Minor Proj Final-EC Tempelate

CENTRALIZED POWER ALLOCATION FOR COOPERATIVE WIRELESS COMMUNICATION

A Minor Project Report

Submitted in Partial Fulfillment of the Requirements

for the Degree of

Bachelor OF TECHNOLOGY

IN

ELECTRONICS & COMMUNICATION ENGINEERING

By Jay R. Dhamsaniya

[08BEC021] Arsh R. Marviya

[08BEC043]

Under the Guidance of Prof. M. A. Upadhyay

Department of Electrical Engineering Electronics & Communication Engineering Program

Institute of Technology, Nirma University Ahmedabad-382481

November 2011

CERTIFICATE

This is to certify that the Major Project Report entitled “Centralized Power

Allocation for Cooperative wireless Communication” submitted by Jay R.

Dhamsaniya (Roll No. 08BEC021) and Arsh R. Marviya (Roll No. 08BEC043) as

the partial fulfillment of the requirements for the award of the degree of Bachelor of

Technology in Electronics & Communication Engineering, Institute of Technology,

Nirma University is the record of work carried out by his/her under my supervision

and guidance. The work submitted in our opinion has reached a level required for

being accepted for the examination.

Date:

Prof. M. A. Upadhyay

Project Guide

Prof. A. S. Ranade

HOD (Electrical Engineering)

Nirma University, Ahmedabad

ABSTRACT

A major problem in operation of wireless communication system is the effective use of radio

resources to promote the quality and efficiency of the system. One such component is the power

control in mobile terminals, which is a measure of energy efficiency.

Cooperation among network users provides transmit diversity in cases where wireless

transmitters, due to size and power limitation, cannot support multiple antennas. We consider

cooperation between M users, where each user achieves space-time diversity by using other users’

antennas as relays. This paper formulates an optimum power allocation scheme appropriate for a

centralized cooperative network using transparent relaying. It will be shown that the proposed

allocation scheme significantly outperforms the equal power allocation scheme.

i

Index

Chapter

No. Title Page No.

Abstract i

Index ii

List of Figures iii

Nomenclature iv

1 Introduction

1.1 Introduction 1

1.2 Conventional point-to-point communication 1

1.3 Cooperative Communication 1

1.4 Relaying Strategies 2

1.5 System Performance 4

2 System Model for Power Control

2.1 System model definition 5

2.2 Signal transmission 5

3 Power Allocation Strategies

3.1 BER performance of 2-node cooperation 7

3.2 BER performance of M-node cooperation 8

3.3 Centralized power allocation approach 9

4 Numerical Simulation

4.1 Numerical simulation for 2-node cooperation 10

Conclusions 11

References 12

Appendix [ MATLAB code ] 13

ii

LIST OF FIGURES

Fig. No.

Title

Page

No.

1.1 Traditional Peer-to-peer Communication 1

1.2 Cooperative Communication 2

1.3 Different Relaying Strategies 2

1.4 Illustrating the difference between the direct and cooperative transmission

schemes, and the coverage extension prospected by cooperative transmission

3

2.1 Cooperation transmission scheme 5

2.2 Implementation of node cooperation using hybrid FDMA-TDMA 5

4.1 2-node cooperation with symmetric mean up link channels, 13 = 12 = 23 10

iii

NOMENCLATURE

Relay power gain

Power allocation factor

Wavelength

Signal to noise ratio (SNR)

b BPSK modulated signal

D Destination node

Eb Energy transmitted per bit

f Frequency

h System response

k Constant depends on PSK scheme (for BPSK=2, QPSK=4, …)

M No. of cooperative node

N0 Noise power

Pe Probability error

Q (.) Standard Gaussian error function

S Source node

w White Gaussian noise

y Received signal

iv

Chapter 1

Introduction

1.1 Introduction

In this chapter, we will discuss shortcomings of conventional point-to-point communications that led

to the introduction of the new paradigm shift for wireless communications, i.e., cooperative

communications. We will define what the relay channel is, and in what aspects it is different from the

direct point-to-point channel. We will also describe several protocols that can be implemented at the

relay channel, and discuss the performance of these protocols which will be assessed based on their

outage probability and diversity gains.

