero(Nulling) according to Th = Tnull. Given the receivedsample rk, then the resulting sample rk, from theclipping technique, is given by

rk =

rk, for |rk| ≤ Tclip

Tclipe j arg(rk), for |rk|> Tclip,

and the resulting sample rk, from the nullingtechnique, is given by

rk =

rk, for |rk| ≤ Tnull0, for |rk|> Tnull

,

where usually Tclip < Tnull.

Zhidkov [35] gave performance analysis and opti-mization of blanking (or nulling) for OFDM receiversin the presence of impulse noise, as well as acomparison of clipping, blanking, and combinedclipping and blanking in [36]. In [37], the authorsadvocated for the clipping technique to combatimpulse noise in digital television systems usingOFDM. The clipping technique, in OFDM, is alsoseen in [38], where the focus is on deriving andutilising a clipping threshold that does not requirethe a priori knowledge of the PDF of impulsenoise. Recently, Papilaya and Vinck [39] proposedto include an additional action (with its threshold)to the clipping and nulling actions, which is termedreplacement. This was done for an OFDM system.The replacement action uses a replacement threshold(Trep) which falls in between the clipping and nullingthresholds, and replaces impulse corrupted sampleswith the average magnitude of the noiseless OFDMsamples.

2. Iterative:With the iterative technique, the idea is to estimate


the impulse noise as accurately as possible and thensubtract the noise from the received vector r. Thenoise estimation can be done in the time and/orfrequency domains. For good iterative methods,the more iterations the better the estimate of theimpulse noise. There is of course a limit to thenumber of iterations, above which there is little orno improvement in the technique. One of the earliestworks on the iterative technique to suppress impulsenoise, in OFDM, was by Haring and Vinck [13]. Ablock diagram of a receiver performing the iterativetechnique in [13] is shown in Fig. 11 (a). Anotherapplication of the iterative technique against impulsenoise, in OFDM, is found in [40], where the iterativealgorithm is applied in the frequency domain afterdemodulation and channel equalization.

3. Error correcting coding:Error correcting coding has become a necessary partof any communications system in order to correcterrors caused by channel noise. In impulse noiseenvironments, error correcting codes are employed tocorrect errors caused by impulse noise. Most researchon using error correcting codes to combat impulsenoise effects in MC systems tend to lean towardsconvolutional coding [41] [42], Turbo coding [43][44] and low density parity-check coding [45] [46] orcodes that are iteratively decoded [15].

The first two techniques of combating impulse noise,clipping and/or nulling and the iterative technique, aretermed pre-processing because they process the receivedvector before the demodulator processing. Error correctingcoding (decoding) is not a pre-processing technique, it isimplemented after the demodulator to correct errors causedby the impulse noise. It can be used alone or together withthe pre-processing techniques.

It has become common practice to implement acombination of the three impulse noise combatingtechniques above in one system in order to combat impulsenoise. Mengi and Vinck [47] employed an impulsenoise suppression scheme which combined the iterativetechnique, and the clipping and nulling techniques, inOFDM. In [48], the iterative and blanking techniquesare used together in OFDM. In [38], clipping and errorcorrecting coding are used to combat impulse noise effectsin OFDM.

Most impulse noise mitigation schemes have been appliedon the memoryless impulse noise models. However, wesee very few attempts, in the literature, at combatingimpulse noise with memory. For an example, in [32] theyemployed the Markov-Gaussian model for impulse noiseand used convolutional error correcting coding.

We give examples of block diagrams of two OFDMsystems to illustrate the clipping and/or nulling anditerative techniques in combating impulse noise (see Fig.11). The figure shows three important points about theclipping and/or nulling and the iterative techniques. Firstly,

in Fig. 11 (a) the iterative process is performed to get agood estimate of the noise vector n(l), which is n(l), wherel represents the lth iteration. Using a good estimate ofn(l), a more accurate estimate of the desired signal vectorS(l) can be obtained. It should be noted that n(l) is foundby subtracting the estimated desired signal vector of thelth iteration, s(l) or S(l), from the received vector r or R.Secondly, it should be noted from both Fig. 11 (a) andFig. 11 (b) that the vector n(l) can be obtained by doing thesubtraction of the desired signal vector from the receivedsignal, either in the time or frequency domain. Thirdly,Fig. 11 (b) shows the combination of clipping and/ornulling and iterative technique.

The combination of clipping and/or nulling and iterativetechnique in Fig. 11 (b) was shown in [47] to give betterperformance than the iterative technique alone in Fig. 11(a). In the system in Fig. 11 (b), the clipping and/or nullingis used for the first iteration to significantly improve theestimation of S(l) in the first iteration. This clipping and/ornulling in the first iteration is the reason for the betterperformance delivered by the system in Fig. 11 (b).

IDFT

DFTDFT

DFT > T

r r(l) R(l)S(l)

S(l)

−N (l)

R

n(l)

n(l)

−ML

Detection

Iterative process

(a)

r R(l) S(l)

S(l)

s(l)n(l)

n(l)

−ML

DetectionDFT

r

Clip and Null

IDFT> T−

(b)

Figure 11: (a) Iterative impulse noise suppression [13] and (b)Iterative impulse noise suppression with clipping and

nulling [47].

The impulse noise combating techniques discussed havebeen in light of MC modulation, OFDM. To combatimpulse noise in SC modulation, the same techniques canbe employed. However, for SC modulation we only seethe importance of the impulse noise combating techniqueswhen they are used together with error correcting coding.For example, clipping and/or nulling the impulse noiseaffected transmitted samples in SC modulation has noeffect in the BER performance without coding. This


is obviously because the demodulator in SC modulationdoes not discriminate between high and low amplitudenoise when making a decision on the transmitted symbol.The benefit of clipping and/or nulling impulse noiseaffected samples, in SC modulation is observed whenperforming soft-decision decoding. Impulse noise inSC modulation has the same effect as narrow-bandinterference (NBI) in OFDM, considering the NBI modelin [49]. Therefore, the same techniques of handlingNBI in OFDM found in [49], clipping and/or nulling anderror correcting coding, can be used to handle impulsenoise in SC modulation. It was shown in [49] thatthe best technique that gives optimal performance whenusing a convolutional decoder, is to combine nulling andconvolutional soft-decision decoding. Combining clippingand convolutional soft-decision decoding gives suboptimalperformance. Impulse noise in SC modulation can behandled exactly the same way. If the impulse noisehas memory, the classical interleaver can be employed torandomise the occurrence of errors, hence improving thedecoded BER performance.

Focusing on the PLC channel, Vinck [50] proposed theuse of a combination of permutation codes and MFSK,to combat impulse noise, as well as other noise typesin the PLC channel. This technique was applied inSC modulation, MFSK. Later on, the idea of employingpermutation codes with MFSK, in [50], to combat noisetypical for a PLC channel (including impulse noise) wastaken further in [51] and [52], where powerful permutationcodes (called permutation trellis codes) were constructedand used not only to combat impulse noise.

Other impulse noise combating techniques

Another technique used to combat impulse noise in OFDMsystems is compressed (or compressive) sensing (CS).With compressed sensing, the idea is to reconstruct adigitized signal using a few of its samples. CS works wellwith sparse signals. Using CS, the impulse noise in anOFDM signal can be estimated by using pilot subcarrierswith their values set to zero. We see the idea of using CSto estimate and cancel impulse noise in OFDM in [53].In [54] the authors proposed channel estimation workingin conjunction with compressed sensing to combatimpulse noise for OFDM based power line communicationsystems. While most research on combating impulse noisefocuses on non-bursty impulse noise, Lampe [55] proposeda CS based impulse noise mitigation technique for OFDMthat can detect bursty impulse noise. After detecting theimpulse noise positions in the OFDM samples, impulsenoise cancellation or suppression was applied.

Another technique for combating impulse noise in OFDM,which is similar to compressed sensing, is using thesimilarity between the DFT (in OFDM) and error correct-ing codes (particularly Bose-Chaudhuri-Hocquengem andReed-Solomon codes). This idea, of using the similaritiesbetween the DFT and error correcting codes to combatimpulse noise, dates back to the 80s where we see Wolf[56] showing that the DFT sequence carries redundant

information which can be used to detect and correct errors.Wolf [56] compared the DFT to BCH codes. In [57] theauthors show that the OFDM modulator is similar to aReed-Solomon (RS) encoder and these similarities can beused in OFDM to cancel impulse noise effects. Whilethe scheme in [57] could correct a very limited numberof impulse errors because the limitation imposed by theamount of redundancy, an improved scheme with bettercorrecting capabilities was proposed by Mengi and Vinck[58]. The Mengi and Vinck [58] scheme also used OFDMas a RS code, where they proposed to observe not onlythe subcarriers containing the redundancy symbols but thesubcarriers containing information symbols as well.Thatway their scheme could correct more impulse errors.

5. CONCLUSION

Our conclusion is mainly a summary of the interestingfacts about impulse noise models. We have also includedTable 1 to summarise some of the important features ofthe noise models. It should be noted that in Table 1 thebandwidth of the noise is narrow or broad in reference tothe bandwidth of the receiver.

Table 1: Summary of the features of the impulse noisemodels.

Class A Bernoulli-Gaussian SαSNoise notBandwidth Narrow-band specified Broad-bandClosed-form doesexpression exists exists not existsPDF exhibits exhibits exhibits

fat tails fat tails fat tailsBursty as as does notnoise Markov- Markov- modelmodelling Middleton Gaussian bursty noise

In this article we have discussed some important impulsenoise models found in the literature. The noise modelsare divided into those without memory (Middleton ClassA and Bernoulli-Gaussian) and those with memory(Markov-Middleton and Markov-Gaussian). We wentfurther to look at the approximation of the PDF of theMiddleton Class A model with five terms. We also showedthat the Bernoulli-Gaussian model has similarities withthe Middleton Class A, and it can be approximated withthe Middleton Class A model. We then showed Biterror rate simulation results of the approximation of theMiddleton Class A with five terms. Using the MiddletonClass A model with five terms we showed equivalentMarkov-Middleton models. In addition to the MiddletonClass A and Bernoulli-Gaussian models, we also discussedthe symmetric alpha(α)-stable distribution used to modelimpulse noise. The Symmetric alpha(α)-stable distributionas an impulse noise model was compared with the PDFsof the Middleton Class A and Bernoulli-Gaussian models.All the three models had PDFs that exhibit fat tails. Wealso showed that single-carrier modulation performs betterthan multi-carrier modulation under low probability ofimpulse noise occurrence. With OFDM transmission,


it is irrelevant whether the noise occurred in bursts orrandomly, what matters is the total noise energy within oneOFDM symbol period. Lastly, we discussed impulse noisemitigation schemes: clipping, nulling, iterative and errorcorrecting coding.

ACKNOWLEDGMENTS

The authors would like to thank Alliander, Netherlandsfor partially funding this work. This work is also asuccessful outcome of the cooperation between Universityof Johannesburg (South Africa) and Duisburg-EssenUniversity (Germany).

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DEVELOPMENT OF A MAINTENANCE STRATEGY FOR POWER GENERATION PLANTS L. Ndjenja* and J.K. Visser* * Department of Engineering and Technology Management, University of Pretoria, Pretoria 0002, South Africa E-mail: [email protected], [email protected]. Abstract: Effective maintenance of power generation systems is essential to ensure that the variable demand for electricity is satisfied on a daily basis. Equipment used on generation plants, e.g. boilers, turbines, generators, compressors and pumps, are becoming more sophisticated and complex, and therefore require more effective maintenance strategies and tactics. A number of maintenance approaches have been developed in the last 4-5 decades, e.g. reliability-centred maintenance, business-centred maintenance, and total productive maintenance. This paper discusses the results of a research study done to investigate strategy in the maintenance environment of power generation systems. The study found that most power stations have a maintenance strategy and use maintenance approaches and different maintenance tactics like run-to-failure, time-based maintenance and condition-based maintenance. It was also found that the SAPTM information system is used by nearly all power stations. Keywords: Availability, Reliability, Productivity, Maintenance, Approach, Strategy

1 INTRODUCTION

1.1 Background

Every business enterprise needs a strategy or strategic framework that provides the general vision and overall direction for management and frontline workers. Strategy can be defined as “a method or plan designed to achieve a desired future state or major goal”. Campbell and Reyes-Picknell [1] define strategy within the context of maintenance as an “overall direction and flexible plan that leads to good choices”. A business strategy usually involves three key elements, i.e. a vision statement, a mission statement, and key objectives to be achieved within a certain time period, typically 3-5 years. A maintenance strategy should therefore also comprise these three aspects. The main objective of any company is to generate profit through delivery of products, systems or services. Profit is determined by the productivity of the physical assets (outputs), and the costs of raw materials (inputs) as well as the cost of production or manufacturing. Maintenance can therefore contribute towards higher profits through effective management of the maintenance process, thereby increasing the availability and outputs of the physical assets. One of the aspects that need to be addressed in a maintenance strategy is whether one of the established and well-documented maintenance approaches should be implemented or whether the company might embark on implementing only certain elements of these approaches. Examples of such approaches are reliability-centred maintenance (RCM) as described by Moubray [2], business-centred maintenance (BCM) that was developed by Kelly [3] and total productive maintenance (TPM) as

described by Nakajima [4] and Suzuki [5]. Examples of approaches that are less well known are risk-based maintenance (RBM) [6], availability-centered maintenance (ACM) [7], availability-based maintenance [8], total maintenance management (TMM) [9] and reliability-based maintenance [10]. To be successful a maintenance strategy should be communicated and accepted throughout the entire organisation. A firm commitment is also needed from top management. Maintenance, like safety and quality, is everyone’s business and inputs are required from various other departments within the enterprise to be successful.

1.2 The role of maintenance strategy

Maintenance management has evolved significantly in the last two or three decades. These changes are due to: Increase in the number of physical assets (plants,

equipment, buildings, vehicles) Increase in the diversity of equipment required in

modern systems More complex designs Extension of the design life of plants and facilities New maintenance techniques and monitoring

equipment Maintenance management needs to incorporate all these changes into better planning, organising and control of the maintenance resources to ensure that business objectives relating to production quantity and quality are met, and that safety, health and environmental goals are not compromised. The changing economic climate in South Africa and the rest of the world has also emphasised the role of the maintenance management team to curb maintenance costs and to evaluate the effect


of any changes to processes and tactics on the total maintenance cost. Deregulation of the power generation and distribution system in Southern Africa in the past decade or two has increased the competition amongst different companies and power generation plants. Power station managers are therefore under pressure to increase availability and to reduce production costs. Graber [11] mentions that maintenance cost could account for about 30% of the total cost of electricity generation. Wang [12] feels that the maintenance function has a key role in achieving higher reliability and availability of generating systems and should therefore receive more attention from maintenance and operations.

1.3 Historical development

Before and during World War II most maintenance was done in a reactive way, i.e. breakdown maintenance. However, some low-level preventive maintenance, e.g. checking oil levels and doing fault-finding on critical equipment, was performed on weapons systems to increase mission availability. The advent of complex systems using new sophisticated technologies necessitated the use of intensive preventive maintenance to increase performance and availability of physical assets. Older power stations predominantly used breakdown maintenance as a maintenance tactic. Maintenance was therefore performed only after a failure had occurred. The advantage of operating-to-failure is that the full design life of the equipment is utilised and it is therefore often the cheapest option. The disadvantage is that failures often occur randomly leading to safety, health and environmental (SHE) consequences and power supply to customers could be disrupted. Customers, e.g. smelter plants, could suffer huge physical and financial losses if power is not provided continuously. The disadvantages of breakdown maintenance often outweigh the advantages and preventive maintenance was therefore introduced in the power generation industry a few decades ago. Wang [12] concluded that a reactive, breakdown approach alone cannot satisfy the requirements of high availability and reliability of modern power generation plants any longer.

