Chip error probability of IEEE 802.15.4 wireless tranmission

ERK'2014, Portorož, A:65-68 65

Chip error probability of IEEE 802.15.4 wireless tranmission

Uros Pesovic1 Peter Planinsic2 Dusan Gleich2

1Faculty of Technical Sciences Cacak, University of Kragujevac, Serbia2Faculty of Electrical Engineering and Computer Science, University of Maribor, Slovenia

E-mail: [email protected]

Wireless transmissions can be significantly affected by in-fluences from its surroundings, which are most commonlyexpressed in a form of error probability statistics. IEEE802.15.4 wireless personal area networks (WPANs) useDirect Sequence Signal Spreading (DSSS) technique inorder to be able to operate together with other types ofwireless networks in 2.4GHz band. By use of DSSS, IEEE802.15.4 transceivers are able in some level to cancelout interference from other types of networks. Such in-terferences have same influence as background noise andare most commonly modeled as Additive White GaussianNoise (AWGN). This work presents mathematically basedchip error probability model of IEEE 802.15.4 wirelesscommunication in presence of AWGN. Presented resultsfor theoretical chip error rate model are confirmed bysimulation of IEEE 802.15.4 transmission through AWGNchannel according to Monte Carlo method.

1 IntroductionIEEE 802.15.4 standard specifies physical and MediumAccess Control layers for Low Power Wireless PersonalArea Networks [1]. It is designed for low power, low costbattery operated devices, which are targeted for a widerange of applications. Its physical layer defines channelsin several frequency bands, where a 2.4 GHz band is mostwidely used. Direct-Sequence Spread Spectrum (DSSS)signal spreading is used to provide coexistence of IEEE802.15.4 WPANs in a crowded 2.4 GHz band, which isalso used by other types of networks (IEEE 802.11 WLANand IEEE 802.15.1 Bluetooth). Knowledge of error prob-ability in such a harsh environment is crucial for efficientdeployment of these networks.

Information bearing signal, sent through a wirelesschannel is received together with some unwanted signals,which are referred as noise. Noise can change the re-ceived signal in such a manner that is decoded with somedata errors. Noise comes from various sources and can beclassified into two groups: background noise and interfer-ence noise. Background noise signals have a small struc-ture and arise from both human and natural sources, suchas thermal noise and deep-space noise. Interference rep-resents man-made signals, which come from other radiosources that occupy the same frequency band as the de-

sired communication signal. If it is not compliant with in-formation bearing signal (partially overlapping frequencyspectrums or different modulation techniques), most likelywill have the same effect as background noise.

State of the art in this field, as far as it is known, an-alyzes error probability of IEEE 802.15.4 transmissionin a presence of background noise [2, 3] and regular in-terference from other types of networks (IEEE 802.11WLAN and IEEE 802.15.1 Bluetooth) [4, 5, 6]. This pa-per presents on how AWGN noise affects chip error prob-ability statistics in IEEE 802.15.4 wireless transmissions.Independent experimental simulations show that a chiperror probability model for IEEE 802.15.4 wireless simu-lation is in close match with experimental data, obtainedby simulations.

2 Structure of IEEE 802.15.4 transceiverRadio devices compliant to IEEE 802.15.4 standard aredesigned as transceivers and they employ transmitter andreceiver on the same chip. Typical functional structure ofsuch transceiver is separated into transmission and recep-tion part (Fig. 1).

O–QPSK HSS

demodulator

Chips to symbols

Symbols to bits

Bits to packetsChips Symbols Bits Packets

Antenna

O -QPSK HSS

modulator

Symbols to chips

Bits to symbols

Packets to bitsChips Symbols Bits

PA

LNA

RF Switch

Packets

Transmitter

Receiver

Figure 1: Structure of IEEE 802.15.4 transceiver

In IEEE 802.15.4 transmitter, packet ready for trans-mission is firstly partitioned into groups of four bits, whichare referred as symbol words. Symbol words are spreadinto one of 16 IEEE 802.15.4 predefined orthogonal se-quences containing 32 binary chips. Chip sequences aremodulated with the use of Offset QPSK with a Half Sinepulse Shaping (O-QPSK HSS) modulation, which is sim-ilar to the Minimum Shift Keying (MSK), as explainedin papers [7, 8]. This modulation uses two orthogonalphases, where even indexed chips are modulated onto in-phase I, while the odd-indexed chips are modulated onto

