Best Relaying Protocol Selection for Cooperative Networks

Edriss Eisa Babikir Adam, Li YuHuazhong University of Science &Technology, Wuhan

National Laboratory for Optoelectronics, Division of Communication & Intelligent Networks, Wuhan 430074,

Peoples R Chinae-mail:bonzoga20@yahoo.com, hustlyu@hust.edu.cn

Doudou Samb and Desheng WangHuazhong University of Science &Technology, Wuhan

National Laboratory for Optoelectronics, Division of Communication & Intelligent Networks, Wuhan 430074,

Peoples R Chinadoudousamb@ieee.org, dswang@ hust.edu.cn

Abstract—Cooperative communication has been recently proposed in wireless communication systems for exploring the inherent spatial diversity in relay channels. In this work we investigate the performance of selecting best protocol between amplify and forward (AF) and decode and forward (DF) in multiple relay networks. In the selection scheme, the best protocol between AF and DF is selected depending on source–relay links qualities. Particularly we derive the asymptotic closed form expression for the symbol error rate (SER) for the system under studied and show that our scheme maintains full diversity order and is better than fixed protocols. Numerical results are also presented to validate the theoretical analysis.

Keywords-Relaying protocol; wireless network; symbol error rate

I. INTRODUCTION

Cooperative communication can be used in wireless network to improve the reliability and the capacity of the system. In cooperative communication the independent paths between source and destination are generated. The surrounding users act as relays to achieve full diversity (i.e, gain diversity). These relays are implemented to help the source to transmit the signal to its destination. Different cooperation protocols of relaying have been designed to improve the communication system performance and robustness in wireless networks. Mainly we have Amplify-and-Forward (AF), Decode-and-Forward (DF), code cooperation and space-time cooperation[1],[2],[3]. Exciting works in cooperative communication are mainly focused on single protocol using AF or DF [4], [5] and as we know AF is limited by noise amplification while DF suffers from error propagation, so a selection between AF and DF turn to be sufficient. That is why the authors in [6] propose to analyze the selection between AF and DF for a single relay scheme with respect to outage probability analysis, but the single relay system is limited by adiversity order that can’t exceed two (the destination can’treceive more than two copies of the signal sent from the source). And to the best of our knowledge nobody has investigated the selection protocol between AF and DF with multiple relay in term of SER. To fill this gab of investigation we propose in this paper to analyze a multiple relay network in

which only a best protocol between AF and DF is selected by the relays for the forwarding scheme. To do this, we first find the cumulative density function (CDF), the probability density (PDF) function and the moment generating function (MGF) of the instantaneous received SNR at the destination from relaying protocol selection. So we obtain then new closed-form expression for the SER. The novel contribution of this paper is that we propose the following claim: during the idle period (when the relay cannot be able to DF) the remains relays can amplify and forward. The purpose of this article is to study a wireless network with the best relaying protocol selection between AF and DF.

This paper is structured as follows. Section II describes the system model. In section III we present the performanceanalysis for SER by establishing closed-form expression for the symbol error rate for the cooperation scheme and analyze the diversity order. Section IV gives numerical results to confirm the theoretical analysis.

II. SYSTEM MODEL AND SNR ANALYSIS As shown in fig. 1 our relaying selecting protocol system

consisting of a source S and n relays Ri ;(i =1,2….,n) and destination D. The system works under Rayleigh fading channel and signals are transmitted orthogonally using multiple access techniques with TDMA for simplicity. Itfollows that the transmitted scheme is divided into two phases. Phase 1: The source broadcasts its signal to the destination and the same information is received by the n relays. The different signals received at the destination and the ith relay can be represented as: SD S SD SDY P h x n� � (1)

i i iSR S SR SRY P h x n� � (2)

Where PS denotes transmitted source power, x is transmitted information symbol, SDn and

iSRn denote the additive white

Gaussian noise (AWGN) with variance 0N between source to destination and from source to ith relay respectively and

SDh and iSRh are fading channel coefficient between source to

___________________________________ 978-1-4673-2101-3/12/$31.00 ©2012 IEEE

destination and from source to ith relay respectively, these coefficients are independent to each other.