1.4 Current state

Simple condition monitoring techniques like visual checks and audible monitoring have been in use for a long time, but more sophisticated techniques like vibration analysis and oil monitoring became popular in the early 1970’s. Condition-based maintenance (CBM), also known in industry as predictive maintenance, use periodic interventions of the asset to determine certain parameters that relate to the condition or state of the asset (Mitchell [13]). In the past 2-3 decades condition-based maintenance has also been implemented in power generation plants and in many cases a significant increase

in performance was achieved as reported by Huang and Huang [14]. Several power generation plants in South Africa have implemented one of the established maintenance approaches like RCM, TPM and BCM. These maintenance approaches have different focus areas, e.g. in RCM the focus is on maximising the built-in reliability of the equipment. In TPM the focus is on improving the quality of the maintenance actions performed and the training of the artisans. In BCM the focus is on achieving corporate objectives through cost-effective maintenance actions and interventions.

1.5 Research objectives

A maintenance strategy provides a road map to achieve the following goals: Increased plant availability and reliability Optimised cost High productivity Reduced environmental impact Increased return on investment The main objective of this study was to determine whether the power stations have a maintenance strategy and what the benefits of this strategy are. Sub-objectives that supported the main objective were to: Obtain an overview of the maintenance strategy

currently being used in power plants. Identify industry or best practise for maintenance

strategy used in power generating plants. Determine which maintenance tactics are used at

power plants. Determine which of the maintenance approaches

like RCM, TPM, BCM or RBM are used at power plants.

Determine availability values for power plants and benchmark against similar power plants.

Establish the status of information system usage.

2 LITERATURE

2.1 Overall maintenance strategy

Various authors have proposed frameworks or models for developing and implementing a strategy for maintenance. Kelly [3] explained a systematic process, starting with an assessment of the corporate vision, mission and key objectives and using the top-down-bottom-approach to develop an overall life plan for the items and components of the physical assets. Campbell and Reyes-Picknell [1] used a “Pyramid of Excellence” framework to progress from a basic level to excellence in maintenance management. The first level of the pyramid is termed a “leadership” level, the second an “essentials” level and a third “excellence” level. The process fully embraces the concept of continuous improvement.


Campos et al [15] propose a new maintenance management model using a combination of elements from existing models and standards. The process starts with the requirements of stakeholders and uses concepts that are aligned with the ISO 9004 [16] standard on a quality management approach for organisations. This model comprises four high-level processes, each containing a number of sub-processes. The four main processes are Planning, Support, Execution & Control and Improvement. Tsang [17] emphasizes the importance of four strategic dimensions of maintenance management, i.e. service delivery, organisation and structuring, maintenance methods and support systems. Murthy et al [18] developed the strategic maintenance management approach (SMM) to link maintenance strategy to business performance. A crucial aspect of this approach is to fully understand how equipment degrades with usage or time and to obtain the right data to assess the status or condition of the equipment. Umar [19] proposed an integrated framework for maintenance strategic planning that combines some individual elements of strategic planning into one model. Moeko and Visser [20] proposed a framework for maintenance management for utilities of the Southern African Power Pool (SAPP). A survey amongst respondents of the SAPP tested the proposed framework.

2.2 Maintenance strategy framework

A strategy is needed in any business enterprise to define how the company will move from a current state to a desired state. A vision statement usually defines the desired state or “dream” for the company. A common vision for all units of a company ensures that efforts are aligned and guided towards achieving specific objectives. Campbell & Reyes-Picknell [1] provide a framework for developing a maintenance strategy as shown in Figure 1. The first step in the process is to develop a vision for the maintenance department or division. This vision is usually related to achieving some level of performance, often expressed in relation to a world class benchmark. One way of determining a score on a world class scale is provided by Wireman [21]. The “maintenance review” step refers to a SWOT (strengths, weaknesses, opportunities and threats) analysis. This involves determining the internal strengths and weaknesses, as well as the opportunities and threats related to the external environment of the maintenance department. The output of the SWOT analysis is compared with the vision of the maintenance department and “gaps” are identified. The next step is to develop a

“business case” to motivate the funds that are required to bridge the gap between the vision and the current status.

Figure 1: Framework for developing a maintenance strategy (Adapted from Campbell & Reyes-Picknell [1])

The road map defines the actions that are required to achieve the desired state, i.e. the maintenance department’s vision. The next step in the process comprises the development and implementation of a maintenance plan. The maintenance plan defines the maintenance work that should be done while the maintenance information and operational systems support the maintenance operational level to steer the department in the right direction as suggested by Coetzee [22]. This typically involves decisions on the maintenance tactic or type for each item or component of the physical asset or system, the frequency of performing the maintenance task, which trade or specialisation is needed to perform the task, and a rough estimate of the duration of the task. The final step in the process is the execution of the maintenance plan. This is an on-going process for the life of the asset and periodic checks are needed to ensure that the maintenance plan is providing the correct outcome in terms of the total maintenance cost, availability, reliability and other key performance indicators. If a significant deviation from the objectives is found, action needs to be taken, usually through changes in the maintenance plan.

Develop Vision

Maintenance Review

Business Case

Develop the Road Map

Implement Plan

ExecuteResult OK

Is th

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sion

real

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?

Is the strategy still sound?

Is the plan still effective?

No

Yes

PLAN

DO

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2.3 Maintenance tactics

Various maintenance tactics or types are applied, usually at the lowest hierarchical system level (components or items). Duffuaa et al [23] list the following six maintenance tactics that are generally used in maintenance decisions. Run to failure (RTF) – equipment is run until a

failure occurs when repair or replacement is done. Time based maintenance (TBM) – replacement or

cleaning is performed at predetermined time or usage intervals.

Condition based maintenance (CBM) – some parameter that indicates the condition of the equipment is measured and action is taken when the condition is no longer acceptable.

Fault finding maintenance (FFM) – periodic checks are performed to determine whether back-up, redundant or protective equipment is able to function when needed. If not, repair or replacement of the item is performed.

Opportunity maintenance (OM) – the repair or replacement of an item is determined by a major outage or overhaul of some higher level unit.

Design-out maintenance (DOM) – the cause of maintenance is removed through re-design or improvement of an item or component.

3 METHODOLOGY

3.1 Background

The operation and maintenance of industrial plants continuously generate performance and other data. This data is typically captured in a data base or information system. Plant data is useful to study some features but some management data usually has to be captured by means of surveys of the operations and maintenance workers. The survey method was selected for this study to determine perceptions and opinions of workers. This method was useful to evaluate the benefits of implementing a maintenance strategy as well as to determine to what extent maintenance approaches and tactics are used at the power plants.

3.2 Data capturing through questionnaires

Considering the objectives of the research as well as issues that were revealed in the literature on maintenance strategy, a questionnaire with 17 questions was developed. The questions were formulated to extract data related to the objectives of the study. For some questions only one option was required from the respondent but in other cases the respondent could tick a number of options that were applicable. The detailed questionnaire is available in the report of Ndjendja [24]. The intent of the research was to obtain an opinion from workers at different types of power plants, from different hierarchical levels and from different countries. Potential respondents were therefore randomly selected from a

number of power stations in the Southern African Power Pool. Most of the respondents were from power plants in South Africa since South Africa has a large number of power plants compared to neighbouring countries. Questionnaires were sent by e-mail to power station managers, maintenance managers, engineering managers, operations managers, planners, engineers, technicians and foremen. Of the 70 questionnaires that were sent by e-mail, 56 completed questionnaires were returned and the analysis of the data is therefore based on this sample of 56. Not all respondents answered all questions and the total percentages for some questions therefore do not add up to 100%.

3.3 Sample profile

No completed questionnaires were returned for the nuclear power plant (only one in Southern Africa). The number of respondents from the other generation plants is shown in Table 1.

Table 1: Final sample profile

Type of Power Station

Number of respondents

Ratio (%)

Hydro 18 32

Coal-Fired 30 54

Diesel turbines 8 14

Total 56 100 The number of respondents from hydro power plants and diesel power plants were not enough to compare the results with coal-fired plants and all data was therefore analysed for the total group of 56 respondents only.

4 RESULTS

4.1 Background

The results from 10 of the 17 questions of the questionnaire are discussed in this paper. These questions relate directly to the main objective of the study and some of the sub-objectives.

4.2 Role of maintenance strategy

The first question asked the respondent to indicate whether a maintenance strategy was in place. The response was 53 out of 56 (95%) that said yes, indicating that a maintenance strategy was a crucial element in the overall business strategy. A second question relating to strategy asked the respondents to indicate which benefits could be obtained when implementing a maintenance strategy for a power generation system. A list of 7 possible benefits was provided and respondents could select more than one of these benefits. The list was compiled from various literature sources and the authors’ own experience in


asset and maintenance management. The results for this question are indicated graphically in Figure 2 below.

Figure 2: Roles and benefits of a maintenance strategy

It is clear from Figure 2 that all respondents felt that the most important roles for a maintenance strategy were to increase the reliability and availability of the assets. The roles mentioned were not independent and increased reliability and availability should have a positive effect on productivity as well as return on investment. The respondents felt that a reduction in cost is not very important since only about 38% indicated it as important. More than 50% of the respondents indicated that the maintenance department has an important role to play in the reduction of the environmental impact of the physical asset and the improvement of safety.

4.3 Maintenance tactics adopted or implemented

Various preventive and corrective tactics are used for the maintenance of individual items and components of a physical asset. The most effective tactic is determined by factors like the failure rate of the specific item or component, the total cost of using the specific tactic and the consequences of a failure. Respondents were asked to indicate which of the six maintenance tactics, as defined by Duffuaa et al [23], that are generally applied in maintenance are also used at the power station. The results of the survey are indicated in Figure 3 below.

Figure 3: Maintenance tactics used on power plants

Run-to-Failure (RTF) is also known as breakdown maintenance. Time-based maintenance (TBM) is also known as Fixed-time maintenance (FTM). Maintenance departments usually aim to achieve a particular “mix” of

the three main tactics, i.e. breakdown, time-based and condition-based maintenance. The optimal mix is unique for a specific plant or system. From Figure 3 it is seen that about 78% of respondents indicated that “breakdown” maintenance is used on the power station, which means that 22% of the power stations do not intend to run equipment to failure. This strategy needs a re-think since it might be too costly to try and prevent all failures from occurring. It is also seen that 70% of the respondents indicated that the power station uses predictive or condition-based maintenance which means that 30% of the respondents do not use condition-based maintenance. This strategy exposes the powers station to a high risk of unexpected failures and is also not cost effective. However, for some components and items there might not be a parameter that can be measured to indicate the condition of the component. In this case “run-to-failure” is the only option and selected if the consequence of failure is not severe. Sophisticated and costly equipment require effective asset “health care”. Predictive maintenance is therefore used extensively in industry to determine when the condition of an item or component is no longer satisfactory for optimal production.

4.4 Maintenance approaches

Respondents were requested to indicate which of the maintenance approaches RCM, TPM, BCM or RBM had been adopted or implemented at the power station. The results are shown in Figure 4 below.

Figure 4: Maintenance approaches used by power plants

It is seen that RCM is by far the most popular approach with TPM and Risk-based Maintenance (RBM) also implemented in some of the power stations. One respondent indicated in the comments that the reliability-based maintenance approach was used [10]. The RCM approach or methodology was developed in the aviation industry and later also implemented in the nuclear power generation industry. It is particularly suited for high-risk systems where the consequence of a failure could be catastrophic in terms of environmental damage and/or safety, as occurred with the Chernobyl power plant in 1986. Fossil fuel power plants can also benefit from

0 20 40 60 80 100

Reduced maintenance cost

Increased return on investment

Reduced environmental impact

Reduced lost time due to injury

Increased productivity

Increased equipment availability

Increased equipment reliability

Respondents (%)

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100

RTF TBM CBM OM FFM DOM

Res

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ents

(%)

0

10

20

30

40

50

60

70

RCM TPM BCM RBM

Res

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the application of RCM to increase reliability, availability and to reduce costs.

4.5 Power plant availability

Availability is an important indicator for most physical assets and respondents were asked to indicate the average availability of the power plant for the past year. Five brackets for availability were given as shown in Figure 5 below.

Figure 5: Average availability of power plants

It appears that the majority of power plants have an availability of more than 80% as would be expected. A benchmark value for availability of power plants is given as 85% by Stallard and Curley [25].

4.6 Planned maintenance

An effective maintenance department needs to perform more planned maintenance than unplanned maintenance, which is mostly emergency maintenance that requires immediate attention. These ratios are typically determined as hours spent on planned or unplanned maintenance/total maintenance hours. Respondents were requested to provide an estimate of how much planned and unplanned maintenance was performed at the power station as a percentage of the total amount of maintenance performed. The results for the ratio of unplanned maintenance are indicated in Figure 6.

Figure 6: Unplanned maintenance

As seen from Figure 6, about 50% of the respondents indicated that the power station had an unplanned maintenance/total maintenance ratio of less than 40%. However, about 29% of the respondents indicated a ratio of more than 40% unplanned maintenance which

indicates too much corrective and emergency work. Mitchell [26] suggests a ‘world class’ ratio for unplanned maintenance of less than 15%. In this area there is therefore room for improvement by the maintenance departments at the power plants.

4.7 Maintenance cost

One indicator which is closely monitored by all maintenance managers is the direct cost of maintenance as a ratio of the total production or manufacturing cost. This ratio can vary from 3-5% for fabrication and assembly to as high as 50% in the mining industry (Campbell and Reyes-Picknell [1]). Respondents were asked to provide an estimate of the maintenance cost ratio for the power station. The results are shown in Figure 7.

Figure 7: Maintenance cost ratio

The average ratio for maintenance cost as ratio of total cost is typically 21-40%. The plants that reported a maintenance cost ratio exceeding 40% should investigate the cause of the high costs of maintenance and implement corrective measures.

4.8 Condition monitoring techniques

The technical complexity of modern power stations requires condition monitoring on most of the equipment and respondents were requested to indicate which of the three most common condition monitoring techniques were used on the power station. The results are indicated in Figure 8 below.

Figure 8: Usage of condition monitoring methods

It is seen that power plants use a combination of all three condition monitoring methods, i.e. oil analysis, vibration analysis, and thermography to predict the deterioration and degradation of equipment. This is useful to perform

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preventive actions like replacement before actual failures occur.

4.9 Maintenance information management

Management information systems are essential in modern high technology systems and respondents were therefore requested to indicate which information systems were implemented to assist the maintenance manager in analysis and decision making. Three options were provided, i.e. SAPTM [27] which is a general enterprise resource planning system, On-KeyTM which is an enterprise asset management system of the Pragma [28] company or WebTATM which is a web-based employee time tracking, attendance and labour management software package from the Kronos Company in the USA [29]. The results indicated that the maintenance module of the SAP information system is used by nearly all power stations (86% of the respondents) with other information systems only used as a complement to the SAP system. None of the other two information systems mentioned were indicated by any of the respondents.

4.10 Benefit of the information management system

A new technology, software or information system is typically introduced in an organisation since it has some financial benefit. Respondents were therefore asked to estimate the return on investment (ROI) for implementing a maintenance information management system at the power station. The results are shown in Figure 9 below.

Figure 9: Return on investment for implementing a

maintenance information system The average ROI was 15% but about 20% of the respondents indicated that an ROI of between 20-25% was achieved. Good planning and execution of the implementation project probably contributed to these results for ROI.

4.11 Method for root cause failure analysis

The root cause failure analysis (RCFA) function should form part of any maintenance strategy. This is a special case of the more general root cause analysis (RCA) method. Respondents were requested to indicate which RCFA methods were used at the power station. The Apollo Root Cause Analysis method (ARCATM) [30] is a 4-step process used for thorough incident investigation.

