A Cooperative Diversity Analysis of Two User Mobile Communication System with Maximal Ratio Combining

Cooperative communication is going to play a vital role in the next generation wireless networks. In this paper we derive the expression for symbol error probability (SEP) of a two-user cooperative diversity system, where two users cooperate through the decode-and-forward (DF) relaying with binary phase-shift keying (BPSK) modulation in a flat Rayleigh fading environment. We compare the computational results obtained by the SEP expression with the simulation results using maximal-ratio combining (MRC), equal-gain combining (EGC) and selection combining (SC) techniques. Numerical results show the performance of a cooperative diversity system with maximal-ratio combining is giving better results compared to SC and EGC techniques.


Introduction
Cooperative diversity is a new form of spatial diversity where diversity is achieved through the cooperation between users presented in the network.The key idea behind this technology is sharing the power, computation and antenna resources of the neighboring users in the network.It is also going to be a promising alternative to combat the multipath fading and to provide the reliable communication [1].An analytical study about the user cooperation is first discussed in [2].The amplify-andforward (AF), decode-and-forward (DF) and coded cooperation methods are discussed in [3].In [4], SEP is derived for a two-user cooperative diversity system.In [5], some new closed form expressions are derived in a flat Rayleigh fading environment.In this paper we consider a fundamental cooperative diversity system, where two users cooperating through the DF relaying with BPSK modulation in a flat Rayleigh fading environment.The rest of the paper has been organized as follows.In Section 2, system model of a fundamental cooperative diversity system is discussed and mathematical expressions are given.In Section 3 different combining techniques are discussed.In Section 4 we derived the SEP expression for a two-user cooperative diversity system.Simulation results are presented in Section 5.In Section 6 we have given the conclusions.

System Model
We consider a cooperative diversity system with two users and a single destination.Let us assume user 1 acts as a source and user 2 relays the data received from user 1 to the destination.In time frame 1, user 1 transmits the data 1 x to the destination directly as well as to the user 2. In time frame 2, user 2 decodes the data 1 x and forwards as 1 x to the destination as shown in the Figure 1.
are the received complex baseband signals at the destination and user 2 respectively in time frame 1. 2d is the complex baseband signal at the destination in time frame 2. 1 1 2 d are complex fading gains from user 1 to destination and from user 1 to user 2 respectively.2d h e complex fading gain from user 2 to destination. 1 x is the transm ed BPSK symbol of user 1 having energy itt , 1d n and 12 n are the addi-

Combining Techniques
a is sent by the user 1 is

Selection Combining
In the cooperation mode the dat decoded as ˆ1 x at user 2, which can be expressed as In the non cooperation mode, the dat from user 1 at the destination.The decoded symbol obta a received directly ined by the coherent detection is 1 x , which can be expressed as 2 sgn Re , ˆ2 sgn Re ,

Let ˆmrc
x denotes final decoded sym tion using MRC is given by bol at the destina-  is the weighting factor of MRC, w pressed as hich can be ex- where kd is the variance of h kd , phase kd kd h

rror alysis n Mode
tained by the coherent

Non-Cooperatio
The SEP conditioned on 1d h , ob detection is given by where   Q  denotes the Gaussian Q-f The instantaneous SNR of the user 1 to destination enot unction.
link is d ed as The average SNR of the user denoted as 1 to destination link is d N Therefore (12) can be written as using Craig's formula (14) can be written as Copyright © 2013 SciRes.

CN
After averaging the (15) over the statistics of 1d , We consider the case when user 1 E transmits symbol 2 s E , the disjoint events which lead cision can be enumerated as to a correct de- Re 0, Re 0, Re 0, Re 0,  can be written as  are defined as Using the integration by parts we get After applying the formula [4], we get where quantities 12d 1 2 , 0 Pr Probability of event 3  can be similarly written as  Pr , , Applying the formula as in [4], we get the probability of 3 The probability of correct decision is given by        the expression (36) can be approximated as

Conclusions
We investigated the performance of a two-user cooperative diversity system using MRC, EGC, SC techniques.First we compared the cooperation and non-cooperation modes for different 12  values.We also compared the MRC, EGC, SC with each other in providing better diversity.The obtained simulation mode is better than the no large range of SNR value creases.From the Figure 3, we observe that the MRC improves the diversity significantly over EGC and SC, when 12 15 dB   and 1d  is varied between 5 to 15 dB.We also observe similar increase in performance when 12 25 dB   and 1d  is varied bet en 5 to 20 and computation results

Figure 1 .
Figure 1.Two-user cooperative diversity system.tive w and om user 1 to user tively.n is the additive are the independent zero-mean complex circular Gaussian random variables having varianc d at the destination are ting factor that com-In this technique signals receive multiplied by a complex weigh pensates the phase rotation of the channel.Let ˆegc x denotes the output of the EGC, which can be expressed as

sults
In this section we show the numerical results of the SNR for BPSK modul serve the performance of the cooperation n-cooperation mode over a s when the 12  value inwe dB.From the Figure4, we also observe that for every 5 dB increase of 12  The diversity range offered by MRC is approximately increases by 5 dB.SEP values of EGC are almost close to the MRC because both the schemes are coherently combining the signals at the destination.The performance of the MRC, EGC, SC is almost similar after the points of intersection

Figure 2 .
Figure 2. Comparison of cooperation and non-cooperation modes.

Figure 3 .
Figure 3.Comparison of computation and simulation results with MRC, EGC and SC.