DS

Ri

R2

R1

Phase1Phase2

Broadcast

Fig. 1 Cooperation model with n-relay

Phase 2: the n relays send what they received from source to the destination using best relaying protocol AF or DF. In case of AF, the n relays amplify the received signal from source and forward it to the destination. The received signal at destination from ith relay is modelled as follows:

i i i iR D R R D SR R DY β h Y n� � (3)

Where iR Dh represents the fading channel coefficient between

ith relay to destination, iR Dn represents (AWGN) with variance

0N between ith relay to destination’ and iR� represents the

amplification factor which is modelled as:

i

i

i

RR 2

SR 0

Pβ

h NSP�

� (4)

This factor scales received signal with factor inversely proportional with received power as given in modelled with

iRP the transmitted power at the ith relay. In case of DF, the n relays re-encode the received signal from the source and forwards it to the destination. The received signal at the destination from ith relay is modelled as:

i i i iR D R R D R DY P h nx� � (5) Where, x is the decoded information at the relay (Ri). By using the maximum ratio combiner (MRC), the signals from source the n relay are combined at the destination after selecting best relaying protocol. And the received SNR is:

S i

n

Ri 1

γ γ γ�

� �� (6)

Where S� and iR� represent the SNR of the direct and the ith

relay link respectively with:

2

s SDS

P hγ

N�

� (7)

For AF: i

i i

i ii

i i

2 2RSSR R D

R AF2 2RS

SR R D

PP h h N N

γ γPP h h 1

N N

� �

� �

� �� �

(8)

And for DF:

i

i i i

2R

0R DF R D

Pγ γ h

N� � (9)

S� ,iAF� and

iDF� follow exponential distribution with

parameters 0S 2

S SD

Nλ

P σ� ,

i

i i i

0 0AF 2 2

S SR R R D

N Nλ

P σ P σ� � [4]

andi i i0

2DF R R Dλ N P σ� respectively.

The mutual information between the source node and the ith

relay node as a function of the fading coefficient is given by:

i

2Si SR

0

P1I ln 1 h( 1) Nn

� � � �� �

(10)

For a given target rate r in the system, a correct decoding scheme from ith relay may be possible if and only if the mutual information is above the target rate

(i.e.i

2(n+1)r2 0SR

S

(2 1)N h ε

PiI r �� �� � ).

For suitable analysis with an aim to investigate also the performance of relaying protocol selection, statistical similar relay channel gains are considered and can be practically realized by carefully placing the relays � �1 2 n 1 2 n

2 2 2 2 2 2SR SR SR R D R D R Dσ σ σ & σ σ σ� ��� � ���

And that � �� �2 αjk jk i iσ D jk SR , R D�� � where jkD

represents the distance between node j to node k and α designs the path loss exponent coefficient. So the analysis can be simplified into two scenarios: first, when the mutual information between the source node and each relay node is above the transmission target rate, then all the relays use DF as relaying protocol. Otherwise, it means that there exist a subset of m relays that can decode the information received from the source (the mutual information between the source and each of the m relays is above the target rate), and then AF is used as relaying protocol since DF cannot achieve full diversity order in multiple relays networks[7]. In the following section we will derive the closed form expression for SER.