The TapRooT® [31] system and software is widely used for the analysis of all types of mission-critical problems. The 5 Why’s methodology [32] attempts to define cause and effect relationships through iterative questioning. The Cause and Effect Tree (C & E Tree) method [33] uses different tree diagrams to establish the root cause(s) after an incident. The results from the survey are shown in Figure 10.

Figure 10: Root cause analysis method used

It is clear that the 5 Why’s method is by far the most commonly used methodology for performing a root cause failure analysis. The other methods are not applied by many power stations and are relatively unknown in industry.

5 CONCLUSIONS AND RECOMMENDATIONS This study investigated, quantified and classified the role, influence and benefits of a maintenance strategy for power generating plants. The conclusions relate the results to the main and sub-objectives of the research project.

5.1 Conclusions

Most of the respondents were employed in South African power plants and the following conclusions therefore apply to the South African generation industry and not to other regions of Africa. Benefit or role of a maintenance strategy: The main benefits of a maintenance strategy were reported as: Increased equipment availability and reliability Reduced environmental impact Higher productivity Reduced maintenance cost Maintenance tactics: All power stations use time-based maintenance, condition-based maintenance and operate-to-failure tactics. Other tactics like fault-finding maintenance are used by only a few power stations. Maintenance approaches: The study found that all power stations have a maintenance strategy in place but the approaches differ from one power station to another. The RCM approach is used by most power plants (64%) but TPM and risk-based maintenance approaches are also used by some plants.

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Power station availability: About one third of respondents indicated an availability of less than 80%. The performance of these plants should be improved. Industry benchmark for maintenance strategy: The study indicated that each power generating plant has its own maintenance strategy. Some strategies are simple, others more complex. Planned and unplanned maintenance: About 50% of respondents indicated that less than 40% of all maintenance work is unplanned. More planned (preventive) maintenance should be done by the power plants to reduce emergency maintenance. Maintenance cost: The average cost of maintenance as a ratio of total production cost is about 22% for the respondents that provided cost data. Maintenance tactics: Time-based maintenance is the tactic that is used most by power stations (93%).

5.2 Recommendations

It is recommended that a similar survey be done with respondents from power plants of all the countries who are members of the Southern African Power Pool (SAPP). The questionnaire could also be expanded to include other performance indicators for maintenance managment. A larger sample size would also be required if comparisons are to be made between different countries or regions as well as between different power plants, e.g. coal-fired, hydro-electric and wind turbines. It is recommended that the model as outlined in Figure 1 be used for developing a maintenance strategy for power generating plants. The objective of this strategy development framework is to: Increase equipment availability Increase equipment reliability Improve overall productivity Increase return on investment (ROI) Reduce environmental impact Reduce maintenance cost Reduce lost time injuries It is also recommended that the design of new power generating plants should consider the importance of maintenance and reliability decisions at the design stage when there is an opportunity to reduce life-cycle operating and maintenance costs and therefore total cost of ownership (TCO).

6 REFERENCES

[1] J.D. Campbell and J.V. Reyes-Picknell, Uptime: Strategies for excellence in Maintenance Management, 2nd edition, Portland, Productivity Press, 2006.

[2] J. Moubray, Reliability-centred Maintenance, 2nd Edition, Butterworth-Heinemann, 1997.

[3] A. Kelly, Maintenance Strategy, Butterworth-Heinemann, 2006.

[4] S. Nakajima, Introduction to TPM: Total Productive Maintenance, Productivity Press, 1988.

[5] T. Suzuki, TPM in Process Industries, Productivity Press, 1992.

[6] L. Krishnasamy, F. Khan and M. Haddara, “Development of a risk-based maintenance (RBM) strategy for a power-generating plant”, Journal of Loss Prevention in the Process Industries Vol. 18 pp. 69–81, 2005.

[7] G.F. Ceschini and D. Saccardi, “Availability centered maintenance (ACM), an integrated approach”, in Proceedings of the Annual Reliability and Maintainability Symposium, January 2002, pp 26-31, Seatle, USA.

[8] M. Organ T. Whitehead and M. Evans, “Availability-based maintenance within an asset management programme”, Journal of Quality in Maintenance Engineering, Vol. 3 (No. 4) pp. 221–232, 1997.

[9] A. Raouf and M. Ben-Daya, “Total maintenance management: A systematic approach”, Journal of Quality in Maintenance Engineering, Vol. 1 (No. 1) pp. 6-14, 1995.

[10] R. Ford, Reliability based maintenance: Using Key Performance Indicators (KPIs) to drive proactive maintenance, GE Power Generation Services, 2014. http://www.plantservices.com/assets/Media/1405/RBM-KPIs-GE.pdf

[11] U. Graber, “Advanced maintenance strategies for power plant operators-introducing inter-plant life cycle management”, International Journal of Pressure Vessels and Piping, Vol. 81, pp 861-865.

[12] L. Wang, J. Chu, W. Mao, and Y. Fu, “Advanced Maintenance Strategy for Power Plants – Introducing the Intelligent Maintenance System”, 6th World Congress on Intelligent Control, pp 21-23, June 2006, Dalian, China.

[13] J.S. Mitchell, “Five to ten year vision for CBM”, ATP Fall Meeting Condition Based Maintenance Workshop, Atlanta, USA, 1998.

[14] Y. Huang and S. Huang, Condition – based maintenance for generating equipment, Beijing, Chinese Electric Power Publisher, 2000

[15] M.A.L. Campos, J.F.G. Fernández, V.G. Díaz and A.C. Márquez, “A new maintenance management model expressed in UML”, Proceedings of the European Safety and Reliability Conference (ESREL), Prague, Czech Republic, 7-10 September 2009.

[16] International Organisation for Standardisation, ISO 9004: 2009. Managing for the sustained success of an organization - A quality management approach.


[17] A.H.C. Tsang, “Strategic dimensions of maintenance management”, Journal of Quality in Maintenance Engineering, Vol. 8 (No. 1) pp. 7-39, 2002.

[18] D.N.P. Murthy, A. Atrens and J.A. Eccleston, “Strategic maintenance management”, Journal of Quality in Maintenance Engineering, Vol. 8 (No. 4) pp. 287-305, 2002

[19] A-T. Umar, “A framework for strategic planning in maintenance”, Journal of Quality in Maintenance Engineering, Vol. 17 (No. 2) pp. 150-162, 2011.

[20] L.M. Moeko and J.K. Visser, “Level of infrastructure maintenance management in utilities of the Southern African Power Pool”, Proceedings of the Africon Conference, IEEE, Mauritius, 2013.

[21] T. Wireman, World Class Maintenance Management, Industrial Press Inc., New York. 1990.

[22] J.L. Coetzee, “A holistic approach to the maintenance problem”, Journal of Quality in Maintenance Engineering, Vol. 5 (No 3), 1999.

[23] S.O. Duffuaa, A. Raouf, and J.D. Campbell, Planning and Control of Maintenance Systems: Modeling and Analysis, John Wiley and Sons, New York, 1999.

[24] L. Ndjendja, “Development of a Maintenance Strategy for Power Generation Plants”, Research Project Report, University of Pretoria, 2011.

[25] S. Stallard and G. M. Curley, “Benchmark Globally, Improve Plant Performance Locally”, Available from: http://www.power-eng.com/articles/print/volume-112/issue-7/features/benchmark-globally-improve-plant-performance-locally.html [Accessed 12 September 2014].

[26] J.S. Mitchell, Physical Asset Management

Handbook, Clarion Technical Publishers, 2001. [27] SAPTM, Available from: http://www.sap.com

[Accessed 1 September 2014]. [28] Pragma, Software Tools – On-KeyTM EAM System,

Available from: http://www.pragmaworld.net/services/on-key-eam-system/ [Accessed 11 September 2014].

[29] Kronos, webTATM, Available from: http://www.kronos.com/industry/government/web-ta.aspx [Accessed 11 September 2014].

[30] D.L. Gano, Apollo Root Cause Analysis: A New Way of Thinking, 2nd Edition, Apollonian Publications; 1999.

[31] Anonymous, Using the TapRoot® System for Process Safety Incident Investigation and Root Cause Analysis, Available from: http://esvc000932.wic047u.server-web.com/dls/TapRooT(R)_System_Explained.pdf [Accessed 11 September 2014].

[32] Institute for Innovation and Improvement, Root cause analysis using 5 Why’s, Available from: http://www.institute.nhs.uk/quality_and_service_improvement_tools/quality_and_service_improvement_tools/identifying_problems_-_root_cause_analysis_using5_whys.html [Accessed 11 September 2014].

[33] Anonymous, Cause and Effect Tree Root Cause Analysis Tool, Available from: www.cdc.gov/nceh/ehs/envphps/Docs/Root_Cause_Analysis_Tool.doc [Accessed 11 September 2014].


MODEL PREDICTIVE CONTROL OF AN ACTIVE MAGNETICBEARING SUSPENDED FLYWHEEL ENERGY STORAGE SYSTEM

K.R. Uren∗, G. van Schoor† and C.D. Aucamp∗

∗ School of Electrical, Electronic and Computer Engineering, North-West University, Potchefstroomcampus, Hoffman street, South Africa. E-mail: [email protected], [email protected]† Unit for Energy Systems, North-West University, Potchefstroom campus, Hoffman street, South Africa.E-mail: [email protected]

Abstract: Flywheel Energy Storage (FES) is rapidly becoming an attractive enabling technology inpower systems requiring energy storage. This is mainly due to the rapid advances made in ActiveMagnetic Bearing (AMB) technology. The use of AMBs in FES systems results in a drastic increasein their efficiency. Another key component of a flywheel system is the control strategy. In the past,decentralised control strategies implementing PID control, proved very effective and robust. In thispaper, the performance of an advanced centralised control strategy namely, Model Predictive Control(MPC) is investigated. It is an optimal Multiple-Input and Multiple-Output (MIMO) control strategythat utilises a system model and an optimisation algorithm to determine the optimal control law. Afirst principle state space model is derived for the purpose of the MPC control strategy. The designedMPC controller is evaluated both in simulation and experimentally at a low operating speed as a proofof concept. The experimental and simulated results are compared by means of a sensitivity analysis.The controller showed good performance, however further improvements need to be made in orderto sustain good performance and stability at higher speeds. In this paper advantages of incorporating asystem model in a model-based strategy such as MPC are illustrated. MPC also allows for incorporatingsystem and control constraints into the control methodology allowing for better efficiency and reliabilitycapabilities.

Key words: state space model, model predictive control, flywheel energy storage system, activemagnetic bearings

1. INTRODUCTION

Early applications of flywheels mainly centred around thesmooth operation of machines. The type of flywheelsused were purely mechanical, and some primitive versionsonly consisted of a stone wheel attached to an axle.The development of flywheel systems continued throughthe years, but rapidly intensified during the IndustrialRevolution. However, it was not until the early 20thcentury, when flywheel rotor shapes and rotational stresseswere thoroughly analysed in the work reported by Stodola[1]. In the 1970s, FES was proposed as a key technologyfor electric vehicles, spacecraft, Uninterruptible PowerSupplies (UPSs) and even planetary rovers [2, 3]. Duringthe 1980s, Active Magnetic Bearings (AMBs) andadvances in motor-generator designs placed FES systemsin a position to compete with chemical batteries in termsof energy density [4–6].

FES systems have a number of attributes that renderthem preferred technology for applications where energystorage is needed. Flywheel systems are made ofenvironmentally friendly material as opposed to chemicalbatteries, and therefore have a lower environmental impact.It is a scalable technology and does not require periodicmaintenance. Flywheels also allow repetitive deepdischarge. The contact-less nature of magnetic bearingsallows for higher energy efficiency, and no lubricants arenecessary. The closed-loop control of magnetic bearingsenables active vibration suppression and on-line control of

bearing stiffness. According to Schweitzer et.al. [7], themost effective and simplest control strategy for a coupledsystem such as a FES system is decentralised and conicalmode control. Examples of these types of strategiesare decentralised PID control, and Centre-Of-Gravity(COG) coordinate control. Modern control techniquesthat give promising results for controlling AMB systemsare H∞ and µ-synthesis, in particular for flexible rotorsystems [8–13]. Schweitzer et.al. [7] continues bystating that observer or state estimator based control suchas Linear-Quadratic-Gaussian (LQG) control offers noappreciable advantage over decentralised control. In fact,observer based techniques can have destabilising effectsdue to uncertain dynamics in AMBs during rotation. Inthe case where the observer based control is designed for arotating system, the controller may be very effective at thedesign speed, but may become unstable at other speeds dueto non-conservative forces introduced by the controller.This is particularly the case for model based controltechniques where the dynamics of the system change as therotational speed changes. This raises the question whetheran advanced model-based control technique such as MPCcan be successfully implemented on a FES system.

MPC has a number of advantages. It is firstlycapable of handling constraints explicitly. Secondly ittreats multi-variable problems in a natural way and itincorporates a model-based design in the sense that ituses an explicit internal model to generate predictionsof future plant behaviour. A number of studies were


previously conducted to evaluate the performance of MPCcontrol strategies on magnetically suspended FES systems.Zhang et. al. [14] conducted a study where a FESsystem was proposed where the radial motion of therotor was controlled by permanent magnet bearings, andthe axial motion was controlled by AMBs that utilisedan MPC strategy. This study was only implementedin simulation, but concluded that MPC yielded superiorstability, sensitivity and robustness as compared to PIDcontrol. Another study conducted by Zhu et. al. [15]focused on the cross-coupling between the top and bottomAMBs of a FES system with a vertical rotor. The studypresented simulation results that indicated that MPC waseffective in reducing the effort needed to ensure robustnessin the presence of disturbances and model uncertainties. Astudy conducted by Nguyen et. al [16, 17] implementedan MPC controller on a FES system and found that MPCwas able to control the FES system effectively for quickacceleration and deceleration scenarios, that is, fast storingand releasing of energy. Current research tends to focuson nonlinear MPC approaches as described by the work ofBachle et. al [18].

In this paper, a linear state space model of an axiallyand radially AMB suspended flywheel is derived. Thismodel is then used for the design of a linear MPC strategy.This control strategy is evaluated both in simulation andon an actual FES system. The results are compared tostudy the effectiveness of the control algorithm. The paperis organised as follows: The experimental setup of theFES system and the linear state space model derivationare discussed in Section 2. Section 3 introduces thelinear MPC and the optimisation algorithm. Section 4presents the simulation and experimental results. Finally,conclusions are drawn in Section 5.

2. FLYWHEEL ENERGY STORAGE SYSTEMMODEL

2.1 Flywheel energy storage system overview

The system under consideration is a Flywheel Uninter-rupted Power Supply (FlyUPS) and is shown in Fig.1. It is designed to deliver 2 kW of electrical energyfor 3 minutes during power dips. The FlyUPS is fullysuspended, which means it has five Degrees Of Freedom(DOF) controlled by two radial AMBs, and one axialAMB. The motor/generator mechanism of the FlyUPScontains a high speed Permanent Magnet SynchronousMachine (PMSM). This PMSM is designed to rotate theflywheel to speeds of up to 30 000 r/min which enables theFlyUPS to mechanically store 527 kJ of energy [19, 20].