1.2 Conventional Point-to-Point Communication

In traditional peer-to-peer communication, most of the transmitted power (energy) is not received at

the destination antenna due to some obstacle in the path. The mobility, size and complexity

constraints of the device prevent the use of directional or multiple antennas at transmitters to achieve

full rank MIMO. Hence, the continuous communication is not guaranteed; all users cannot be

guaranteed high data rate; all users are competing for the use of available resources.

Fig. 1.1 Traditional Peer-to-peer Communication

1.3 Cooperative Communication

As a solution of these problems, the cooperative communication technique is developed. In

cooperative communication, one independent path is generated between the user and the base station

by introducing a Relay channel. The Relay channel is a one kind of an auxiliary channel. The distance

between source node and destination node is greater than some wavelength. It guaranteed to fade

independently and we get full rank-MIMO channel. As a solution of these problems, the cooperative

communication technique is developed.

1

Fig. 1.2 Cooperative Communication

1.4 Relaying Strategies

The different relaying processing schemes result in different cooperative communications protocol.

Cooperative communications protocols can be generally categorized into fixed relaying schemes and

adaptive relaying schemes. This categorization is shown in fig. 1.3.

Fig. 1.3 Different Relaying Strategies

In fixed relaying, the channel resources are divided between the source and the relay in a fixed

(deterministic) manner. The processing at the relay differs according to the employed protocol. In a

fixed amplify-and-forward (AF) relaying protocol, the relay simply scales the received version and

transmits an amplified version of it to the destination. Another possibility of processing at the relay

node is for the relay to decode the received signal, re-encode it and then retransmit it to the receiver.

This kind of relaying is termed a fixed decode-and-forward (DF) relaying protocol. Fixed relaying

has the advantage of easy implementation, but the disadvantage of low bandwidth efficiency. This is

because half of the channel resources are allocated to the relay for transmission, which reduces the

overall rate. This is true especially when the source–destination channel is not very bad, because in

such a scenario a high percentage of the packets transmitted by the source to the destination could be

received correctly by the destination and the relay’s transmissions would be wasted. Adaptive

relaying techniques, comprising selective and incremental relaying, try to overcome this problem.

Fixed relaying has the advantage of easy implementation, but the disadvantage of low

bandwidth efficiency. This is because half of the channel resources are allocated to the relay for

transmission, which reduces the overall rate. This is true especially when the source–destination

channel is not very bad, because in such a scenario a high percentage of the packets transmitted by

the source to the destination could be received correctly by the destination and the relay’s

transmissions would be wasted. Adaptive relaying techniques, comprising selective and incremental

relaying, try to overcome this problem.

2

Fig. 1.4 Illustrating the difference between the direct and cooperative transmission schemes, and the

coverage extension prospected by cooperative transmission

In selective relaying, if the signal-to-noise ratio of the signal received at the relay exceeds a

certain threshold, the relay performs decode-and-forward operation on the message. On the other

hand, if the channel between the source and the relay has severe fading such that the signal-to-noise

ratio is below the threshold, the relay idles. Moreover, if the source knows that the destination does

not decode correctly, then the source may repeat to transmit the information to the destination or the

relay may help forward information, which is termed as incremental relaying. In this case, a feedback

channel from the destination to the source and the relay is necessary.

Since a mobile terminal cannot relay information at the same time and in the same frequency

band. A practical multiple access methods are

1. Frequency Division Multiple Access, FDMA

2. Time Division Multiple Access, TDMA

3. Hybrid FDMA-TDMA and

4. Space Division Multiple Access, SDMA.

In this paper, it is assumed that an orthogonal bandwidth (FDMA) and time slot (TDMA) (i.e.,

hybrid FDMA-TDMA) allocation with transparent relaying scheme is used.