III. SER PERFORMANCE ANALYSIS From the above formulation a conditional closed form expression for the SER with M-PSK modulation is written as follows [8]:

� �M 1 πM

SER γ 20

1 bP MGF dθπ sin θ

�

�� �� � �� �� (11)

The SER for the system is given by averaging equation (11) through the distribution of the total SNR and can be expressed as:

� � � �� �

� �� �

i i

i

1 2 2

SER 1 rob SR rob SR0 i 1 i 1

M 1 πM n

2 2i 10

n 2

rob SRi 1

M 1 πM n

2 2i 10

P P h P h <

1 b bMGF MGF dθπ sin θ sin θ

P h

1 b bMGF MGF dθπ sin θ sin θ

AFi

S DFi

nmn

m m

S

m n

C

�

� �

� �

�

�

�

�� � � �

�

�

�

�

�

� �

� �� � � �� � � �� � � �

� �

� �� � � �� � � �� � � �

�

�

�

(12)

Where � �

!! !

mn

nCm n m

��

represents the binomial coefficient.

and

n n

ii 1 i 1

MGF MGF i� �� �

� ��� �

� �� (13)

By averaging over Rayleigh fading channels , and

i iSD SR R Dh h h with variance , and i iSD SR R D! ! ! since the

fading channels are independent of each other then the moment generating function of the source node and relay can be written as follows; respectively [9].

1

2 2S.

b bMGF 1sin θ λ sin θS�

�� ��� � � �� �� �

� � � � (14)

1

2 2i.

b bMGF 1sin θ λ sin θi�

�� ��� � � �� �� �

� � � � (15)

by substituting (14),(15) into (12) we get the following equation in high SNR:

� �

� �

i

i

i

SER

1M 1 πn10

1 2 20 S SR Si 1 0

1 1M 1 πn

2 2i 1 AF S0

1n

2i 1 DF

P

δN b1P σ λ sin θ

b b1 1 1 dθλ sin θ λ sin θπ

b 1λ i

*

s n θ

Mnmn

m m

M

C���

�� � �

� ��

�

�

�

� �� �� ��� �� �� �� �� �� � � �

� �� �� � � �� �� �� �� �� �� �� �

�� �� �� ��� �

�

� �

�

�

� �

�

(16) Note that in high SNR region:

� �0

2 .S SRi

i

i

δNn n n2 P σ 0

rob SR 2i 1 i 1 i 1 S SR

δNP h 1 1e

P σ�

�

� � �

� �� �" � � �� ��

"�

(17)

And

� � 2 .0

S SRi

i

δNn 2 P σ

rob SRi 1

P h e 1��

�

� � # (18)

The expression given in (16) is too complex about analysis so we can find tight upper bound approximation as follows: 2sin 1$ % , then it follows that,

i i

i

2 2S. S.

2S.

2 2AF . AF .

2AF .

λ sin θ λ sin θ ,

bλ sin θ b

λ sin θ λ sin θ

bλ sin θ b

%�

%�

(19)

And: i i

i

2 2DF DF

2DF

λ sin θ λ sin θ

bλ sin θ b%

� (20)

Hence we can find the SER upper bound as follows:

UP i

i

i

n n1s

SER 1 AF2 n 10 i 1

0

S SRi 1

ns

DFn 1i 1

δN λ1P λ CπP σ b

λ1 λ Cπ b

nmn

m m

C�

� �� �� �

��

�

�

�

(21)

Assuming that the n relays have same power then the equation (21) can be simplified as:

� �� �UP

i i i i i i

10

SER 1n 1 20S SD

n

0 0 0 02 2 2 2

S SR S SR R R D R R D

NP C

πb P σ

δN N N N +

P σ P σ P σ P σ

nmn

m

n m n

C�

���

�

��

�

� � � � � ��� � � � � �� � � � � �

� � � � �� �

�

� (22)

where

� �M 1 πM

2n 2

0

1C sin θdθπ

�

�� �

Next we analyze the performance of the propose scheme compared to fixed protocols. Given that DF cannot always achieve full diversity order due to error propagation problems [10], [7]. In this article, we compare the propose scheme with fixed AF which has low complexity and can achieve full diversity order. A SER approximation for fixed AF is given as in [11] as:

