Performance Analysis of Amplify and Forward Cooperative Networks over Rayleigh and Nakagami-m Channels based Relaying Selection

In this paper investigates the performance, analysis of amplify and forward (AF) cooperative networks with the relay selection over Nakagami-m and Rayleigh fading channels and M-ary phase shift keying (MPSK) modulations. New closed form expressions are derived for the general cases of Rayleigh and Nakagami-m fading channels. cumulative density function (CDF), probability density function (PDF) of the end –to - end signal –to – nois ratio (SNR) of a dual-hop opportunistic AF relaying system, moment generating function (MGF), symbol error rate (SER) and outage probability (P out ). and the first closed-form study for opportunistic AF relaying system where the best node is selected from a number of candidate intermediate nodes to relay the data signal between the source and the destination. Simulation results reveal that the PDF , CDF, P out and SER performance downgrades either the m parameter or the number of relays increases. Our simulations compared between Rayleigh and Nakagami-m links for a different number of relays. In addition, different modulation techniques are examined to show the effect of the modulation scheme which was used over Rayleigh and Nakagami-m fading channels on the cooperative networks. The obtained results proved the impact of m parameters, relay selection and modulation index on the p out and SER performance.


INTRODUCTION
Cooperative Networks schemes have been recently proposed as a promising technique for high quality wireless communication services. The concept of cooperative networking represents a technique that can significantly increase the system capacity and diversity gain in wireless networks [1][2][3].
[4] The authors used amplify and forward (AF) relaying over Nakagami-m fading channels to derive a new lower bound and asymptotic expression for the outage probability of cooperative diversity in direct sequence code-division multiple access (DS-CDMA). In their work, they studied the performance and analysis of downlink multiuser relay networks using single-relay in amplify and forward (AF) where the outage probability was evaluated at a high SNR [5][6].
For example, [7][8] analyzed the performance of cooperative diversity wireless networks using amplify-and-forward relaying over independent, non-identical (i.n.d), Nakagami-m fading channels. The error rate and outage probability are determined using the MGF of the total SNR at the destination. Furthermore, closed form expressions for the CDF, probability density function (PDF) and MGF of the total SNR [9][10]. The authors also show performance analysis of the best relay selection scheme which has robustness based on selecting only the best single relay. Analytical expressions for the PDF, CDF and MGF of the SNR are used to derive the expressions for outage probability over Rayleigh Fading channels. In [11], a performance analysis has been performed for the lower bound SER performance of BPSK signal and for the outage capacity of AF cooperative diversity systems with best relay selection, and the SER expression given only for the BPSK signal and is involved with an integral requiring numerical calculations.
In this paper, we present a performance analysis of all relays for the AF cooperative networks of the half-hop and we derive new closed-form expressions for the cumulative density function (CDF), probability density function (PDF) of the end -to -end signal -tonois ratio (SNR) of a dual-hop opportunistic AF relaying system, moment generating function (MGF), symbol error rate (SER) and outage probability (Pout) .we also compared performance study the effect of increasing the number of relays over Nakagami-m and Rayleigh fading channels we also analytical investigation of the

SYSTEM MODEL
We consider a dual hop cooperative network model composed of a source, half duplex relay(s) (1 ≤ i ≤ R) and a destination, as shown in Fig. 1 Assume that the channel state information is distinguished at the destination. We utilize time division multiplexing (TDM) to ensure the transmission from the source and the relay(s) occur in consecutive time slot. In the first time slot, the source transmits a signal x to the relays. The received signal from the ith relay can be given as: h is the channel gain between the source and the i th relay.
Gaussian noise (AWGN) between the source and the i th relay while N 0 is the noise variance.
In the second time slot, the i th relay amplifies its received signal and forwards it to the destination. The destination receives the transmission as: h is the channel gain between the i th relay and the destination and is the complex additive white noise. Between the i R and D by G i is the amplified gain expressed as: with Es as the average energy per symbol [12]. From (2), we can estimate the SNR at the destination as follows: Therefore, the upper bound for the equivalent SNR can be written as: The upper bound SNR given by (5) is more suitable for analysis and is shown to be quite accurate at medium and high SNR values [10].

PERFORMANCE ANALYSIS
In order to find the expressions of the outage probability, and average SER, we need to derive the MGF, thus we first

NUMERICAL RESULTS
In this section, we provide numerical results for the PDF, CDF, outage probability (pout) and SER expressions. Our results are obtained from different values of M-PSK modulation index, m and R. We validate and compare our derived expressions using Monte Carlo simulations under Nakagami-m and Rayleigh fading channels. The results obtained using the exact analysis of dual-hop AF relaying with end-to-end SNR selection are presented. Recall that no exact solutions for such systems, in the case of general fading environments, are known and only performance bounds have been reported in the literature.  1,2, 4). We can see that n increasing the number of relays significantly decreases the SER. increasing the number of relays significantly decreases the SER.
In Fig. 4 and Fig. 5 we compare the PDF and CDF values respectively for both therotical and simulation . The results are obtained from different values of m parameter over Nakagami-m . The figures reveal that if m increases both the PDF and the CDF shift to the right direction. Moreover, the peak value of the PDF becomes smaller which means that it will be more

CONCLUSION
In this paper, we have derived exact closed-form expressions for the PDF , CDF and the MGF for the channels state information operates in a halfduplex mode, we had also derived and analyzed indeed closed-form expressions for the SER and Pout over Nakagami-m and Rayleigh fading channels and We compared between the cumulative density function (CDF) and probability density function (PDF) for throtical and simulation links in which the best relay scheme is adopted for different SNRs that analyzed the performances of AF cooperative relaying in wireless communication systems with mean channel gains over the Nakagami-m fading channel in high SNR. We also provided Numerical results to shown the performance of SER for different M-PSK modulation signals improvement of our scheme compared Nakagamim with Rayleigh fading channels, for a different number of relays and m parameters.