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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.

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 [

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 to the destination directly as well as to the user 2. In time frame 2, user 2 decodes the data and forwards as to the destination as shown in the

are the received complex baseband signals at the destination and user 2 respectively in time frame 1. is the complex baseband signal at the destination in time frame 2. are complex fading gains from user 1 to destination and from user 1 to user 2 respectively. is the complex fading gain from user 2 to destination. is the transmitted BPSK symbol of user 1 having energy

, and are the addi-

tive white Gaussian noises from user 1 to destination and from user 1 to user 2 respectively. is the additive white Gaussian noise from user 2 to destination. are the independent zero-mean complex circular Gaussian random variables having variances. respectively and are independent of the additive noises. are independent and identically distributed zero-mean complex circular Gaussian random variables with variance, i.e. having a distribution.

In the cooperation mode the data is sent by the user 1 is decoded as at user 2, which can be expressed as

In the non cooperation mode, the data received directly from user 1 at the destination. The decoded symbol obtained by the coherent detection is, which can be expressed as

denotes the signum function. Let denotes the final decoded symbol at the destination using SC is given by

In this technique signals received at the destination are multiplied by a complex weighting factor that compensates the phase rotation of the channel. Let denotes the output of the EGC, which can be expressed as

is the weighting factor of EGC, which can be given by

where phase for. are the magnitudes of the weighting factors which are same and do not depend on the signal-to-noise ratio (SNR) values of the communication links.

Let denotes final decoded symbol at the destination using MRC is given by

is the weighting factor of MRC, which can be expressed as

where is the variance of, phase for.

The SEP conditioned on, obtained by the coherent detection is given by

where denotes the Gaussian Q-function.

The instantaneous SNR of the user 1 to destination link is denoted as

The average SNR of the user 1 to destination link is denoted as

Therefore (12) can be written as

using Craig’s formula (14) can be written as

After averaging the (15) over the statistics of, we obtain SEP in the non-cooperation mode as

Let and denote the instantaneous SNR of the user 1 to user 2 link and instantaneous SNR of the user 2 to destination link respectively, given by

Let and denote the average SNR of the user 1 to user 2 link and average SNR of the user 2 to destination link respectively, given by

We consider the case when user 1 transmits symbol, the disjoint events which lead to a correct decision can be enumerated as

Probability of the event conditioned on and can be written as

and are defined as

Averaging (22) over the exponential statistics of and, we obtain the probability of the event as

Probability of the event can be written as

Averaging (25) over the statistics of and under the condition can be simplified into

Using the integration by parts we get

After applying the formula [

where quantities and are defined as

We finally obtain the probability of event

Probability of event can be similarly written as

Averaging the (31) over the statistics of and under the condition can be simplified into

Using the integration by parts we get

Applying the formula as in [

The probability of correct decision is given by . Therefore the end-to-end SEP, which is denoted as in cooperation mode can be expressed as

After substituting the (24), (30) and (34) in (35) we finally obtain the end-to-end SEP expression as

For the expression (36) can be approximated as

In this section we show the numerical results of the SEP vs average SNR for BPSK modulation scheme. From the

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 values. We also compared the MRC, EGC, SC with each other in providing better diversity. The obtained simulation and computation results

agree with each other. Further we also presented some choice of SNR values with different combining techniques to obtain low SEP values. Finally we proved that two-user cooperative diversity with MRC implementation was performing better for low SNR values compared to SC and EGC techniques.