## 1 Introduction  
The relentless demand for data in wireless networks has revealed some communication constraints. In fact, wireless links have always had a lower bandwidth limit than wired links. This limit forces users to use applications reminiscent of wired networks from several decades. New technologies like multiple-input and multiple-output (MIMO) systems increase the bandwidth in number of bits per second per hertz with the help of techniques like spatial multiplexing, and improve the reliability (and coverage) of the wireless link by exploiting the spatio-temporal coding and the directionality of the antennas (beamforming). However, all these improvements can be realized at the cost of several radio frequency (RF) components at the transmitter and the receiver. In addition, the size of mobile equipment may limit the number of antennas to be deployed. Even if MIMO technology is feasible, other constraints on the allocation of frequency bands to users are encountered due to historical and regulatory reasons. With this limitation, the free frequency bands show a lot of interference because of the large number of users. In order to solve these problems, the concept of cooperation between users is introduced. In a cooperative communication, several relay nodes operate together with the source node to transmit the information to the destination. Therefore, the exploitation of MIMO techniques becomes possible without the need to locate several antennas at the nodes of the network. Communication thus benefits from spatial diversity since the signals are transmitted over independent fading channels, which ensures better detection to the receiver. Cooperation techniques take advantage of the broadcasting property of the wireless signals. The fact that the signal from a source to a destination can be \"listened to\" by neighboring nodes allows the later to process the \"listen\" signal and to transmit it to the destination. The concept of cooperative diversity emerged with the study of a multi-way channel proposed by [PERSON], where the author discussed the problem associated with the three terminal communication system and provided bounds on the capacity of the relay channels [1; 2]. [PERSON] et al. were first to propose the application of diversity to enhance system performance, the authors have proposed a cooperative beamforming where source and relay nodes perform a phase adjustment to facilitate the coherent reception of multiple copies at destination node [3; 4]. A major work on a cooperative diversity scheme was done by [PERSON] et al., namely, fixed relaying, incremental relaying, and selected relaying with single source-relay and destination with no availability of channel state information (CSI) at transmitter end [5; 6]. To overcome the problem of spectrum inefficiency caused by use of relaying terminals, relay-selection schemes have been proposed in the literature. Several researchers have proved the significance of using log-likelihood ratio over SNR based schemes as log likelihood ratio (LLR) magnitude provides the reliability of hard decision. Therefore, this paper presents a LLR based dual-relay selection scheme for cooperative amplify and forward relaying system. Furthermore, a time varying characteristic of the fading environment is modelled through a three state Markov Channel.  
The rest of this paper is organized as follows: In Section 2, related work on the relay selection in a cooperative communication system has been elaborated. In Section 3, a LLR based dual relay selection scheme is discussed. In Section 4, the simulation results for the proposed scheme have been presented and, finally, Section 5 concludes this paper.