The transmission through wireless channels suffers from random fluctuations in signal level known as attenuation and co-channel interference . Diversity is a powerful technique to mitigate fading and improve sturdiness to interference. In classical diversity techniques, the data signal is transmitted to the receiver in multiple (ideally) independent fading signal paths (in time / frequency / space) . An appropriate combination in the receiver achieves a diversity gain, thus improving link reliability. There are several approaches to implementing diversity in wireless transmission. Multiple antennas can be used to achieve diversity. But several antennas are not always available or the destination is too far to get good signal quality. Recently, co-operative communications for wireless networks have gained much interest because of their ability to mitigate wireless network fading through the achievement of spatial diversity, while at the same time solving the difficulties of installing multiple antennas in small communications terminals. The basic idea in cooperative communication is that in addition to direct transmission from the transmitter to the receiver, there may be other nodes, which can be used to enhance diversity by retransmission of the source signal to its destination, Multiple Output ). In a cooperative communication system, users act as sources of information, as well as relays. There are two main cooperative methods: amplification and advancement (AAF) (non-regenerative relays) and decoding and advancement (DAF) methods (regenerative relays). In the AAF method, the relay receives a noisy version of the signal transmitted by the source and then amplifies its received signal and retransmits it to the destination . In the DAF method, the relay decodes the noisy version of the signal transmitted by the source and then re-encodes it and transmits it again to the destination. In cooperative networks with multiple relays, cooperative diversity protocols can generally be categorized into fixed and adaptive retransmission protocols. Relay selection is attractive due to its high performance, energy efficient use and bandwidth resources, and simplicity .
The best relay selection scheme for cooperative networks has been introduced in and called it opportunistic retransmission. According to opportunistic retransmission, a single relay is selected from a set of N retransmission nodes, depending on the relay that provides the best "end-to-end" route between the source and the destination. The authors of showed that this scheme has the same order of diversity as cooperative diversity using space-time-coding in terms of the interruption of the decoding-and-forward and amplify-and-forward probability Schemes. However, this important result was obtained using an asymptotic semi- analytical analysis only with high SNR (without deriving a closed-form expression for the probability of interruption). Many different schemes have been proposed for the selection of a single relay . The authors of analyzed the adaptive DAF retransmission technique where among N relays that can participate, only k relays (k <N), with good channels to the source to decode and retransmit the information from source to destination. The authors of demonstrated that increasing the number of potentially participating relays, N, does not always decrease the probability of interruption. To improve the performance of the interrupt probability, the authors in suggested that only the best relay between the decoding group, Đ will send another copy of the source signal to the destination. Therefore, the total number of channels (or time intervals) required is reduced from k +1 to only two. For this proposed scheme, the authors in derived the high SNR interrupt probability approximation and showed that it exceeds the space-time distributed codes for networks with more than three retransmission nodes. The authors presented a performance analysis for AAF cooperative communications with relay selection and derived closed expressions for the average SER yield for the BPSK, M-PSK and M-QAM signals, also deriving a closed-form expression for The probability of interruption, and an analytical expression for the average end-to-end SNR gain obtained from relay selection.