2.2 State space model

A similar approach to [21] has been followed in this paperfor deriving a state space model of the rotor and stator ofthe system. The effects of the sensors, filters and poweramplifiers are also included to give a total state spacesystem model of the FlyUPS. As illustrated in Fig. 2 themodel includes five DOF: The translations in the x-, y-

Figure 1: Experimental setup of the FlyUPS [19]

and z-directions, as well as the rotations about the x- andy-axes. The rotation about the z-axis is controlled by thePMSM. In order to develop a model for the rigid rotor,

Figure 2: Rotor, bearing and sensor coordinate frame

a frame of reference (coordinate framework) first needsto be established. A rigid body can be represented bysix coordinates: three displacement coordinates and threerotational coordinates. However, since the rotational speedis taken as constant and displacement in the axis of rotationis decoupled from the rest, the rotor can be representedby four coordinates only [22]. Hence, the coordinateframework is:

z = [x,β,y,−α]T , (1)

which represents the displacement (x,y) and inclination(β,α) about the centre of mass.

Once the coordinate framework is defined, the rotor andbearing dynamics are represented. The rotor dynamicsof a simple gyroscopic beam can be represented by theNewton-Euler equations of motion [7]:

mx = fx, (2)

Iyβ− IzΩα = py, (3)

my = fy, (4)


−Ixα− IzΩβ = px. (5)

The variables fx and fy are the forces acting on the centreof mass and py and px are the force couple moments.The rotor mass is represented by m, and Ω represents theconstant angular velocity in rad/s about the z axis. Ix, Iy andIz are the moments of inertia in the x, y and z directionsrespectively. The Newton-Euler equations above can besimplified by combining them with the selected coordinateframework in (1) to create the model

Mz+Gz = f, (6)

with f = [ fx, py, fy, px]. M is the mass matrix defined as

M =

m 0 0 00 Iy 0 00 0 m 00 0 0 Ix

, (7)

and G, the gyroscopic coupling matrix defined as

G =

0 0 0 00 0 0 10 0 0 00 −1 0 0

IzΩ. (8)

The actual system is current-controlled, necessitating coilcurrent as input to the model [20]. A model with currentas input and displacement as output is therefore required.However, since the actual position of the rotor is notavailable but only the measured position at the bearingsensor locations, it would be essential to transform orreference the above equations of motion to the bearingpositions. The transformation from the centre of mass tothe equivalent mass at the bearing locations, a and b, isdone with the transformation matrix

TB =1

b−a

b −a 0 0−1 1 0 00 0 b −a0 0 −1 1

. (9)

The coordinate framework in (1) becomes

z = TBzB = TB

xaxbyayb

, (10)

and the mass, gyroscopic and force matrices become

MB = TTBMTB, (11)

GB = TTBGTB, (12)

and

fB =

faxfbxfayfby

. (13)

Finally the equation of motion can be written as

MBzB +GBzB = fB. (14)

The forces of the AMBs acting on the rotor are derivedfrom a simple AMB model. The AMB plant constitutesa stator, coils and rotor as shown in Fig. 3. The positionof the rotor is measured by two perpendicularly arrangedposition-sensors and subtracted from the reference positionsignal applied as the system input. The resulting errorin position is converted by a compensator into currentreferences, which in turn are realised by power amplifiers.In the AMB plant these currents exert electromagneticforces on the rotor to restore the rotor position. Active

Figure 3: Stator of an 8-pole heteropolar AMB [23]

magnetic suspension (for a single magnet 1-DOF AMB)entails that an attractive magnetic force be exerted byan electromagnet that will counteract the gravitationalforce exerted by the earth. The attractive electromagneticforce exerted by a current-carrying coil on a ferromagneticmaterial is also known as a reluctance force [7]. Thisforce is derived from the energy stored in the magneticfield. Any small change in the volume of the airgap wouldresult in an increase in the energy stored in the field. Thisincrease in energy must be supplied by an external force. Ifonly the coils of the pole pair 1 (PP1) in Fig. 3 are allowedto carry a current and electromagnetic cross-coupling isignored, the resulting force exerted in the y direction canbe approximated by

fm = µ0

(Ni

lc/µr +2xg

)2

Acos(θ) (15)

with the symbols as described in Table 1.

The force equation for a 1-DOF AMB given in (15)shows the relationship between the applied current in thecoil, the position of the shaft within the airgap and the


electromagnetic force exerted on the rotor by the statorpole. Clearly, the force is proportional to the square ofthe current as well as inversely proportional to the squareof the airgap between the stator and the rotor.

Table 1: Symbol description of AMB force equation

Symbol Descriptionlc length of the magnetic path

(excluding the airgap)µ0 permeability of free spaceµr relative permeability of the AMB statorxg size of the airgap between the stator

and rotorN number of turns per coili current in the coilsA pole-face areaθ angle between the vertical axis and

the normal line to the pole face

This equation disregards the effects of fringing and leakageof magnetic flux and is only valid under the followingassumptions [7]:

• permeability of the iron is constant;

• only small variations in the airgap are allowed; and

• uniform flux in the airgap (i.e. a homogeneous field).

Even when the effects of magnetic saturation andhysteresis have been disregarded, AMBs are still nonlineardevices, as can be seen from (15). In order to takeadvantage of the existing body of knowledge of linearsystems, most AMB designers opt for linearising the AMBaround a setpoint and controlling it as if it were a linearsystem. The range over which a linear approximation isvalid, can be increased by driving opposing electromagnetsin the AMB stator with mirror images of the same currentsignal. This is known as differential driving mode and isexhibited in Fig. 4 [7]. The schematic diagram in Fig. 4

Figure 4: Schematic diagram of differential driving mode

only illustrates differential driving mode for the top andbottom electromagnets of the AMB in Fig. 3, but thesame principle also holds for the other two electromagnets.

The output of the controller is a current reference signalwhich is added to and subtracted from a bias current level.The bias current is typically chosen such that the AMB isoperated in the centre of the linear region of the magneticmaterial’s hysteresis curve. The end result is that thenett force exerted by the top and bottom electromagnets issymmetrical about some bias force level. In the absence ofgravity, the net electromagnetic force applied to the pointmass is consequently given by:

fm = k[(i0 + iy)2

(xg)2 − (i0 − iy)2

(xg)2

](16)

where the constants µ0, N, A and cos(θ) have beensubsumed into the constant k.

After linearising (16) for small position deviations (δy)around some bias position (y0), the force exerted by anAMB in the vertical degree of freedom can be expressedas follows:

fm = kiiy + ksδy (17)

where the current- and position stiffness constatns arerespectively given by [20]:

ki = 2µ0N2i0A

y20

cos(θ), (18)

and

ks =−2µ0N2i0A

y30

cos(θ). (19)

According to (17) the bearing forces are dependent oncurrent and displacement. These linearised forces are nowintroduced into the equation of motion (14) and result in

MBzB +GBzB = KiiB +KszB. (20)

The displacement-force constants, Ks and current-forceconstants, Ki of the raidal bearings are simply diagonalmatrices of the previously mentioned, ks and ki constants:

Ks =

ks ax 0 0 00 ks bx 0 00 0 ks ay 00 0 0 ks by

, (21)

and

Ki =

ki ax 0 0 00 ki bx 0 00 0 ki ay 00 0 0 ki by

. (22)

The current-force and displacement-force values in the xand y directions at a and b are identical, i.e. ks ax = ks ay,and ki bx = ki by. The current vector is given by

iB =[

iax ibx iay iby]T

. (23)

By rearranging (20) and setting iB = u the followingequation is obtained

zB =−M−1B GBzB +M−1

B KszB +M−1B Kiu. (24)


This gives the standard state-space formulation of theradial AMB system at the bearing coordinates as

xB = ABxB +BBuyB = CxB

(25)

with

xB =

[zBzB

],AB =

[0 I

M−1B Ks −M−1

B GB

],

BB =

[0

M−1B Ki

],C =

[I I

].

Next the transformation to sensor coordinates is done. Thebearing coordinate state-space system in (25) is referencedto the sensor coordinate system by transforming the statematrices AB and BB to

As = TsABT−1s ,

Bs = TsBB(26)

with

Ts =

[SsTB 0

0 SsTB

], (27)

and

Ss =

1 c 0 01 d 0 00 0 1 c0 0 1 d

. (28)

This results in the final state-space model

xs = Asxs +Bsuys = Cxs

(29)

with

xs =[

xc xd yc yd xc xd yc yd]T

. (30)

The rotational speed of the rotor is taken into account inthis model, and it can be seen from (20), that there isa coupling between the moment in the x plane and themoment in the y plane. As a consequence, this radial AMBmodel is a fully coupled system with four current inputsand eight outputs in terms of displacements and velocitiesrespectively.

In addition to suspending the rotor horizontally, theFlyUPS system is required to lift and suspend the flywheelvertically. Consequently, the addition of an axial thrustbearing is required. The axial AMB is situated at the top ofthe FlyUPS rotor, and will use the thrust disc to exert therequired lifting force. The axial AMB is taken as a simple1-DOF point mass system, since axial rotor movement isassumed decoupled form the rotational movement due torigid simple body motion, hence not influencing the centreof mass of the radial AMBs. There is no need to transformthe axial model to bearing or sensor coordinates, as itrepresents vertical movement of a point mass system only.

The force acting on the axial AMB is calculated in a

similar manner as to (16), with the current-force anddisplacement-force values calculated similarly to (17), butwith values for the axial AMB:

f (iz,xz) = kiziz + kszz = mz. (31)

The state space model for the axial AMB is given by

xz = Azxz +Bzuz

yz = Czxz(32)

with

xz =

[zz

],uz = [iz],Az =

[0 1kszm 0

],

Bz =

[0kizm

],Cz =

[1 1

].

The model for the axial AMB is simply appended to themodel of the radial AMBs, as illustrated in Fig. 5 and theparameter values are. The sensors are modelled as five

Figure 5: System state space model of FlyUPS

cascaded second order low-pass transfer functions withbandwidths of 10 kHz, and connected to the outputs of theAMB model [22]:

Tsens(s) =ω2

s

s2 +2ζωss+ω2s, (33)

with damping ζ= 0.707 and bandwidth ωs = 2 ·π ·10×103

rad/s.

The power amplifier (PA) model consists of a closed loopPI controlled system with a bandwidth of 2.5 kHz as shownin Fig. 6. The closed loop transfer function of the PA is


given by

TPA(s) =iout(s)ire f (s)

=2Vbus(Ki +Kps)

Ls2 +(2KpVbus +R)s+2KiVbus, (34)

where Vbus = 51 V is the bus voltage, R = 0.152 Ω is

Figure 6: PA small signal closed-loop system

the coil resistance, L = 6.494 mH is the nominal coilinductance, Kp = 1 is the proportional constant and Ki =0.1 is the integral constant [20]. The cascaded PA model isconnected to the input of the AMB model.

3. MODEL PREDICTIVE CONTROL DESIGN

A conceptual diagram of a model predictive control systemis shown in Fig. 7. A plant model is used to predict futurevalues of the output variables. The differences between thereference signals and predicted outputs, serve as the inputto an optimisation algorithm. At each sampling instant thecontrol law uses the predicted information to generate theoptimal inputs to the plant. Linear inequality constraintson the input and output variables, such as upper and lowerlimits, may be included in the calculation. The objectiveof the MPC control scheme is to determine a sequence ofcontrol moves (changes in the input variables) so that thepredicted response moves to the set point in an optimalmanner.

Figure 7: Conceptual diagram of MPC

Let the 5-DOF state space model be represented in alinearised, discrete-time, state space form

x(k+1) = Ax(k)+Bu(k),y(k) = Cx(k),

(35)

where x is an n-dimensional state vector, u is an-dimensional input vector and y is an m-dimensionaloutput vector.

It is assumed that not all the state variables can bemeasured, and are therefore estimated/predicted. Thefollowing notation will be used to denote future values for

the variables u,x,y at time k+ i, as assumed at time instantk:

u(k+ i|k),x(k+ i|k),y(k+ i|k).

The cost function V(k) penalises deviations of thepredicted controlled outputs, y(k + i|k), from the vectorreference trajectory r(k+ i|k). The cost function is definedas

V(k) =Hp

∑i=Hw

‖y(k+ i|k)− r(k+ i|k)‖2Q(i)

−Hu−1

∑i=0

‖∆u(k+ i|k)‖2R(i).

(36)

Hp is the prediction horizon and Hu is the control horizon.It may not necessarily penalise the deviations of y from rimmediately (if Hw > 1), since there may be some delaybetween applying the input and seeing the effect. It will beassumed that Hu ≤ Hp, and that ∆u(k+ i|k) = 0. Q(i)≥ 0and R(i)≥ 0 are weight matrices.

It will be assumed that Hu ≤ Hp, and that ∆u(k+ i|k) = 0for i ≥ Hu. That means

u(k+ i|k) = u(k+ i+Hu|k) for all i ≥ Hu. (37)

This cost function also implies that the predicted errorvector e(k+ i|k) = y(k+ i|k)− r(k+ i|k) is penalised atevery point in the prediction horizon, in the range Hw ≤i ≤ Hp.

The states of the system are predicted by iterating the statespace model as follows:

x(k+1|k) = Ax(k)+Bu(k|k)x(k+2|k) = Ax(k+1)+Bu(k+1|k)

= A2x(k)+ABu(k|k)+Bu(k+1|k)...

x(k+Hp|k) = Ax(k+Hp −1|k)+Bu(k+Hp −1|k)= AHp +AHp−1Buu(k|k)+ · · ·+Bu(k+Hp −1|k)

(38)

The predicted input sequence is given by

u(k|k) = ∆u(k|k)+u(k−1)u(k+1|k) = ∆u(k+1|k)+∆u(k|k)+u(k−1)

...u(k+Hu −1|k) = ∆u(k+Hu −1|k)+ · · ·

+∆u(k|k)+u(k−1)(39)

Substituting (39) into (38) results in the predicted state


equation

X(k) = Ωx(k)+Γu(k−1)+Φ∆U(k) (40)

where

X(k) =

x(k+1|k)...

x(k+Hp|k)

, (41)

and

∆U(k) =

∆u(k|k)...

∆u(k+Hu −1|k)

, (42)

for suitable matrices Ω, Γ and Φ.

The prediction of the output equation is obtained as

y(k+Hw|k) = Cx(k+Hw|k)y(k+Hw +1|k) = Cx(k+Hw +1|k)

...y(k+Hp|k) = Cx(k+Hp|k)

(43)

By substituting (39) and (38) into (43) the followingcompact representation of the output equation is obtained

Y(k) = Ψx(k)+ϒu(k−1)+Θ∆U(k), (44)

where

Y(k) =

y(k+Hw|k)...

y(k+Hp|k)

, (45)

for suitable matrices Ψ, ϒ and Θ.

The tracking error may then be defined as

E(k) = T(k)−Ψx(k)−ϒu(k−1) (46)

where

T(k) =

r(k+Hw|k)...

r(k+Hp|k)

, (47)

is the vector containing the reference signals.

The cost function may then be rewritten as follows

V(k) = ‖Y(k)−T(k)‖2Q +‖∆U(k)‖2

R (48)

where

Q =

Q(Hw) 0 · · · 00 Q(Hw +1) · · · 0...

.... . .

...0 0 · · · Q(Hp)

(49)

and

R =

R(0) 0 · · · 00 R(1) · · · 0...

.... . .

...0 0 · · · R(Hu −1)

(50)

Equation (48) may be written in its expanded form as

V(k) = E(k)T QE(k)−2∆U(k)T ΦT QE(k)

+∆U(k)T [ΘT QΘ+R]∆U(k).(51)

This equation may also be written in the form

V(k) = const−∆U(k)T G+∆U(k)T H∆U(k), (52)

whereG = 2ΘT QE(k) (53)

andH = ΘT QΘ+R (54)

and neither G nor H depends on ∆U(k). In order to findthe optimal U(k), the gradient of V(k) is set to zero

∇∆U(k) =−G+2H∆U(k) (55)

implying that the optimal set of future input moves is

∆U(k)opt =12

H-1G. (56)

It should be remembered that due to the use of the conceptof a receding horizon, only the first part of the solutioncorresponding to the first step is used. Therefore, if theplant has inputs, then only the first rows of the vector∆U(k)opt are used. This may be represented as follows

∆u(k)opt =[

I, 0, · · · 0]]

∆U(k)opt, (57)

where I is the × identity matrix, and 0 is the × zeromatrix.