66

quadrature-phase Q. Chips for both I and Q phases areshaped by half sine pulses, Q phase is delayed by onechip period and added to I phase. O-QPSK HSS modu-lation is continuous phase modulation which can be usedwith energy-efficient nonlinear amplifiers; such as thoseused in IEEE 802.15.4 transceivers. Resulting basebandsignal is modulated onto 2.4 GHz carrier, amplified andtransmitted via antenna. O-QPSK HSS modulation canbe mathematically described with equations (1) to (4) [3]:

Ii(t) =

15∑n=0

ci2nh(t− 2nTc) (1)

Qi(t) =

15∑n=0

ci2n+1h(t− 2(n+ 1)Tc) (2)

h(t) =

{sin( πt2Tc

) 0 ≤ t ≤ 2Tc0 otherwise

(3)

si(t) =1√2[Ii(t)cos(ωct) +Qi(t)sin(ωct)] (4)

On receiver’s side, wireless signals received by an an-tenna, are amplified and filtered by an analog front-end.After processing, they are brought to O-QPSK HSS de-modulator, where information is extracted in a form ofdigital chips. In process of decoding, depending on thequality of the received wireless signal, some of the chipscould be decoded incorrectly. Using signal despreading,received chip sequences are correlated with predefinedchip sequences in order to choose most likely sequence.Beginning of the IEEE 802.15.4 packet is reserved forpreamble field which consists of eight repeating symbols.Each time the preamble symbol word is received, it is cor-related with expected symbol sequence. During the re-ception of preamble, receiver phase is shifted in order toachieve synchronization with incoming signal. After suc-cessful synchronization, beginning of packet is pointedby start frame delimiter, which is followed by informa-tion about packet length. Received symbol words aretranslated to bits, which are when reception is complete,are grouped into packets which are forwarded to the up-per protocol layer. Since IEEE 802.15.4 does not use anykind of error correction technique on a bit level, evena single bit error will corrupt the packet and the packetneeds to be retransmitted.

3 Chip error probabilityUnlike constellations of QPSK and O-QPSK modulations,which have distinct symbols according to the phase value,phase of the O-QPSK HSS modulation continuously shiftsthrough constellation quadrants, around a circle of radius√Es (Fig. 2). For simplification, we can assume that

during one symbol period, the phase is stationary and lo-cated half way on the phase transition through constella-tion quadrant (Fig. 3). Consider that the alphabet usedby O-QPSK HSS modulation is a set of four symbols(S0,S1,S2,S3) located in quadrants of a complex plane.

−0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4−0.4

−0.2

0

0.2

0.4

I phase

Q p

hase

Figure 2: Constellation diagram of O-QPSK HSS with AWGN

Figure 3: O-QPSK HSS constellation in presence of back-ground noise

In a presence of the background noise, phase of theO-QPSK HSS modulated signal can change and positionof the received symbol can move in any direction. Back-ground noise is usually modeled as AWGN, which ampli-tudes the following Gaussian Probability Density Func-tion (PDF)[9] presented in equation (5), where µ repre-sents mean value and σ2 represents distribution variance(σ2 = N0

2 ).

n(x) =1√2πσ2

e−(x−µ)2

2σ2 (5)

Relative strength of background noise signal is usu-ally given in terms Energy of Symbol to Spectral NoiseDensity (EsN0

) which represents ratio between symbol en-ergy and noise spectral density. Since O-QPSK HSS codestwo bytes per symbol, energy of each symbol is equaltwice the energy of individual bit (Es = 2Eb). Whenbackground noise is added to the received symbol, theresulting amplitude follows Gaussian probability distri-bution. For example, under influence of noise, symbolS0 will be successfully decoded only if it stays inside itsquadrant (light gray hashed regions of Fig. 2) as pre-sented by equation (6).

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Pc(S0) = P (< > 0 | S0) · P (= > 0 | S0) (6)

If an influence of the noise is that big, it could causesymbol S0 to shift to another quadrant and to be decodedincorrectly (dark gray hashed regions of Fig. 2). The in-fluence of a background noise on the modulated signalcan be represented by the probability of a received sym-bol error as in equation (7).

Pe(S0) = 1− Pc(S0) (7)

The probability of a successful symbol reception S0

represents a product of probabilities that, on both axis,symbol is successfully decoded. This probability repre-sents a surface of gray hashed regions in Fig. 2 and iscalculated through integration of Gaussian PDF on theinterval [0,∞] [9] and presented by equation (8). Thisintegral is known as Gaussian tail integral or complemen-tary error function.

Pe(S0) = erfc

(√Es2N0

)− 1

4erfc2

(√Es2N0

)(8)

The obtained formula shows that error probability is afunction of ratio between symbol energy and noise spec-tral density. O-QPSK HSS modulation alphabet is Graycoded, so neighboring symbols differ only in one chipposition while the opposite symbols differ in two chippositions. If symbol error flips symbol to its neighboringquadrant, a single-chip error will occur; if a symbol flipsto opposite quadrant double chip the error will occur. Theprobability of received chip errors, known as Chip Errorrate (CER) can be expressed by equations (9) to (15).

