Performance analysis of dual-hop relay systems with single relay selection in composite fading channels

https://doi.org/10.1016/j.aeue.2011.04.013Get rights and content

Abstract

In this paper, we present novel and easy-to-evaluate expressions for the performance of dual-hop relaying with best relay selection operating over generalized-K fading channels. Since it is hard to find a closed-form expression for the probability density function (PDF) of the exact end-to-end signal-to-noise ratio (SNR) at the destination node even for the single dual-hop system with amplify-and-forward (AF) relaying, we use a tight upper bound value instead. Using the approximate value for the end-to-end SNR, closed-form expressions for the statistics of the SNR, the average bit and symbol error probabilities, and the ergodic capacity for the single dual-hop AF relay system, are derived. Moreover, assuming independent nonidentical fading conditions across multiple dual-hop relay links, we derive lower performance bounds for the single relay selection scheme with AF relaying. The final expressions are useful in the performance evaluation of AF opportunistic relaying in a generalized composite radio environment. Simulation results are also given to verify the analytical results.

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]fX(x)=4(m/Ω)(k+m)/2Γ(m)Γ(k)xk+m1Kkm2mΩ1/2x,x0where 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]γend()=γ1γ2γ1+γ2+1.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 mi=1,ki=1.5i=1N, 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

References (25)

  • J.N. Laneman et al.

    Cooperative diversity in wireless networks: efficient protocols and outage behavior

    IEEE Trans Inform Theory

    (2004)
  • A. Bletsas et al.

    A simple cooperative diversity method based on network path selection

    IEEE Trans Commun

    (2006)
  • M.O. Hasna et al.

    End-to-end performance of transmission systems with relays over Rayleigh-fading channels

    IEEE Trans Wireless Commun

    (2003)
  • M.O. Hasna et al.

    Harmonic mean and end-to-end performance of transmission systems with relays

    IEEE Trans Commun

    (2004)
  • T.A. Tsiftsis et al.

    BER analysis of collaborative dual-hop wireless transmissions

    Electron Lett

    (2004)
  • S.S. Ikki et al.

    Performance analysis of cooperative diversity wireless networks over Nakagami-m fading channel

    IEEE Commun Lett

    (2007)
  • S.S. Ikki et al.

    Performance analysis of dual-hop relaying communications over generalized Gamma fading channels

  • S.S. Ikki et al.

    Performance of multi-hop relaying systems over Weibull fading channels

    New Technol Mobil Secur

    (2007)
  • Ikki SS, Ahmed MH. Performance of multiple-relay cooperative diversity systems with best relay selection over Rayleigh...
  • Y. Zhao et al.

    Symbol error rate of selection amplify-and-forward relay systems

    IEEE Commun Lett

    (2006)
  • D.S. Michalopoulos et al.

    Performance analysis of single relay selection in Rayleigh fading

    IEEE Trans Wireless Commun

    (2008)
  • E. Beres et al.

    Selection cooperation in multi-source cooperative networks

    IEEE Trans Wireless Commun

    (2008)
  • Cited by (27)

    • Novel MGF expressions of F composite fading channels with applications

      2021, AEU - International Journal of Electronics and Communications
    • Performance analysis of OFDM based 3-hop AF relaying network over mixed Rician/Rayleigh fading channels

      2018, AEU - International Journal of Electronics and Communications
      Citation Excerpt :

      In this work, AF relaying is preferred over DF due to its low computational complexity and reduced implementation cost, however, DF outperforms the AF in terms of bit error rate (BER) in high SNR regime. A detailed study of various relaying schemes and their advantages and disadvantages are described in [3,11–16]. Further, AF relaying can be categorized into variable-gain and fixed-gain relaying.

    • Performance analysis of space shift keying for AF relaying with relay selection

      2017, AEU - International Journal of Electronics and Communications
      Citation Excerpt :

      Therefore, there is a trade-off between data rate and the error performance in cooperative networks. In this context, relay selection, which provides improved error performance compared to single-relay transmission and avoids the reduction in the spectral efficiency at the same time, can be an efficient solution [14,15]. Many studies have combined SM and SSK schemes with cooperative networks in recent years.

    • A simplified exact expression of SEP for cross QAM in AWGN channel from M × N rectangular QAM and its usefulness in Nakagami-m fading channel

      2017, AEU - International Journal of Electronics and Communications
      Citation Excerpt :

      The applicability of the proposed SEP expressions to Nakagami-m fading channel is also addressed in this paper. The approach proposed for AWGN and Nakagami-m fading (including Rayleigh fading) can be easily extended to other complex fading statistics by solving the related SEP integrals as in [12]–[15] and [16]. The proposed SEP analysis can also be applied to diversity reception like in [17]–[22] and [23].

    View all citing articles on Scopus
    View full text