4. RESULTS

The MPC control was implemented on a hardwareplatform as depicted in Fig. 8. The code for the MPCcontroller was implemented in Simulink. Using theReal-Time Workshop, the Simulink code is convertedto C code and compiled as an executable file. Theexecutable file is then linked and embedded on adSPACE real-time control target board.

The user can monitor the FlyUPS with a hostcomputer through dSPACE ControlDesk software.ControlDesk is used for displaying the system status inreal-time. From here the PMSM drive can be activatedand changes to the reference signals can be made.

4.1 Memory usage and cycle time

Memory usage of the controller is described in terms ofthe size of the executable file that needs to be embedded


Figure 8: Implementation method of MPC on FlyUPS

on the dSPACE hardware. The full five DOF MPCcontroller for the FlyUPS uses 12.7 MB of memory, whichis well below the limit of 16 MB maximum storage of thedSPACE target.

The execution time of the controller indicates the period oftime it takes to implement the control strategy during onecontrol cycle. This includes reading the measured outputsof the system, calculating the optimal control signal, andimplementing the optimal control action. In order todetermine the execution time of the MPC controller thedSPACE Profiler is used. The profiler logs the periodof time that passes from the start of the control cycle untilthe control action is implemented.

Various factors influence the execution time of the FlyUPScontrol system. These factors include the order of themodel from which the controller is derived, the use ofconstraints in the design, and the lengths of Hp and Hu.This is expected as these factors increase the complexityand number of operations that are performed during eachcycle.

It was determined experimentally that the largest samplingperiod for the FlyUPS control system to maintain stabilityis 200 µs, corresponding to a sampling frequency of 5kHz. For the unconstrained 5 DOF MIMO MPC controlstrategy, the execution time is 174 µs. This unconstrainedcontroller is derived from a reduced tenth order state spacemodel. However, when constraints were included thecontroller became unstable due an execution time largerthan 200 µs. The effects of the prediction and controlhorizons were investigated by keeping one parameter fixedand varying the other parameter. It turned out thatthe optimal choice of these parameters adhering to themaximum execution time, was Hp = 50 and Hu = 5.

4.2 Sensitivity analysis

A comparison of the measured and simulated sensitivityfunctions for the axial AMB (Z), top radial AMB (X1) andbottom radial AMB (X2) at standstill are given in Figures9, 10 and 11 respectively.

From Fig. 9 the peak measured sensitivities of the axialAMB are 4.15 dB at 44.21 Hz and 16.22 dB at 81.76Hz corresponding to the first two rigid modes of the axialAMB. The peak of 16.22 dB places the axial AMB of theFlyUPS in class D of the ISO CD 14839-3 standard. Thismeasured result reveals that the axial AMB of the FlyUPSis very sensitive to parameter changes from 82 Hz to 96.5Hz. The simulated sensitivity function clearly does notpredict this sensitivity. The simulation result indicates asingle peak sensitivity of 4 dB at 160 Hz placing the axialAMB in zone A of the ISO CD 14839-3 standard. Thisdifference indicates that the model of the axial AMB maynot be accurate enough to meet the requirements of MPC.

Figure 9: Sensitivity function of the axial AMB at standstill

Fig. 10 and Fig. 11 give the results for the sensitivityfunctions of the top and bottom radial AMBS respectively,at standstill. These results indicate a larger correlationbetween the simulated and measured results. However, itis also clear from these results that the actual system hassome inherent dynamics that are not contained in the modeland thus do not appear on the simulation results.

Figure 10: Sensitivity function of the top radial AMB atstandstill

Fig. 10 shows three peak sensitivities of -4.82 dB, 4.728dB and 4.14 dB at 15.38 Hz, 42.16Hz and 57.63 Hz,respectively, in the measured sensitivity of X1 at standstill.This places the top radial AMBs within zone A of the ISOCD 14839-3 standard of AMBs. The simulated sensitivityexpects a single peak of 5 dB at 58 Hz corresponding tozone A of the ISO CD 14839-3 standard.

At standstill, the measured sensitivity function of X2 givenin Fig. 11 shows peaks in the sensitivity of 3.18 dB and4.13 dB, at 15.13 Hz and 34.93 Hz, respectively. This


Figure 11: Sensitivity function of the bottom radial AMB atstandstill

places the bottom radial AMBs within the class A ofthe ISO CD 14839-3 standard on AMBs. The simulatedsensitivity of X2 indicates a single peak of 4.1 dB at 35 Hzcorresponding to zone A of the ISO CD 14839-3 standardas well.

Despite the low sensitivities of the radial AMBs toparameter changes, the system is classified according tothe worst case measured sensitivity. This means thatthe FlyUPS falls within class D of the ISO CD 14839-3standard due to the peak sensitivity of the axial AMB. ForMPC the shape of the sensitivity function is expected asthe controller is derived from the model of the FlyUPS atstandstil. This means that low sensitivities are expected atlow frequencies, with the gain of the sensitivity functionincreasing as the operating speed increases.

The sensitivity functions of Z, X1 and X2 only changemarginally from operation at standstill to an operatingspeed of 500 r/min in both simulation and implementation.These results are given in Fig. 12, Fig. 13 and Fig. 14for Z, X1 and X2, respectively. The major change thatis noted in the results is the increase in the frequencycomponents corresponding to integer multiples-of-twoharmonics of the operating speed, indicating the presenceof an unbalance [7]. These harmonics do not appear tohave a large effect on the sensitivity of the axial AMB.However, in the case of the radial AMBs the sensitivityat these harmonic frequencies is driven into zone D of theISO CD 14839-3 standard for AMBs.

Figure 12: Sensitivity function of the axial AMB at 500 r/min

Figure 13: Sensitivity function of the top radial AMBs at 500r/min

Figure 14: Sensitivity function of the bottom radial AMBs at500 r/min

4.3 MPC operating range

The operating range is defined as the amount by whichthe operating speed can be adjusted about the designspeed of the MPC controller before the system responsebecomes unstable. This is done by implementing an MPCcontroller derived for the model of the FlyUPS at standstilland increasing the operating speed until the maximumoperating speed is attained where the radius of the orbitalpattern about the origin reaches 120 µm.

An increase in the operating speed introduces a visiblechange in the performance of the MPC controller insimulation and implementation where the radius of theorbital pattern increases nearly exponentially as theoperating speed is increased. In the case of the simulation,the maximum operating speed reached is 2440 r/min for anorbital radius of 120 µm in X1. In the experimental setupthe orbital radius of 120 µm in X1 is already reached at1500 r/min. Any further increase in the operating speed ofthe implementation causes the open-loop PMSM control tolose synchronism with the rotor. This point along with therestriction in terms of cycle time resulted in the choice ofthe 500 r/min operating speed for the test results.

5. CONCLUSIONS

In order to evaluate the implementation of MPC onthe FlyUPS the MPC controller was firstly validated bycomparing the performance of the implementation to thesimulated performance. This comparison showed that theperformance of the practical implementation correlated to


the performance expected in simulation with regard to thesensitivity analysis.

However, at an operating speed of 500 r/min an unbalancedisturbance is noted in the response of the radial AMBs.This unbalance is seen as the sinusoidal disturbance in theposition output of the radial AMBs and can be identifiedby the integer multiples-of-two harmonic componentsin the frequency response that are introduced by theunbalance at the operating speed. From these results itis clear that the MPC controller is limited to the designparameters derived at standstill, which cannot implementenough stiffness in the AMBs to eliminate the unbalance.Some limitations regarding the operating range due tounmodelled dynamics, as well as long execution times duethe computational load have also been noticed.

In this paper it was shown that MPC is a viable controlstrategy for the FlyUPS, however some limitations of thecurrent MPC strategy needs to be addressed to improveperformance at higher operating speeds.

One of the main limiting factors is the optimisationalgorithm of the MPC control strategy that utilises a modelof the actual system. In this regard other types of modelssuch as artificial neural networks or fuzzy models can beincorporated. These models are also able to update on-lineas the operating point changes. This may be very beneficialin terms of the operating speed range.

For the optimisation algorithm various techniques havebeen proposed for the reduction of the computational loadwhen calculating the optimal control action for a MIMOsystem. The most prominent technique involves convexoptimisation algorithms that reduce the computationalload by exploiting special patterns in the formulation ofthe objective function. This technique is common inapplications involving quadratic programming problemssuch as the formulation of the MPC cost functionwhen constraints are implemented on the output andthe increment of the control signals. Alternativelythe parameters that do not change during the plantoperation can be identified and calculated offline to reducethe computational load. These parameters can thenbe implemented in a gain-scheduling algorithm duringoperation.

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APPENDIX A

Parameter values used in the state space model are given inthe following Tables.

Table 1: Parameter values of the FlyUPS

Symbol Description Value UnitIx Moment of inertia 0.11575 kg ·m2

in the x planeIy Moment of inertia 0.11575 kg ·m2

in the y planeIz Moment of inertia 0.10669 kg ·m2

in the z planem Mass of the rotor 17.65 kga Bearing displacement −160×10−3 mb Bearing displacement 64.4×10−3 mc Bearing displacement −190×10−3 md Bearing displacement 95.4×10−3 m

Table 2: Parameter values for the radial bearings

Symbol Description Value Unitki Force-current 30 N/A

constantks Force-displacement −15000 N/m

constantµ0 - 4π×10−7 -A - 204.026×10−6 m2

N - 80 -i0 - 2.5 Ay0 - 500×10−6 mθ - 22.5 -

Table 3: Parameter values for the axial bearings

Symbol Description Value Unitkiz Force-current 54.9 N/A

constantksz Force-displacement −329693 N/m

constantµ0 - 4π×10−7 -A - 168.45×10−6 m2

N - 104 -i0 - 3 Az0 - 500×10−6 mθ - 0 -


INCENTIVES AND SOUTH AFRICA’S AUTOMOTIVE INDUSTRY PERFORMANCE: A SYSTEM DYNAMICS APPROACH M. Kaggwa* and J. L. Steyn** * Sam Tambani Research Institute, PO Box 32202, Braamfontein 2017, South Africa Email: [email protected] ** Department of Engineering and Technology Management, Graduate School of Technology Management, University of Pretoria, Private Bag X20, Hatfield 0028, South Africa Email: [email protected] Abstract: Investment in robotic automotive manufacturing and inherent electronics has played a pivotal role in the growth and competitiveness of the South African automotive industry. Government's offering of incentives was intended to lessen the cost of local industry’s expensive, but necessary investment. Despite the growth, industry trade balance has been declining systematically. To explain the apparent contradiction in industry performance, a model of South Africa’s automotive incentives – including the Productive Asset Allowance (PAA) and the Import-Export Complementation (IEC) – was developed. Model simulations reveal that, while the IEC had a significant effect on the industry trade balance, the role of the PAA in this regard is trivial. Ultimately, the study reveals that combining strictly investment incentives with other ‘non-investment’ incentives can have unintended consequences for the local automotive industry. Keywords: Investment incentives, robotic automotive manufacturing, system dynamics, competitiveness

1. INTRODUCTION

For many countries that were late to develop and wished to improve their domestic manufacturing capacity, the question is no longer whether to give or not to give industry incentives, but how to structure such incentives to serve the national interest. The automotive industry is a key industry in South Africa and has been receiving government incentives for over a decade. The aim of incentives is to support the industry to become globally competitive in the long term [1]. There was consensus that government had to motivate the local industry to invest in costly robotic manufacturing and electronics, as well as control systems engineering competencies that are of key importance, among others, to the competitiveness of automotive manufacturing. Initially, the incentives were offered under an envelope programme: the Motor Industry Development Programme (MIDP). The programme has since been renamed the Automotive Production Development Programme (APDP). However, the effectiveness of the incentive dispensation in supporting industry competitiveness is being questioned. The increasing industry trade deficit that characterised the MIDP period is a particular concern.

Despite a steady increase in investment in state-of-the-art automated equipment, accompanied by a concomitant increase in vehicle production and exports, industry trade deficit increased from R12 billion in 1995 to R33 billion in 2006 [2]. The deteriorating trade deficit is threatening domestic vehicle production and the local sourcing of automotive components, contrary to intended objectives. The MIDP policy framework was based on intuition and consensus among stakeholders. As such, some of its assumptions remain embedded in the mental models of its historical promoters, making it hard to uncover internal inconsistencies. The problem with intuitive models is that they cannot be scientifically assessed to allow objective improvement. Formalising intuitive mental models enhances mental model quality and increases the reliability of their simulations, which is a critical aspect of improving policy interventions [3]. This paper uses a system dynamics approach to formalise the Productive Asset Allowance (PAA) and Import-Export Complementation (IEC) incentives of the MIDP. The model is used to simulate the two incentives’ medium-term effects on the industry trade balance under existing policy rules. The industry trade deficit has been identified as the main threat to the MIDP’s success. Concluding remarks are based on the simulated model results.


2. INCENTIVES AND INDUSTRY PERFORMANCE

Industry incentives have been widely used as a tool to address industrial development in both developed and developing countries [4]. Offering incentives implicitly assumes a positive relationship between industry investment and investment incentives on the one hand, and between investment and industry performance on the other [5]. Conventional economic theory on the relationship between investment and investment incentives is often based on a neo-classical economic model of a profit-maximising firm. It is argued that such a firm will invest up to a point where revenue received from the sale of an additional product or service equates to the cost of the additional capital required for its production. The incentives offered reduce the cost of capital acquisition, hence motivating more investment, which holds other factors constant [6]. However, this literature is based on perfect market conditions that hardly exist in real-life situations. For this reason, its usefulness to practical policy makers is limited. Hall and Jorgenson [7] pioneered earlier work on establishing the relationship between industry performance and the offer of incentives. They derived an investment function for a profit-maximising firm with user-cost of capital as one of the explanatory variables. They postulated that industry incentives reduce the user-cost of capital, thereby increasing investment and the subsequent expansion of productive activities. Nevertheless, Hall and Jorgenson’s model is criticised for its failure to determine the rate of investment and relying on an ad hoc stock adjustment mechanism instead [8]. As an improvement on the model of Hall and Jorgenson, Tobin [9] proposed the q-theory model. In this theory, ‘q’ is defined as the ratio of the market value of capital to its replacement cost. According to Hayashi [10], the q-value motivates investment. The q-theory introduced the cost of installing new investment in the firm’s optimisation decisions. Consequently, it captures the role of fiscal and non-fiscal industry incentives, as these have a direct effect on the cost of acquiring capital for investment regarding value to the firm derivable from it. Again, a major limitation of Hall and Jorgenson’s model and of Tobin’s investment incentive theory is their inability to bridge the gap between theory and practice. The theoretical framework proposed does not account explicitly for demand constraints. Yet, in reality, what can be sold in a particular market has a significant influence on investment decisions in that location, which is sometimes more than the cost of capital. Moreover, strategic investment decisions may not necessarily be based on cost of capital per se. Strategic investment is common in the automotive

industry. Global vehicle manufacturers locate production around the world, depending on which markets they plan to penetrate or protect in the long run. Theories on investment and investment incentives in the literature do not address these practical considerations. Nonetheless, Hall and Jorgenson’s investment model and Tobin’s q-theory set the foundation for empirical work on establishing how incentives influence industry performance. Unfortunately, the number of empirical studies that have concluded that incentives positively influence industry performance and should therefore be encouraged [11, 12, 13] are as many as those against the use of industry incentives [14, 4]. Since findings on incentives and industry performance are mixed and inconclusive, each incentive offer has to be judged on its own merit, based on the unique location characteristics [15]. This applies to incentives offered to South Africa’s automotive industry.

