AEU - International Journal of Electronics and Communications
Performance analysis of dual-hop relay systems with single relay selection in composite fading channels
Introduction
It is well known that the cooperative diversity realized through relays can provide an increase in link quality and reliability, high data rate coverage, and mitigate channel impairments in next generation wireless systems. An overview of cooperative diversity protocols is presented in [1]. In general, there are two types of processing that can be performed at the relays. In a decode-and-forward (DF) scheme, the relay station decodes the received signal, re-encodes and then retransmits the restored signal to the destination. On the other hand, amplify-and-forward (AF) relays simply amplify and forward the signal to the destination and have attracted a lot of attention recently as they provide a simple way to implement collaborative/cooperative wireless communication systems. Furthermore, Bletsas et al. proposed in [2] a cooperative diversity protocol named opportunistic relaying technique, which selects (using a selection policy) the best relay among multiple available relays. It was then shown that the best-relay selection reduces the amount of required resources while improving the performance.
For dual-hop AF relay systems, the end-to-end SNR at the receiving end depends on the amplification gain employed at the relays. For relays with channel state information (CSI) of the first link, the end-to-end SNR has been obtained in [3]. For this relay transmission scheme, analytical performance results have been obtained by approximating the end-to-end SNR by the harmonic mean of the SNRs of the two hops [4], their geometric mean [5], and the minimum SNR of the two hops [6], [7]. In particular, using the minimum SNR approximation for the end-to-end SNR, the performance of dual-hop relaying has been studied in terms of outage probability and average bit error rate (BER) in various fading conditions, such as Rayleigh [3], Nakagami-m [6], Weibull [8] and generalized Gamma [7] fading channels.
The minimum SNR of the two hops has also been used as a selection policy as well as a bound in the performance evaluation of the best relay selection scheme based on AF [2], [9], [10] and DF [11], [12] relaying protocols. For example, in [10], the authors presented an asymptotic analysis (at high SNR values) of the average symbol error rate (SER) of an AF best relay selection scheme, and compared it with the regular cooperative systems. Furthermore, in [11], the authors derived closed-form expressions for the outage probability and the average BER of opportunistic relaying with DF relays. However, in the existing literature, almost all performance results of this transmission scheme have been restricted to the case of Rayleigh fading channel.
Recently, the generalized-K fading model [13] has attracted considerable attention as one of the most general wireless fading models that can characterize the combined effects of small and large-scale fading on the received signal. This model corresponds to a Nakagami–Gamma composite distribution and is controlled by two shaping parameters m and k, where m is the Nakagami parameter for the small-scale fading and k is the parameter of the Gamma distribution for the received average power due to shadowing [13]. Note that the K distribution [14] is derived as a special case of the generalized-K distribution by letting m = 1 (i.e., Rayleigh multipath fading). The performance analysis of single link communication systems in this fading model was given in [15], whereas for relay systems, results that have recently appeared in the literature, are restricted to the performance of dual-hop single relay systems with CSI-assisted [16] and fixed gain [17] transmission schemes. However, the analytical expressions in [16] are too complicated to be used in the performance analysis of the best relay selection scheme.
In this paper, we focus on AF dual-hop cooperative diversity networks to study their end-to-end performance over independent nonidentical generalized-K fading channels when the best relay selection scheme is employed. The main contribution of this paper includes the derivation of novel closed-form expressions for the PDF, CDF, and moment generating function (MGF) of a tight upper bound on the total SNR at the destination of the single dual-hop relayed signal. Then, using the derived CDF expression, we present performance metrics such as the outage probability and the average BER for the multiple dual-hop relay system with best relay selection operating in a generalized-K fading model with integer values for fading parameter m and arbitrary values for fading parameter k.
The rest of the paper is organized as follows. In Section 2 we present the channel model statistics. In Section 3, we derive the statistics of an upper bound approximation to the end-to-end SNR of a single dual-hop AF relay system and closed-form expressions for various performance metrics. Then, in Section 4, for the case of independent nonidentical fading across multiple relay links, we derive analytical lower performance bounds for dual-hop relay systems with single relay selection. Numerical and simulation results are given in Section 5, followed by concluding remarks in Section 6.
Section snippets
The generalized-K fading model
In many fading environments, the received signal envelope can usually be characterized by the Nakagami-m distribution. In a shadowed environment, the average power of the received signal is also random. In this work, we assume that the fading environment is such that the signal envelope X in a receive antenna is a generalized-K distributed random variable with PDF given by [13]where k and m are the distribution’s shaping parameters, Ω = E[X2]/k is
Performance analysis of single dual-hop relay system
In this section we study the performance of a single dual-hop AF relay system operating in the generalized-K fading channel. Assuming CSI-based amplification gain at the ℓ th relay (see Fig. 1), the exact end-to-end SNR of the ℓ th dual-hop link is given by [3], [4]In the literature, this relay transmission scheme is usually considered as a benchmark for cooperative performance. Since it is hard to find a closed-form expression for the PDF of the exact end-to-end SNR of
Extension to the best relay selection scheme
We now consider a cooperative diversity system where a source node communicates with a destination node through N relays, as depicted in Fig. 1. Assume that the CSI-assisted opportunistic AF relaying protocol is employed. Following the work in [2], in the opportunistic relaying mechanisms, one best relay among the multiple relays is selected during a predetermined transmission period and only that chosen relay forwards packets to the destination while the other relays are kept idle. Therefore,
Numerical results
In this section we present some numerical and simulation results for the performance of dual-hop relay transmission scheme with best relay selection, in the absence of a direct link, operating over generalized-K fading channels. The generalized-K fading model can describe different fading conditions by the appropriate choice of fading parameters m and k. For demonstration purposes, we assume N parallel dual-hop relay links with i.i.d fading conditions given by , i.e., Rayleigh
Conclusions
In this paper, we used a tight upper bound on the end-to-end SNR of a single dual-hop AF relay system to derive novel closed-form expressions for its SNR statistics, outage probability, bit error probability, and ergodic capacity. Then, using the CDF based approach, we studied the performance of the best-relay selection scheme for cooperative diversity networks operating over independent but not necessarily identical generalized-K fading channels. Computer simulation results verified the
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