3

1.5 System Performance

The end-to-end performance of the system in terms of bit error rate (BER) and capacity, depends on

the performance of each relaying node. For optimum performance of the system, all types of

resources must be allocated properly. The resource allocation includes

1. Bandwidth allocation,

2. Time slot allocation,

3. Power allocation.

In this paper, the case of transparent relaying with an arbitrary inter-user channel signal-to-noise-

ratio (SNR) will be examined. A method to optimize the end-to-end BER performance is proposed

and solutions obtained using numerical optimization at various average SNR values is presented.

4

Chapter 2

System Model for Power Control

2.1 System Model Definition

The cooperative scenario illustrated in Figs. 2.1 and 2.2 shows an amplify-and-forward (AF) scheme

between two transmitting nodes and one destination node.

The modulation is assumed to be binary phase shift keying (BPSK), and each node receiver

maintains the instantaneous channel fading coefficients. Coherent detection with Maximum Ratio

Combining is employed. The channels between nodes (inter-node channels) and from each node to

the destination (uplink channels) are mutually independent and subject to flat fading.

Each node is allocated different frequency bands (f1 and f2) and in each band a node transmits

signals in two different time frames, one frame is dedicated for its own bits and the other is for

relaying the partner’s bits.

Fig 2.1 Cooperation transmission scheme

Fig 2.2 Implementation of node cooperation using hybrid FDMA-TDMA

2.2 Signal Transmission

In the first time interval, user 1 transmits b1(n) and the received signal at user 2, y2(n) and at user 3,

y3(n) can be expressed as,

… (1)

and

5

… (2)

Where,

Eb = energy per transmitted bit in the case of direct (non-cooperative) transmission,

b1 = BPSK modulated symbols with unit energy,

hij = captures the effect of path loss and static fading on transmissions from node i to

node j, and

wj(n) = models additive receiver noise, which is white Gaussian with a variance of N0.

Note that in the 2- node cooperation scheme, to maintain the same total power consumption, the

energy available per bit for the cooperative scheme is half of that for the direct transmission scheme

(hence the factor of 1/2).

In the (n + 1)th time frame node 2 amplifies the signal by the relay gain 2 and transmits:

... (3)

During the two consecutive time frames, the destination, i.e., node 3, receives y3(n) and y3(n+1).

... (4)

One choice for the relay power gain, which amplifies the received signal to a power level similar

to that of a node’s signal power level before relaying it to the destination, is given as

... (5)

Finally, note that this approach may be extended to the situation where more than two nodes

cooperate in a straight forward manner.

6

Chapter 3

Power Allocation Strategy

3.1 BER Performance of 2-Node Cooperation

The performance of cooperative networks can be characterized in terms of BER performance, ergodic

capacity, and outage capacity. In this paper we focus on BER performance as the metric to be

optimized. Utilizing the approximate expression for BER in, we can find an optimum power

allocation such that the end-to-end average BER performance is minimized.

Statistically, we model the fading coefficients hij as zero mean, mutually independent complex

jointly Gaussian random variables with variances (hi,j)2 and we model the additive noise wj(n) as

zero-mean, mutually independent, white complex jointly Gaussian sequences with variance N0. For a

2-cooperating user system, the equivalent received SNR at the destination, node 3 at time n + 1 due to

the 2-hop path, eq can be expressed as

... (1)

For cooperative scenario, let us define

... (2)

Substituting (5) into (6) and making use of the definition in (7) leads to eq given by:

... (3)

Combining the received signal for 2 consecutive timeslots using the Maximum Ratio Combining

(MRC) method, the conditional SNR of the combined signal given the channel fading coefficients h i

j ;i {1, 2}, j {2, 3} is

... (4)

and the probability of error conditional on the SNRs of the combined signal can be expressed as

... (5)

where, Q(.) is the standard Gaussian error function. At high SNR values, the unity term in the

denominator of (4) is negligible, and thus (4) can be approximated as

7

... (6)

Using the approximate expression for SNR in (11), Ribeiro and Giannakis [6] derive the

approximate BER expression for the high SNR region by looking at the pdf of the SNR around zero,

i.e., p MRC. The authors argue that since in fading channels the probability of error is dominated by

the probability of having deep fades, or equivalently, the probability that the channel coefficient is

very small, the probability of error can be approximated by observing the behavior of the pdf of the