3. METHODOLOGY AND DATA SOURCES Against the background of inconclusive relationships between industry incentives and industry performance, a system dynamics (SD) approach was used to model the effects of the PAA and IEC on the automotive industry trade balance. Basic econometrics was also used to establish the extent to which independent variables included in the model explained industry trade balance, which is the dependent variable of interest. It is acknowledged that econometrics is the most used approach in industrial policy analysis. The methodology focuses on quantitative measurement and an analysis of economic phenomena. It is particularly useful in forecasting [16]. The forecasting power of econometrics and subsequent policy recommendations are based on a strong assumption that the previously observed phenomena will hold in future, which may not necessarily be the case. As such, the methodology is less appropriate for policy analysis that focuses on changing observed phenomena. In this case, the focus of analysis should be the understanding of dynamics pertaining to causality, rather than correlations or impact. SD methodology, based on operational thinking and control theory, provides a useful way to analyse policy interventions with the objective of changing performance. The SD approach allows the building of simulation models of complex situations using both quantitative and qualitative data so that such situations can be better understood and managed [17]. The MIDP incentive framework seems like a simple concept, yet its effects on industry dynamics are vast. The working of the MIDP incentives shows interrelationships between sector and industry variables without explicit cause and effect, which is a characteristic of a complex system.


The approach is based on the premise that the internal structure of any system determines the system’s behaviour. Capturing feedback effects and non-linear relationships within a system and facilitating understanding of the relationship between the behaviour of the system and its underlying policy decision rules are at the core of the approach [18]. 3.1 Data sources Quantitative historical data was collected from the South African Department of Trade and Industry (thedti) and the National Association of Automotive Manufacturers of South Africa (NAAMSA). Thedti carries out annual surveys to capture industry performance data as part of its monitoring mandate. Although part of this data is confidential, data relating to general trends in industry performance is published in the Department’s annual publication Current developments in automotive industry and is available in the public domain. Thedti data is triangulated with other internal, but confidential data sources, thereby increasing its reliability. NAAMSA is the national association of all local light, medium and heavy commercial vehicle manufacturers. It is also the representative organisation for franchise holders that market vehicles in South Africa. NAAMSA collects performance data from all its members. The data is published in the organisation’s annual reports and is periodically disseminated to the public through press briefings. The NAAMSA data is more comprehensive and disaggregated, but can potentially be biased due to vested interests. NAAMSA data was compared with thedti data and, in cases of significant deviation between the two data sets, thedti data was preferred. Thedti and NAAMSA data was supplemented by qualitative data collected from archive documents. Board of Tariffs and Trade (BTT) reports and government gazettes on the rationale for the introduction of the MIDP were specifically reviewed.

4. THE MIDP INCENTIVE MODEL 4.1 PAA model structure The PAA is awarded according to the amount of the investment in productive assets. These should be assets that are directly applied during the conversion of raw material to finished goods. Such assets make up the largest proportion of industry investment, with a notably high cost associated with automated vehicle paint plants and robotic vehicle assembly stations replicated many times to carry out numerous consecutive operations. Significant investment in land, buildings, equipment and software for other major operations, such as marketing, finance, human resource

administration, procurement and sales is excluded. To allow for this, total industry investment has to be multiplied by a fraction α to obtain the amount to be used for assets qualifying for the PAA, as shown by the following equation:

α=AA t tP I I (1)

Where: AA tP I = investment qualifying for the PAA in year t

tI = total industry investment in year t

The PAA is awarded to claimants in the form of import rebate certificates. The use of these certificates is severely restricted. They can only be used by vehicle manufacturers/assemblers to import fully built-up vehicles. These imports are almost exclusively models that are not manufactured in the country. The underlying rationale is that this allows local vehicle manufacturers to rationalise production in the country to the one or two most viable models, while making a wider range of models available that are required in the local market. PAA certificates cannot be traded between vehicle manufacturers. With regard to component manufacturers, only direct suppliers (Tier 1 suppliers) qualify for the PAA. Furthermore, the suppliers can only access PAA benefits if they provide government with an undertaking from vehicle manufacturers that they will only purchase components manufactured by qualifying assets. The relevant vehicle manufacturer commits itself to purchasing the PAA certificates generated at a fixed rate of 80% of the value. According to an explanation obtained from a government expert, these restrictive conditions were put in place because of the uncertainty of the potential drain from the pool of available duty rebates in addition to the existing IEC. The value of the rebate is 20% of the amount of the investment that qualifies for the PAA. The value of rebates that a claimant can obtain from a particular qualifying investment can therefore be presented as follows:

0.2=AA AA tP RG P I (2)

Where: AAP RG = PAA rebates generated in year t

0.2 = PAA benefit fraction as legislated. Furthermore, the legislation stipulates that the value of the PAA rebates is spread over five years, starting in the year after capitalising the investment. The value of


annual rebate certificates that can be generated is then as follows:

/ 5= AARCR P RG (3)

Where: RCR = the value of rebate certificate release per year 5 = the five-year period over which the PAA benefit is spread The value of vehicles that can be imported in a particular year using PAA rebates depends on prevailing import duty and the value of PAA rebates issued in that particular year according to the following equation:

/=AAP RI RCR IMPORTDUTY (4)

Where: AAP RI = the value of imports in the year under

consideration using the PAA rebates IMPORTDUTY = the prevailing import duty rate in that year To capture the feedback effect of the PAA, industry investment is made endogenous through the introduction of the investment rate variable. Therefore, annual industry investment is set to increase according to the following equation:

1(1 )−= +t t rateI I I (5)

Where: rateI = the annual industry investment growth rate

In addition to the value of rebatable imports introduced in (4) above, two other factors that determine the value of planned production are introduced in order to close the PAA incentive model loop, namely domestic market size by value and value of exports. This is done because it can be reasonably assumed that the value of investment will depend on the value of planned production. The size of the domestic market is assessed by industry representatives to be the most important motivation for multinational vehicle manufacturers to invest in southern Africa [19]. Exports, on the other hand, augment the domestic market size, while imports, whether rebated or otherwise, reduce the effective domestic market. PAA rebatable imports add to the

stock of industry imports into the country on which the industry does not pay duties. Given that the only way industry can benefit from the PAA incentive is through importing vehicles and offsetting duties payable using earned rebate certificates, firms will import until they have exhausted issued rebates [1]. To account for the difference that the PAA makes to production planning, a normal investment growth fraction variable is introduced. The normal investment growth rate is defined as the rate that would result from the influence of the size of the domestic market and export potential only, in the absence of PAA import duty rebates. To the extent that PAA rebatable imports also affect investment, actual investment growth fraction will differ from the normal growth fraction. The difference emanates from the planned production, which is postulated to be proportional to (domestic market + exports – PAA rebatable imports) / (domestic market + exports). The effect of PAA rebatable imports on the planned value of production, which in turn affects actual investment growth fraction, constitutes a closed loop of the PAA incentive model. The feedback loop is implicitly nonlinear if the dynamics of the value of rebatable imports and the value of exports are considered. An increase in the value of rebatable imports relative to the value of exports reduces the rate of increase in investment through the actual investment growth fraction and vice versa. The PAA model can be used to simulate values of rebatable imports under different scenarios. This can be done by specifying initial model values and rate of change values. Scenarios related to different values of the PAA benefit fraction, certificate spread period and import duty level can then be run. However, in isolation, the PAA model underestimates the effect of rebatable imports on value of production planned, because the model does not consider additional rebatable imports generated under the IEC dispensation. The following section extends the PAA model to include the IEC contribution to the value of rebatable imports in the industry. 4.2 IEC incentive model The IEC scheme is linked to the value of exports, but it also allows the import of vehicles using credits generated by the export of vehicles and components. The benefit is in the form of import rebate credit certificates (IRCCs), which are based on a proportion of exported local content. In order to model the IEC scheme’s contribution to the value of rebatable imports, one can start by assuming that the value of exports is determined by an export growth rate parameter, which is assumed to be


exogenously determined. By obtaining an appropriate initial value, the following equation can be used to model industry exports per year:

1(1 )β−= +t tE E (6)

Where: tE = total industry exports per annum in the year t

β = the export growth rate fraction As IRCCs are based on a proportion of exported local content, the following additional equation is required:

= ∗ tELC ELCF E (7)

Where: ELC = exported value of local content ELCF = exported local content fraction The IRCC value to be awarded to an exporting firm is calculated by discounting the value of exported local content at a predetermined rate that is scheduled to reduce over time as established in the initial MIDP framework. It is subject to adjustment in reviews. The schedule was introduced, in part, to encourage industry to grow its competitiveness. The IRCC value generated is therefore not only a function of exported local content, but also of the exported local content beneficiation fraction (ELCBF), as determined for a particular year and reflected in the equation below:

= ∗IRCCVALUE ELC ELCBF (8)

Where: IRCCVALUE = the value of IRCCs generated in a year ELCBF = the export local content beneficiation fraction in the year under consideration IRCCs are credits earned based on the value of exports used to offset duty payable on imports. The value of products that a company can import free of duty is equal to the value of the IRCCs that it can present against such imports. This value is independent of the import duty rates so no import duty factor, as in the case of the PAA in Equation (4), is required.

The value of imports paid for by IRCCs under the IEC incentive dispensation augment PAA-rebated imports. To account for the combined value of PAA- and IEC-funded imports on planned value of production, the PAA model was linked to the IEC model. A new variable, industry rebatable imports, was introduced. This is the sum of PAA-rebatable imports and IRCC-funded imports. A direct link between the value of industry rebatable imports and the value of planned production was then set up [1]. The model was extended to include the industry trade balance variable as the dependent variable of interest. This enabled simulation of the industry trade account, including sensitivity analyses of the trade balance account to changes in the PAA’s policy rules and the IEC scheme. In model simulations, the value of industry imports is specified as being endogenous, depending on the import decision, while exports are assumed to be dependent on annual export growth that can be estimated from historical data. It is assumed that the import decision is influenced by the value of the domestic market and the value of the rebatable imports at industry level. Before a firm within the industry can import, it has to estimate what value of imports the domestic market can absorb. After establishing the import absorption capacity of the domestic market, the firm will have to consider the almost mandatory import it has to undertake in order to make use of import rebates earned. Hence, it is postulated that the value of the domestic market, together with the value of rebatable imports, determine the import decision. It is likely that industry imports will also increase as rebatable imports increase. If there is no commensurate increase in the value of the domestic market, the value of planned production will decrease. One way in which this manifests is that vehicle manufacturers and assemblers may not continue local supply of a certain type of component on model change, but rather import from a marginally lower cost source. In terms of the policy objectives, this would be an undesired outcome of incentive value oversupply. The impact of domestic market and rebatable imports on the imports growth fraction is dependent on the ratio of industry rebatable imports and the domestic market. 4.3 Adequacy of independent variables used in the

simulation model SD modelling protocol does not provide formal procedures for establishing the adequacy and relevancy of variables used in a model to explain a particular problem. The determination of the adequacy and relevancy of variables in the model is often a subjective process, which a researcher has to motivate.


To reduce subjectivity in determining the adequacy of independent variables in the model, trade balance was regressed against the size of the domestic market and industry investment. These key variables were not linear functions of the trade balance. Regression results showed that the size of the domestic market was statistically significant in determining industry trade balance as shown by the high t-value and low probability value. A unit increase in the size of the domestic market would increase trade balance by 0.74 units, which holds other factors constant. Investment was not found to be statistically significant in determining industry trade balance. Its t-value of 0.346947 was too low and there was a high probability that its regression coefficient may not be different to zero. An R2 value that indicated that the two variables explained more than 89% of the variation in the trade balance (Table 1) was important in establishing that the domestic market size and investment sufficiently explained changes in the trade balance.

Table 1: Regression results of trade balance, investment and domestic market size

Dependent variable = TBAR Variable Coefficient t-statistics Prob. INV 0.398 0.347 0.733 MKT 0.744 5.83 0.000 C -19.7 -5.38 0.000 R-squared 0.896 Sum of squares explained by model 1833 Sum of squares explained by residual 212.1

4.4 Model validation There is no rule of thumb in terms of the number of tests that should be carried out in order to establish the validity of a particular model. The onus is on the modeller to decide on the set of tests that would adequately create reasonable confidence in a model developed for a particular purpose. Given the applied nature of this research project, establishing model structural validity was not contentious because the qualitative and intuitive industry incentive framework was already in place and well documented. The researcher’s role in this respect was to formalise the intuitive policy framework into an SD model by capturing the major source of dynamics relevant to the research problem and question. In formalising existing policy frameworks, structural tests are continuously carried out in the sequential model-building process [20]. By the time the researcher develops a complete model on which behavioural tests can be performed the structural tests and validity would have been largely accomplished. Structural validity is evaluated through careful documentation of qualitative information on the policy framework and verifying the structure with stakeholders and experts at each stage of

the model-building process. In this regard, the PAA guidelines and thedti archive documents on MIDP incentives provided well-documented reference notes on the structure of the PAA and IEC schemes. Furthermore, before the scenario simulation, a base run of the model was performed to explore the extent to which the model replicated the reference behaviour of interest. Although the objective of SD modelling is not point prediction of system performance, but rather probing dynamics underlying a particular behaviour, it is important that an SD model can endogenously reproduce the reference mode of interest. Without replication of the reference mode, the model becomes irrelevant in providing insight into the problem’s situation and cannot be useful. Richardson and Pugh [21] argue that if a model cannot reproduce its reference behaviour mode, it is invalid. The first behavioural test was to assess whether and to what extent the model reproduced the reference mode behaviour, which is the exponentially increasing industry trade deficit. The base run showed that the model could endogenously replicate the reference mode behaviour. Replication of the reference behaviour from an indigenous perspective indicated that the model could be useful in highlighting leverage variables or points of action that could influence the deteriorating industry trade balance.

5. EFFECTS OF THE PAA AND IEC ON THE AUTOMOTIVE INDUSTRY TRADE

BALANCE The generation process of PAA rebates and IEC IRCCs and their joint contribution to the industry trade balance account were translated into a set of stock and flow equations using Stella Version 9.0.1 modelling software. By providing initial values and model equation parameters, simulation of the effect of change in the two incentives’ policy rules on the industry trade balance account trend was performed. The model equations used for the base run are presented in Appendix 1. 5.1 Effect of change of PAA policy rules on the

industry trade balance The PAA dispensation has two policy rule parameters that government can change. These rules have bearing on the industry trade balance account, namely the PAA benefit fraction and industry import duty. Model simulations showed that the effect of a change in the PAA benefit fraction on industry trade balance was marginal. Figure 1 shows how industry trade balance trends changed with PAA benefit fraction set at 20%, 30% and 40%. The lines practically coincide.


Figure 1: Effect of PAA benefit fraction on industry

trade balance

The negligible effect of a change in PAA benefit fraction on the industry trade balance trend can be attributed to the relatively low value of PAA rebate certificates compared to the overall industry import value. Similarly, the effect of a change in the import duty rate on industry trade balance trends was also trivial and comparable to that of the PAA benefit fraction. Model simulations showed that at an import duty of 20% and 30%, the impact of import duty on industry trade was almost synonymous to that of a change in the PAA benefit fraction. Even the further lowering of the import duty to 10% did not change the trade deficit trajectory (Figure 2). Within the assumptions of the model, import duty adjustment, just like the PAA benefit fraction, could not be used to influence industry trade balance under the PAA incentive dispensation. It should be noted, though, that the duty rate of 10% is sufficiently low that it could cause manufacturers to exit the industry and continue their commercial activities by only importing vehicles and components. This option was not included in the model, but could readily be included in an extension of it.