� �� � i i i

nn 1

0AF 2 2n 1 2

S SR R R DS SD

N 1 1P C P σ P σb P σ

�

�

� � � �� �� �� � �� ��

(23)

For simplicity we assume equal power � �iS RP P P� � and the

values of all variances i i

2 2 2SD SR R Dσ σ σ� � as unity. Hence

equation (22) becomes:

� � � �

UP

i

SER

n-mn 1 1

n0 01 2n 1 n 1

0 S SR

P

N δNC 2 1

P σb P

nmn

mC

� �

�� ��

�

� � � �� �� �� �� �� �

i

n-m1

n 01 2

0 S SR

δN=K 2 1

P σ

nmn

mC

�

��

� �� �� ��� �� �� �� �� �� (24)

And (23) becomes:

� � i i

nn 1

n0AF 2 2n 1 n 1

SR R D

N 1 1P C 2 Kσ σb P

�

� �

� � � �� � �� �� � �� ��

(25)

where � �n 1 n 1 n 10K C N b P� � ��

At high SNR: i

20 S SRδN P σ 1≪

UPSER AFP P� "

This means mathematically the SER is minimized using best relaying protocol than fixed AF protocol. In following step we analyze the system in term of diversity which is a very important parameter in wireless communication. The definition of diversity order is given in [10] as:

UPSER

SNR

log Pd lim

logSNR&#� � (26)

� � i

n-mn 1 1

n01 2n 1 n 1

0 S SR

SNR

N δlog C 2P σb P

limlo P

1

g

nmn

mC

&

� �

�� ��

#

� � � �� �� � �� �

�� �

�

�

� �n 1 log P

d n 1log P�

' � � � (27)

Therefore our scheme achieves full diversity of order n+1 for n relays.

IV. SIMULATION RESULTS In this section we confirm the advantage of best relaying

protocol. The total limited power is equally distributed over all the nodes. Also, the variance of the noise (N0) is set as unity and the value of each channel variance is normalized as

unity � �2 2 2 1i iSD SR R D! ! !� � � . In Figure 2 we present the SER

according to SNR for n=2 relays. From the figure, we can observe the tightness of the analytical result with the simulation in high SNR regime as discussed in the theoretical analysis. Figure 3 shows the performance comparison of the proposed selection scheme with that one with fixed AF. As we can see, our selection scheme performs much better than fixed AF protocol as discussed with about 2dB, which mean that in high SNR region, the AF and DF selective cooperation can always improve the SER performance substantially as compared with fixed AF.

V. CONCLUSION This work analyzed the performance of selecting best

protocol between AF and DF cooperative relaying in wireless communication systems with mean channel gains over the Rayleigh fading channel in high SNR. After establishing the expressions for the SNR and the SER using MPSK signal of the system under studied, we found a tight SER higher bound. We showed that our selection scheme not only performs much better than fixed AF but also maintains full diversity of order n+1 for a number of relays n. Numerical result are also presented to validate the theoretical analysis and to show the advantage of using relaying protocol selection in wireless cooperative communication systems.

ACKNOWLEDGMENT This work is sponsored by the National 863 Program of China (2009AA01Z205), National Natural Science Foundation of China (NO.60972016), and China-Finnish cooperation project (2010DFB10570), Hubei Funds for Distinguished Young Scientists (NO.2009CDA150), Fund of National

Optoelectronics Laboratory (P080010), Program for New Century Excellent Talents in University (NCET070339), and two other projects (No.2010ZX03003-001-02 and No. 2012QN076).

0 5 10 15 20 25 30 35 4010

-12

10-10

10-8

10-6

10-4

10-2

100

102

104

P/No (dB)

SE

R

Analytical Upper BoundSimulation

Figure 2. SER vs.SNR using two relays

15 20 25 30 35 40

10-10

10-8

10-6

10-4

10-2

100

P/No (dB)

SER

AFproposed

Figure 3. SER vs.SNR, performance comparison with AF scheme

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