SNR around zero. The resulting asymptotic average BER for user 1 is

... (7)

Where, k is a constant depending on the type of modulation, e.g., for BPSK, k = 2. In the case of

Rayleigh fading,

... (8)

3.2 BER Performance of M-Node Cooperation

For M-user cooperative diversity, the approximate BER expression for user l communicating with

destination node d is

... (9)

Where, nm = power allocation factor for user n to transmit the data of user m, M = number of

cooperating nodes between the node l and destination d and C(M) = is a constant

depending on the number of cooperating nodes. Note that

... (10)

And

... (11)

8

3.3 Centralized Power Allocation Approach

This power control problem can be approached in a centralized or a distributed manner, as will be

described in the following sections.

With centralized power allocation, the nodes firstly inform the network controller about the

quality of their channels to the destination and to other nodes. Then the network controller calculates

the optimum power allocation factors for each link. Finally, the network controller conveys the

results to the various nodes, which will then adjust their transmit power accordingly.

In the centralized approach, the problem of finding a set of power allocation factors, n,m that

minimizes the total BER can be posed as follows.

Problem (P1) : Find the set of power allocation factors n,m, for n, m = 1, 2, ..., M which solves

the following constrained optimization problem

... (12)

subject to the linear constraints (10) and (11).

To analytically illustrate the optimization method, let us consider the 2-node highly symmetrical

scenario where the mean uplinks and inter-node link SNRs are similar, i.e., 13 = 12 = 23. Note that

in this highly symmetrical case the power allocation factors, 1,1 = 2,2 = and 1,2 = 2,1 = 1 - . We

can obtain the optimum value of parameter by differentiating the average end-to-end BER with

respect to and setting the resulting expression to zero. The resulting optimum cooperation level in

this case is = 2/3, which is independent of the uplink SNRs. On the contrary, in the existing

literature the value of = 1/2 is often used.

The result of the optimization using the centralized approach in (12) serves as the reference value

for the lowest achievable total average BER.

9

Chapter 4

Numerical Simulation

4.1 Numerical Simulation for 2-Node Cooperation

To test the effectiveness of the proposed power allocation strategy, numerical simulations have been

performed. The channel is assumed to obey flat Rayleigh fading. For the situation where the terminals

are mobile, the power allocation needs to be updated dynamically to ensure an optimum end-to-end

performance. However, if the mobiles are of low mobility there will be enough time to properly

update the power allocation. Note that for high mobility applications operating in a fast fading

environment, there are other alternatives to exploit diversity, for example coding.

For highly symmetric channels, same SNR can be assumed for all channels in coding. By taking

large number of fraction value of which follows conditions shown in equations (3.10) and (3.11),

BER can be found out by equation (3.9) and we can select minimum value of BER for one source

node to destination node path out of M path. Then, by finding minimum average BER for all paths,

we achieve optimum power allocation for centralized wireless network. For this kind of model we get

result as shown in fig. 4.1.

Fig. 4.1 2-node cooperation with symmetric mean up link channels, 13 = 12 = 23

10

Conclusion

Most previous work on power allocation in cooperative networks considers centralized approaches.

This implicitly assumes the existence of a network controller that monitors and calculates the power

allocated for each of the direct and cooperative links. This approach has two major drawbacks: First,

there are the storage and computational demands placed on the network controller since it needs to

know the signal-to-noise-ratio (SNR) of each of the cooperative/inter-node links. Second, the loss in

timeslots/ bandwidth efficiency due to the need to broadcast the inter-node information to the

network controller as well as for the network controller to inform the various nodes of their power

allocation factors.

From the fig. 4.1, for 2-node cooperative highly symmetric scenario, we get 1.9 dB BER at 10

dB SNR for direct BPSK transmission and 2.9 dB BER at 10 dB SNR for centralized power

allocation. So, we better BER response in centralized power allocation than direct BPSK transmission

scheme.

11

References

[1] A. Sendonaris, E. Erkip, and B. Aazhang. “User cooperation diversity- Part I: System

description”, IEEE Trans. Commun., vol.51, pp.1927-1938, Nov. 2003.