Figure 2: Effect of import duties on industry trade

balance

5.2 Effect of change in IEC policy decisions on the industry trade balance

The IEC dispensation has one effective policy lever under the control of policy makers: ELCBF. Setting the ELCBF at 0% was equivalent to complete neutralisation of the incentive, while setting the benefit fraction at 100% benefits industry equivalent to the full value of exports. Since there were no indications to reduce the benefit fraction below 50% at the time of research, the trade balance sensitivity to ELCBF was done by setting the fraction at 50%, 80% and 100%. Simulation results showed that the model was very sensitive to the ELCBF. With the fraction set at 50%, there was the minimum deterioration in the industry trade balance relative to the 1995 status before the deficit started to decline. The increase in trade deficit, before the decline set in was more pronounced at 100% benefit fraction when compared to 80% (Figure 3). Generally, the lower the ELCBF, the less is the decline in industry trade balance. It should be noted, however, that the analysis above was based on the effect of ELCBF on the supply of IRCCs in value terms. An increase in ELCBF may also have a ‘demand effect’ in terms of motivating the industry to export products with higher local content. In order to do so, industry has to increase its local sourcing of products. Local sourcing of products offsets potential imports; hence it has a positive effect on the industry trade balance. The opposite results of the supply and demand side effects on the industry trade balance may question the soundness of the trade balance trend captured in Figure 3. However, given the limited capacity of the domestic component manufacturing sector to meet vehicle assemblers’ component supply requirements, even if there was intention to increase local sourcing, the increase would not be drastic.

Figure 3: Effect of exported local content benefit

fraction on industry trade balance

From this reasoning and from on-going observation of industry activity, it was judged that the effect of change in the ELCBF was more likely to increase IRCC supply than increase local component sourcing. By


implication, model simulations pointed to the fact that the deteriorating industry trade deficit witnessed under the MIDP period could have been mitigated effectively by adjusting IEC ELCBF, unlike the limited effectiveness of adjusting PAA parameters.

6. INSIGHTS The IEC, rather than the PAA incentive, was the major contributor to the industry trade deficit. Adjustment of PAA benefit fraction and import duty rate would have had little effect on the industry trade balance trend. The IEC, on the other hand, provided a high leverage policy to potentially influence the industry trade balance account. The deteriorating industry trade deficit could be influenced significantly by adjusting policy rules pertaining to the IEC incentive dispensation. In general, this research and modelling indicates that production, rather than investment-based incentives, are effective in influencing South Africa’s automotive industry performance in terms of industry trade balance. Without negating the need to provide incentives for investment in high-technology robotic manufacturing and accompanying electronics and control systems engineering competences, the study reveals that combining such incentives with other ‘non-investment’ incentives may have unintended consequences, a phenomenon SD literature refers to as policy resistance. Persistent trade deficit was not anticipated in the process of coming up with an incentive package for the South African automotive industry. This finding can be useful in the future structuring of new automotive incentives for South Africa and against the background of the country’s desire to maximise the socio-economic benefits of local manufacturing activities. Potential synergies and trade-offs of a combination of industry incentives have to be taken into account to minimise the likelihood of policy resistance. It should be noted that the modelling process, as explained in this paper, has limitations, even though they are not significant enough to change the paper’s contributions. Firstly, the model was not accurate in point prediction of trade balance over time, but it could replicate the general trade balance trend. This weakness is typical of SD modelling. It tends to emphasise the overall trend replication of a research aspect of interest rather than point prediction. Secondly, exogenously determined rates of change based on historical data were used in model simulation. These rates were assumed to hold in future, which may not necessarily be the case. In terms of future research on the topic, it is suggested that some of the assumed exogenous rates are made endogenous through a careful process analysis of what drives these rates in reality. This will make the model more robust.

7. REFERENCES [1] M. Kaggwa, J.L. Steyn and A. Pouris: “Modelling

effects of incentives for industry competitiveness using a system dynamics approach”, Proceedings: Portland International Centre for Management of Engineering and Technology (PICMET), Cape Town, pp. 47-78, July 2008.

[2] NAAMSA (National Association of Automobile

Manufacturers of South Africa): Annual Report, Durban Publishers, Pretoria, chapter 3, pp. 5-21, 2001.

[3] B. Richmond: An introduction to systems

thinking, ISEE Systems, USA, third edition, chapter 1, pp. 3-35, 2002.

[4] R. Bronzini and G. Blasio: “Evaluation of the

impact of investment incentives: The case of Italy’s law 488/992”, Journal of Urban Economics, Vol. 60 No. 2, pp. 327-349, 2006.

[5] N. Driffield: “The impact on domestic

productivity of inward investment in the UK”, The Manchester School, Vol. 69 No. 1, pp. 103-119, 2001.

[6] D. Brunker, T. Offner and J. Ryan: “Effectiveness

of investment incentives”, Bureau of Industry Economics (BIE), Australia, Working Paper, No. 33, pp. 31-43, 1985.

[7] R.E. Hall and D.W. Jorgenson: “Tax policy and

investment behaviour”, American Economic Review, Vol. 57 No. 3, pp. 391-414, 1967.

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incentives for business investment: A primer for policy makers in developing countries”, World Development, Vol. 30 No. 9, pp. 1497-1516, 2002.

[9] J. Tobin: “A general equilibrium approach to

monetary theory”, Journal of Money, Credit and Banking, Vol. 1 No. 1, pp. 15–29, 1969.

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neoclassical interpretation”, Econometrica, Vol. 50 No. 1, pp. 213-224, 1982.

[11] D. Lim: “Fiscal incentives and direct foreign

investment in less developed countries”, The Journal of Development Studies, Vol. 19 No. 2, pp. 207-212, 1983.

[12] M.L. Moore, B.M. Steece and C.W. Swenson:

“Analysis of the impact of state income tax rates and bases on foreign investment”, The Accounting Review, Vol. 62 No. 4, pp. 671-685, 1987.


[13] K.A. Hassett and R.G. Hubbart: “Are investment incentives blunted by changes in prices of capital goods?”, International Finance, Vol. 1 No. 1, pp. 106-125, 1998.

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Phelan: “Seeking greener pastures: theoretical and empirical investigation into changing trend of foreign direct investment flows in response to institutional factors”, International Business Review, Vol. 11 No. 6, pp. 685-705, 2002.

[15] S. Tung and S. Cho: “The impact of tax incentives

on foreign direct investment in China”, Journal of International Accounting, Auditing and Taxation, Vol. 9 No. 2, pp. 105-135, 2000.

[16] A.H. Studenmund: Using econometrics: A

practical guide, Boston, Pearson, third edition, chapter 1, pp. 1-23, 2011.

[17] C.W. Caulfield and S.P. Maj: “A case of system

dynamics”, Global Journal of Engineering Education, Vol. 6 No. 1, pp. 25-34, 2002.

[18] J. Sterman: Business dynamics: Systems thinking

and modeling for a complex world, Boston, Irwin/McGraw-Hill, first edition, chapter 3, pp. 72-128, 2000.

[19] C. Jenkins and L. Thomas: “Foreign direct

investment in Southern Africa: Determinants, characteristics and implications for economic growth and poverty alleviation”, CREFSA Research Report, London School of Economics, London, pp. 1-57, October 2002.

[20] M. Kaggwa: “Modelling South Africa’s

incentives under the motor industry development programme”, PhD dissertation, University of Pretoria, Pretoria, chapter 5, pp. 83-109, March, 2009.

[21] G.P. Richardson and L.A Pugh: Introduction to

System Dynamics Modelling with DYNAMO, Cambridge, MIT Press, chapter 3, pp. 309-344, 1981.

8. APPENDIX 1

8.1 Equations for the PAA-IEC model base-run

Domestic_market(t) = Domestic_market(t - dt) +

(Market_growth) ∗ dtINIT Domestic_market = 33.6 Rand billion (1)

Inflows: Market_growth = Domestic_market ∗

Market_growth_fraction (2)

Exports(t) = Exports(t - dt) + (Exporting) ∗ dtINIT

Exports = 4.2 Rand billion (3) Inflows: Exporting = Exports ∗ Export_growth_fraction Rand

billion (4) Imports(t) = Imports(t - dt) + (Importing) ∗ dtINIT

Imports = 16.4 Rand billion (5) Inflows: Importing = Imports ∗ Import_growth_fraction (6) Investment(t) = Investment(t - dt) + (Investing) ∗

dtINIT Investment = 0.85 Rand billion (7) Inflows: Investing = Investment ∗ Actual_growth_fraction

Rand billion (8) IRCCs(t) = IRCCs(t - dt) + (IRCC_generation -

IRCC_release) ∗ dtINIT IRCCs = 0 Rand billion (9)

TRANSIT TIME = varies (10) INFLOW LIMIT = INFINITE (11) CAPACITY = INFINITE (12) Inflows: IRCCgeneration = Local_content_benefit_fraction ∗

Exported_local_content Rand billion (13) Outflows: IRCC_release = CONVEYOR OUTFLOW (14) TRANSIT TIME = IRCC_release_delay Rand

billion (15) PAA_Rebates[Annual_Certificate](t) =

PAA_Rebates[Annual_Certificate](t - dt) + (Rebate_generation[Annual_Certificate] - Rebate_certificate_release[Annual_Certificate]) ∗ dtINIT PAA_Rebates[Annual_Certificate] = 0 Rand billion (16)

Inflows: Rebate_generation[Annual_Certificate] =

Qualifying_investment ∗ Benefit_fraction / Certificate_spread Rand billion (17)

Outflows:


Rebate_certificate_release[1] = CONVEYOR OUTFLOW (18)

TRANSIT TIME = Rebate_Certificate_delay[1] (19) Rebate_certificate_release[2] = CONVEYOR

OUTFLOW (20) TRANSIT TIME = Rebate_Certificate_delay[2] (21) Rebate_certificate_release[3] = CONVEYOR



OUTFLOW (26) TRANSIT TIME = Rebate_Certificate_delay[5] Rand

billion (27) Actual_growth_fraction = Normal_growth_fraction *

production_potential_factor (28) Annual_certificate_release =

ARRAYSUM(Rebate_certificate_release[∗ ])Rand billion (29)

Benefit_fraction = 0 + STEP(0.2, 2001) (30) Certificate_spread = 5 (31) Exported_local_content = Exports ∗ Exported_

local_content_fraction Rand billion (32) Exported_local_content_fraction = 0.7 (33) Export_growth_fraction = CGROWTH(27) (34) Import_duty = 0.3 (35) Import_growth_fraction = (CGROWTH(12) ∗

Impact_of_rebatable_imports_and_domestic_market_on_imports) (36)

Industry_rebatable_imports = IRCC_rebatable_imports

+ PAA_rebatable_imports Rand billion (37) Industry_trade_balance = Exports - Imports Rand

billion (38) IRCC_rebatable_imports = IRCC_release ∗ 1 Rand

billion (39) IRCC_release_delay = 1 (40)

Local_content_benefit_fraction = 0.9 (41) Market_growth_fraction = CGROWTH(9) (42) Normal_growth_fraction = 0.15 (43) PAA_rebatable_imports = Annual_certificate_release /

Import_duty Rand billion (44) Production_potential_factor = (Domestic_market +

Exports - Industry_rebatable_imports)/ (Domestic_market + Exports) (45)

Qualifying_investment = Investment ∗ Qualifying_

investment_fraction Rand billion (46) Qualifying_investment_fraction = 0.8 (47) Rebate_Certificate_delay[1] = 1 (48) Rebate_Certificate_delay[2] = 2 (49) Rebate_Certificate_delay[3] = 3 (50) Rebate_Certificate_delay[4] = 4 (51) Rebate_Certificate_delay[5] = 5 (52) Import decision Impact_of_rebatable_imports_and_domestic_market_

on_imports = GRAPH (Industry_rebatable_imports/Domestic_market) (0.00, 1.00), (0.04, 1.00), (0.08, 1.20), (0.12, 1.31), (0.16, 1.43), (0.2, 1.51), (0.24, 1.61), (0.28, 1.71), (0.32, 1.76), (0.36, 1.76), (0.4, 1.75), (0.44, 1.70), (0.48, 1.60), (0.52, 1.55), (0.56, 1.50), (0.6, 1.46), (0.64, 1.41), (0.68, 1.36), (0.72, 1.35), (0.76, 1.32), (0.8, 1.30), (0.84, 1.29), (0.88, 1.29), (0.92, 1.29), (0.96, 1.29), (1.00, 1.00) (53)


ANALYSIS AND OPTIMIZATION OF AUTO-CORRELATIONBASED FREQUENCY OFFSET ESTIMATION

I.M. Ngebani∗ , J.M. Chuma† and S. Masupe‡

∗ Dept. of Information Science and Electronics Engineering, 38 Zheda Road, Zhejiang University,Hangzhou 310027, China E-mail: [email protected]† College of Engineering and Technology, Botswana International University of Science andTechnology, Private Bag 14, Palapye, Botswana E-mail: [email protected]‡ College of Engineering and Technology, Botswana International University of Science andTechnology, Private Bag 14, Palapye, Botswana E-mail: [email protected]

Abstract: In this letter, a general auto-correlation based frequency offset estimation (FOE) algorithmis analyzed. An approximate closed-form expression for the Mean Square Error (MSE) of the FOEis obtained, and it is proved that, given training symbols of fixed length N, choosing the number ofsummations in the auto-correlation to be N

3 and the correlation distance to be 2N3 is optimal in that

it minimizes the MSE. Simulation results are provided to validate the analysis and optimization.

Key words: Auto-correlation, frequency offset estimation, optimization, performance analysis,un-biased estimator.

1. INTRODUCTION

Carrier Frequency Offset (CFO), caused by frequencydeviation between a transmitter and a receiver existsin most communication systems and may result insevere performance degradation or even system failure.Therefore, estimation and compensation of frequencyoffset in communication systems is important in order toallow coherent demodulation of the transmitted signals.Compared to single-carrier modulation, Orthogonal Fre-quency Division Multiplexing (OFDM) is more sensitiveto frequency offset because it introduces Inter-CarrierInterference (ICI) and destroys the orthogonality amongsub-carriers [1]. To mitigate the negative impact offrequency offset, continuous efforts have been madeto develop efficient Frequency Offset Estimation (FOE)algorithms.

FOE can be done in the time or frequency domain. InOFDM systems, time-domain algorithms are typicallyused to estimate the initial frequency offset andfrequency-domain algorithms are used to track theresidual frequency offset. Time-domain FOE algorithmsgenerally rely on the auto-correlations between twospecially designed training signal segments [2–5]. Furtherenhancements of utilizing training signals composedof multiple identical segments have been proposedin [7, 8]. [9] gives a comparative study of the Schmidl-Cox(SC) [5] and Morelli-Mengali (MM) [6] algorithms forfrequency offset estimation in OFDM, along with a newleast squares (LS) and a new modified SC algorithm.In [10], the author proposes a novel maximum likelihood(ML) based algorithm for estimating the timing offset andcarrier frequency offset in OFDM systems under dispersivefading channels.

Although auto-correlation based FOE algorithms havebeen used in many practical systems, the performance

Figure 1: Autocorrelation based FOE

analysis and optimization of the algorithms has not yetbeen thoroughly investigated. In this letter, a generalauto-correlation based FOE algorithm is analyzed, aclosed-form expression for the Mean Square Error (MSE)is derived, and it is proved that if the training symbollength is fixed to be N, to minimize the MSE, the optimalnumber of summations in the auto-correlation should beN

3 and the optimal auto-correlation distance equals 2N3 .

This letter is organized as follows: Section 2 introduces ageneral auto-correlation based frequency offset algorithm.The main result is presented in Section 3. Section 4presents simulation results and some discussions. Finally,conclusions are drawn in Section 5.