CER =Pe(S0 → S1) + Pe(S0 → S3) + 2Pe(S0 → S2)

2(9)

Pe(S0 → S1) = P (< < 0 | S0) · P (= > 0 | S0)

= 12erfc

(√Es2N0

)·(1− 1

2erfc(√

Es2N0

))(10)

Pe(S0 → S2) = P (< < 0 | S0) · P (= < 0 | S0)

=(

12erfc

(√Es2N0

))·(

12erfc

(√Es2N0

))(11)

Pe(S0 → S3) = P (< > 0 | S0) · P (= < 0 | S0)

=(1− 1

2erfc(√

Es2N0

))· 12erfc

(√Es2N0

)(12)

CER = 12 · 2

(1− 1

2erfc(√

Es2N0

))· 12erfc

(√Es2N0

)+ 1

2 · 2(

12erfc

(√Es2N0

))·(

12erfc

(√Es2N0

))(13)

CER =1

2erfc

(√Es2N0

)=

1

2erfc

(√EbN0

)(14)

4 Simulation resultsIn order to evaluate the mathematical model for chip errorprobability of IEEE 802.15.4 transmission, the indepen-dent simulation model has been developed in MATLAB.This simulation model consists of implemented IEEE 802.15.4 transmitter and receiver, which communicate throughAWGN channel. Transmitter employed signal spread-ing and O-QPSK HSS modulation, while the receiver isbased on a coherent O-QPSK HSS demodulator with sig-nal despreading and hard decision decoding. Simulationsare carried out according to Monte Carlo method, withlarge number of packets with random content, in orderto accurately simulate probability of chip error. Pack-ets used in simulation have random content and constantlength of 133 Bytes or 8512 chips. Accuracy of suchsimulations mainly depends of sample size, in this case,number of transmitted packets. Number of samples n,required to test probability p of some event with marginof error σ is [10] as in equation (16), where q representscomplementary probability of p (q = 1 − p), zα is ordi-nate value of normal distribution function of correspond-ing error of precision estimate α .

n = z2α

(p · qσ2

)(15)

Margin of error σ, can be replaced with relative errorε, which represent ratio of margin of error σ and expectedprobability p, as in equation (17).

n = z2αq

p

(1

ε

)2

(16)

Number of transmitted packets, required to test ex-pected probability of smallest calculated chip error prob-ability with relative error ε of 5 %, at 95 % confidence(z(0.05) = 1.96), is just under 1000 packets. Table 1presents results of chip error rate simulation as well asrelative error between calculated and measured chip er-ror probability.

Results of the mathematically derived chip error prob-ability model, presented by line, are in a close matchwith results obtained by independent MATLAB simula-tion, presented by dots, for IEEE 802.15.4. wireless trans-mission in presence of AWGN (Fig. 4). This confirmsthat mathematically chip error probability model is cor-rectly derived.

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Table 1: Calculated and simulated chip error rateEbN0

Calculated Number of Simulated Rel.errorCER packets CER (%)

-8 0.2867 1000 0.2869 0.06-6 0.2392 1000 0.2392 0.01-4 0.1861 1000 0.1863 0.14-2 0.1306 1000 0.1307 0.020 0.0786 1000 0.0786 0.122 0.0375 1000 0.0376 0.234 0.0125 1000 0.0125 0.326 0.0024 1000 0.0024 0.998 0.0002 1000 0.0002 1.72

−8 −6 −4 −2 0 2 4 6 810−4

10−3

10−2

10−1

100

Eb/N0 [dBm]

Ch

ip E

rror

Rat

e

Figure 4: Chip error probability of IEEE 802.15.4 wirelesstransmission

5 ConclusionWireless transmission can be affected by influences ofvarious disturbing sources from its surrounding. Thoseinfluences can be expressed in error probability of the re-ceived binary data. This paper presents new mathemati-cal model which can be used to express chip error prob-ability for IEEE 802.15.4 wireless transmission in thepresence of AWGN. Correctness the proposed model wasconfirmed by MATLAB simulation of a IEEE 802.15.4wireless transmission through AWGN channel, where re-sults show a great similarity. Future work will be focusedon development of an error probability models for bit andpacket error probability of IEEE 802.15.4 wireless trans-mission.

6 AcknowledgementPart of the work presented in this paper was funded bygrant TR32043 for the period 2011-2014, by the Ministryof Education and Science of the Republic of Serbia.

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