[2] A. Sendonaris, E. Erkip, and B. Aazhang. “User cooperation diversity- Part II:

Implementation aspects and performance analysis”, IEEE Trans. Commun., vol. 51, pp.

1939-1948, Nov. 2003.

[3] J.N. Laneman, D. N. Tse, and G. W. Wornell. “Cooperative diversity in wireless networks:

Efficient protocols and outage behavior”, IEEE Trans. Inform. Theory, vol. 50, no. 12, pp.

3062-3080, Dec. 2004.

[4] Jaime Adeane, Miguel R.D. Rodrigues, and Ian J. Wassell. “Optimum Power Allocation in

Cooperative Networks”

[5] K. J. Rayliu, Ahmed K. Sadek, Weifeng Su, Andres Kasinski; “Cooperative Communication

and Networking”

[6] T. E. Hunter and A. Nosratinia, “Diversity through coded cooperation,” submitted to IEEE

J. Select. Areas Commun.

[7] M. Dohler, A. Gkelias, and H. Aghvami. “Resource allocation for FDMA - based

regenerative multi – hop links, ” IEEE Trans. on Commun. , vol. 3, no. 6, pp. 1989-1993,

Nov. 2004.

[8] A. Ribeiro, X. Cai, and G. B. Giannakis. “Symbol error Probabilities for general

cooperative links,” IEEE Trans. On Wir.Commun., vol. 4, no. 3, May 2005.

[9] E. Telatar. “Capacity of multiantenna Gaussian channels,” AT & T Bell Laboratories,

Technical Memorandum, Jun. 1995.

12

Appendix

MATLAB

code for 2-node highly symmetric centralized wireless network and it contains following

files. Here, pa.m is a main Program and CM.m, betaV.m, piV.m are supporting functions.

pa.m %------------------------------------------------------------------------------->

clc;

M = 2;

k = 2;

index = 1;

N = 11; % B sample value

for p = 0:5:20

pe=[];

for l=1:M

b = -(1/(N-1));

pe_min = 10; % assumed value

for i=1:N;

b = b + (1/(N-1));

B = betaV(b);

f = piV(b,l,p,M);

pel = CM(M)*f / ( k^(M+1) * B(l,l)*p );

if pel <= pe_min

pe_min = pel;

else

pe_min = pe_min;

end

end

pe=[pe pe_min];

end

snr(index) = p;

ber(index) = sum(pe)/M;

[ snr(index) ber(index)]

index = index + 1;

end

%------------------------------------------------------------------------------->

N=10000;

f=sqrt(0.5);

index=1;

for k=0:5:20

x=10^(k/10);

p=sqrt(1/x);

bera(index)=0.5*(1-sqrt(x/(x+1)));

snrb(index)=k;

[snrb(index) bera(index)]

N=N+6000;

index=index+1;

end

%------------------------------------------------------------------------------->

semilogy(snr,ber,snrb,bera)

legend('OPA','bpsk');

xlabel('SNR db');

ylabel('BER');

title('BER performance');

%------------------------------------------------------------------------------->

13

Functions: CM.m %------------------------------------------------------------------------------->

function[cm]=CM(M)

%------------------------------------------------------------------------------->

cm = 1;

k = 2;

for i = 1:(M+1)

cm = cm * ((2*i)-1);

end

cm = cm / ( 2 * (factorial(M+1)) * (k^(M+1)) );

%------------------------------------------------------------------------------->

betaV.m %------------------------------------------------------------------------------->

function [B] = betaV(b)

%------------------------------------------------------------------------------->

b11 = b;

b12 = 1-b;

b21 = 1-b;

b22 = b;

B = [ b11, b12 ; b21, b22 ] ;

%------------------------------------------------------------------------------->

piV.m %------------------------------------------------------------------------------->

function [pi] = piV(b,l,p,M)

%------------------------------------------------------------------------------->

B = betaV(b);

pi=1;

for i=1:M

pi = pi * ( ( 1/(B(l,l)*(p)) ) + ( 1/(B(i,l)*(p)) ) );

end

%------------------------------------------------------------------------------->

14