2. AUTO-CORRELATION BASED FREQUENCYOFFSET ESTIMATION

A quasi-static dispersive channel that contains L resolvablemulti-paths can be denoted by hlL−1

l=0 . Let sn be the n-thtransmitted training symbol with unit energy, then the n-threceived symbol can be expressed as

yn = e jθnL−1

∑l=0

hlsn−l + vn, (1)

where vn is the AWGN with zero mean and variance σ2

and θn is the rotation angle at the n-th symbol caused by


the frequency offset. In (1), it is assumed that the rotationangles for L consecutive symbols are approximately thesame, this is valid if the frequency offset is not absurdlylarge.

Let Δ fs be the true frequency offset and Ts be the symbolinterval, then θn can be expressed as θn = nΔθ, where Δθis the rotation angle per symbol, and is defined as

Δθ 2πTsΔ fs. (2)

Auto-correlation based FOE relies on training symbols oflength N that are composed of multiple identical segments,each segment has Ms symbols. A sensible design shouldhave Ms L.

The auto-correlation metric between yn and yn+D1 is

Q(M1) =1

M1

M1

∑n=1

(y†n)(yn+D1), (3)

where ()† denotes complex conjugation, D1 is calledthe“auto-correlation distance”, M1 is the number ofsummations in the auto-correlation and is called the “com-plementary auto-correlation distance”. Fig.1 illustratesthe autocorrelation based FOE, from Fig.1 it is clear thatD1 = N −M1.

Having obtained Q(M1), the frequency offset can beestimated as [2, 3]

Δ fs =∠Q(M1)

2πD1Ts. (4)

If Δ fs is in the range(− 1

2D1Ts, 1

2D1Ts

), equation (4) can

provide correct estimation, otherwise there exists a 2πor multiples of 2π phase ambiguity. In this case, thecorrect rotated angle should be ∠Q(M1)+ 2πd instead of∠Q(M1), where d is an integer. To resolve the phaseambiguity, another auto-correlation metric with a shorterauto-correlation distance D2 (N −M2) can be used, i.e.,calculating

Q(M2) =1

M2

M2

∑n=1

(y†n)(yn+D2), (5)

where M2 is the corresponding complementaryauto-correlation distance. Clearly, the two auto-correlationmetrics have the relation

D1

D2∠Q(M2)≈ ∠Q(M1)+2πd, (6)

and the 2πd phase ambiguity can be estimated as

d =

⟨ D1D2

∠Q(M2)−∠Q(M1)

2π

⟩, (7)

where · is the rounding operation. Then, the estimated

Figure 2: Illustration of angle approximation induced by v(M1)

frequency offset equals

Δ fs =∠Q(M1)+2πd

2πD1Ts. (8)

In the autocorrelation based FOE algorithm introducedabove, the FOE precision is mainly determined by M1 andthe range of resolved frequency offset is determined byM2. In the following, we analyze the performance of theauto-correlation based FOE algorithm, and show how tooptimize the algorithm.

3. PERFORMANCE ANALYSIS AND PARAMETEROPTIMIZATION

For the auto-correlation based FOE algorithm, clearly, thelarger the auto-correlation distance (i.e., D1 or D2) is, thefiner the estimated frequency offset, and the better theperformance. However, given a fixed training symbollength N, large auto-correlation distances mean smallercomplementary auto-correlation distances (i.e. M1 orM2). The smaller the complementary auto-correlation,the lesser the number of samples used to calculatethe auto-correlation metric and thus leading to poorperformance. Therefore, given N, there is an optimalauto-correlation distance where the MSE is minimized.

Since M2 is only used to resolve the ambiguity, it issufficient to choose M2 to satisfy the following inequality

−π < 2π(N −M2)Δ fsTs < π. (9)

In the following, we only focus on how to optimize theparameter M1. We first derive the MSE of the estimatedfrequency offset with complementary auto-correlationdistance M1.

Because of the repeated segments, D1 is a multiple of Ms,


and yn+D1 equals

yn+D1 = e j(n+D1)ΔθL−1

∑l=0

hlsn+D1−l + vn+D1

= e j(n+D1)ΔθL−1

∑l=0

hlsn−l + vn+D1 . (10)

Let us define zn ∑L−1l=0 hlsn−l . Assuming independent

and unit energy training symbols sn, we have E[zn2

]=

h2 ∑L−1l=0 hl2, and as M1 gets large, we have the

following approximation

1M1

M1

∑n=1

zn2 ≈ h2. (11)

Substituting (10) into (5) and using the above approxima-tion, Q(M1) can be expressed as

Q(M1) =1

M1

M1

∑n=1

zn2e jD1Δθ + v(M1)

≈ h2e jD1Δθ + v(M1), (12)

where v(M1) is called the “noise term” for FOE and isgiven by

v(M1) = A+B+C, (13)

where A, B and C are defined as:

A 1M1

M1

∑n=1

(v†

nzne j(n+D1)Δθ), (14)

B 1M1

M1

∑n=1

(vn+D1 z†

ne− jnΔθ), (15)

C 1M1

M1

∑n=1

(v†

nvn+D1

). (16)

Using equation (12) and resolving the 2πd ambiguity, weobtain

∠Q(M1)+2πd = D1Δθ+α, (17)

where α is the angle induced by noise term v(M1). Notethat α = ∠v(M1), instead, it is the angle between Q(M1)and e jD1Δθ (See Fig.2).

The estimation of Δ fs in equation (8) can be derived as

Δ fs = Δ fs +α

2πD1Ts. (18)

Δ fs is later shown to be an unbiased estimator, and theMSE of the estimated frequency offset is given by

R E[α2

]

4π2D21T 2

s. (19)

To get optimal FOE performance, M1 should be chosen tosatisfy

Mopt1 = argmin

M1R . (20)

The following theorem summarizes the main result of thisletter, which gives Mopt

1 , and the minimum MSE.

Theorem 1: For a system with N training symbolsfor FOE, the optimal complementary auto-correlationdistance that minimizes the MSE of the estimated frequencyoffset is

Mopt1 =

⟨N3

⟩

and the corresponding minimum MSE is approximately

Rmin ≈ 1

8π2T 2s(N −

⟨N3

⟩)⟨N3

⟩2

(2

SNR+

1SNR2

),

where SNR h2

σ2 .

Proof: Expanding the expectation of v(M1)2 in(13), we have

E[v(M1)2] = E

[A+B2]+E

[(A+B)C†

]

+E[C(A+B)†

]+E

[C2] .

Since vn is a complex Gaussian random variable with zeromean, we have E

[(A+B)C†

]= 0 and E

[C(A+B)†

]= 0.

Therefore, E[v(M1)2

]can be simplified to

E[v(M1)2]= E

[A+B2]+ σ4

M1. (21)

Case 1: M1 ≤⟨N−1

2

⟩

In this case, there is no overlap between vn and vn+D1 forn = 1,2, · · · ,M1, so A and B are independent zero meancircular complex Gaussian random variables. Since v(M1)does not favor any specific direction, we have E [α] =0. This makes Δ fs given in equation (18) an unbiasedestimator.∗

Based on the illustration in Fig.2, assuming M1 is large, inhigh SNR scenarios, the angle α can be approximated as

α ≈ v(M1)sinϕh2 , (22)

where ϕ is the angle between v(M1) and e jD1Δθ. In this

∗It is important to note that the distribution of α in equation(18) isunknown even though the first and second moments are known. Since thedistribution is unknown, the CRLB cannot be derived for this dedicatedcase.


case, R can be approximated as

R ≈E(v(M1)2

)−E

(cos2ϕv(M1)2

)

8π2D21T 2

s h4.

We also have

E[cos2ϕv(M1)2]= 0, (23)

where we have applied the property that ϕ is uniformlydistributed and independent to the length of v(M1).

The expectation E[v(M1)2

]equals

E[v(M1)2] = E

[A2]+E

[B2]+ σ4

M1

≈ 2h2σ2 +σ4

M1. (24)

Using the relation D1 = N −M1 and combining equations(23) and (24), R becomes

R1 ≈ 2h2σ2 +σ4

8π2T 2s h4M1(N −M1)2

=1

8π2T 2s M1(N −M1)2

(2

SNR+

1SNR2

). (25)

The optimization problem (20) is now equivalent to

Mopt1 = argmax

M1

M1(N −M1)

2 . (26)

It is not difficult to show that

Mopt1 =

⟨N3

⟩, (27)

and the corresponding minimum MSE is

Rmin =2

SNR + 1SNR2

8π2T 2s(N −

⟨N3

⟩)⟨N3

⟩2 . (28)

Case 2: M1 >⟨N−1

2

⟩

In this case, A and B are NOT independent anymorebecause the (k+D1)-th term in A, which is

Ak+D1 =v†

k+D1zk+D1e j(k+D1)Δθe jD1Δθ

M1, (29)

and the k-th term in B, which is

Bk =vk+D1z†

ke− jkΔθ

M1=

vk+D1 z†k+D1

e− jkΔθ

M1, (30)

are correlated, and the terms Ak+D1 + Bk for k =

1,2, · · · ,(M1 −D1) are along the same direction as e jD1Δθ,

because Ak+D1 +Bk can be written as

Ak+D1 +Bk =2ℜ

v†

k+D1zk+D1e j(k+D1)Δθ

e jD1Δθ

M1.

Regrouping the terms in A+B, we obtain

A+B =D1

∑n=1

(An +Bn+M1−D1)+M1

∑k=D1+1

Ak +Bk−D1

︸︷︷︸w(M1)

,

where w(M1) is the summation of correlated terms and isalong the direction of e jD1Δθ, so it has no contribution tothe angle α. Then, v(M1) can be re-written as

v(M1) =

(D1

∑n=1

(An +Bn+M1−D1)+C

)

︸︷︷︸=u(M1)

+w(M1). (31)

Using similar arguments as in Case 1, we have E [α] = 0,which leads to an unbiased estimation of Δ fs given byequation (18).

Based on the illustration in Fig.2, we can approximate theangle α as

α ≈ u(M1)sinϕh2 , (32)

where ϕ is the angle between u(M1) and e jD1Δθ.

Following the same procedure as in Case 1, we have

E[u(M1)2

]≈ 2(N −M1)h2σ2

M21

+σ4

M1, (33)

and the corresponding MSE equals

R2 ≈(

2SNR

8π2T 2s M2

1(N −M1)+

1SNR2

8π2T 2s M1(N −M1)2

).

(34)Define L(M1) 1

8π2T 2s M1(N−M1)2SNR and D L(Mopt

1 ),

where Mopt1 is given by equation (27). R1 and R2 given by

equations (25) and (34), respectively can then be re-writtenas

R1(M1) = L(M1)

(2+

1SNR

)

R2(M1) = L(M1)

(2NM1

−2+1

SNR

)

We know that L(M1) ≥ D, and the minimum value of R1is Rmin

1 = D(2+ 1SNR ). To complete the proof we show that


0 100 200 300 400 500102

103

104

105

Value of M1 (Samples)

Mea

n S

qure

Err

or o

f Fre

quen

cy O

ffset

Est

imat

e

Simu:SNR=0dBSimu:SNR=5dBSimu: SNR=10dBTheoretic:SNR=0dBTheoretic:SNR=5dBTheoretic: SNR=10dB

Figure 3: Validation of approximated analysis and parameteroptimization.

R2(M1)> R1(Mopt1 ) = D

(2+ 1

SNR

).

L(M1) ≥ D (35)

R2(M1) ≥ D(

2NM1

−2+1

SNR

)(36)

(37)

R2 is bounded by

R2(M1) > D(

2N(N/2)

−2+1

SNR

)(38)

R2(M1) > D(2+A) = Rmin1 (39)

Therefore, the minimum MSE in Case 1 is a globalminimum.

4. SIMULATION VALIDATIONS AND DISCUSSION

To validate the analysis and optimization, we consider acommunication system that has N = 500 symbols, Δ fs =10kHz, and 1/Ts = 1MHz. To satisfy (9), we choose M2 =480 symbols.

The simulated and theoretical results of MSE vs. M1 areshown in Fig.3. It can be seen that the MSE calculatedfrom our analysis matches the simulated MSE very well,and the minimum MSE is achieved when M1 = 167 =⟨ 500

3

⟩, as predicted by Theorem 1.

From Fig.3, it can be observed that the curve for SNR =10dB is more symmetric than the curve for SNR = 0dBand the local minimum in the curve of SNR = 10dB iscloser to the global minimum. This is because at highSNRs, the 1

SNR2 term in (25) and (34) can be ignoredand the MSE becomes R ≈ 2

8π2T 2s M1(N−M1)2(SNR) and R ≈

28π2T 2

s M21(N−M1)(SNR)

, for Case 1 and Case 2, respectively.

They are symmetric to the center M1 =⟨N−1

2

⟩and reach

the same minimum when M1 =⟨N

3

⟩and M1 = N −

⟨N3

⟩,

respectively.

As a last comment, from the closed-form MSE formulas,we can see that, when N is fixed, the MSE of FOE is just afunction of M1 and SNR, and is independent of Δ fs.

5. CONCLUSION

In this letter, a general auto-correlation based FOEalgorithm was analyzed, closed-form expressions of theMSE were derived, and it was proved that the optimalcomplementary auto-correlation distance equals

⟨N3

⟩,

where N is the total number of training symbols. Theresults obtained in the letter can be of practical usagewhen designing training symbols in the implementation ofauto-correlation based FOE algorithms.

REFERENCES

[1] T. Pollet, M. V. Bladel, and M. Moeneclaey“BER sensitivity of OFDM systems to carrierfrequency offset and Wiener phase noise ,” IEEETrans. Commun., vol. 43, no. 234, pp. 191-193,Feb./Mar./Apr. 1995.

[2] J. Van De Beek, M. Sandell, and P. O. Borjesson,“ML estimation of time and frequency offset inOFDM systems,” IEEE Trans. Signal Processing,vol. 45, no. 7, pp. 1800-1805, July 1997.

[3] M. Morelli, A. Andrea, and U. Mengali, ”Feedbackfrequency synchronization for OFDM applications,”IEEE Commun. Lett., vol. 5, no. 1, pp. 28-30, Jan.2001.

[4] P. H. Moose, “A technique for orthogonal frequencydivision multiplexing frequency offset correction,”IEEE Trans. Commun., vol. 42, pp. 2908-2914, Oct.1994.

[5] T. M. Schmidl and D. C. Cox, “Robust frequencyand timing synchronization for OFDM,” IEEE Trans.Commun., vol. 45, no. 12, pp. 1613-1621, Dec. 1997.

[6] M. Morelli and V. Mengali, “An improved frequencyoffset estimator for OFDM applications,” IEEECommun. Lett., vol. 3, no. 3, pp. 75-77, Mar. 1999.

[7] Y. H. Kim, I. Song, S. Yoon and S. R. Park,”An efficient frequency offset estimator for OFDMsystems and its performance characteristics,” IEEETrans. Veh. Technol., vol.50, pp. 1307-1312, Sep.2001.

[8] Z. Zhang, K. Long, and Y. Liu,, “Complex efficientcarrier frequency offset estimation algorithm inOFDM systems,” IEEE Trans. Broadcast, vol. 50, no.2, pp. 159-164, June 2004.

[9] Z. Cvetkovic, V. Tarokh, and S. Yoon, “On frequencyoffset estimation for OFDM,” IEEE Trans. WirelessCommun, vol.12, no.3, pp.1062,1072, Mar 2013.


[10] C. Wen-Long “ML Estimation of Timing andFrequency Offsets Using Distinctive CorrelationCharacteristics of OFDM Signals Over DispersiveFading Channels,” IEEE Trans. Vehicular Technolo-gy, vol.60, no.2, pp.444,456, Feb. 2011


NOTES


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