Physical Communication 20 (2016) 85–92 Contents lists available at ScienceDirect Physical Communication journal homepage: www.elsevier.com/locate/phycom Full length article Error rate analysis of AF-relay wireless networks under different SNR levels Muhammad I. Khalil ∗ , Stevan M. Berber, Kevin W. Sowerby Department of Electrical and Computer Engineering, University of Auckland, New Zealand article info Article history: Received 16 October 2015 Received in revised form 23 April 2016 Accepted 16 June 2016 Available online 30 June 2016 Keywords: Amplify-and-forward Asymptotic bit error rate Exact bit error rate Signal-to-noise ratio abstract This paper presents a new method for analyzing the Bit Error Rate (BER) performance of two-hop Amplify-and-Forward Multiple Relay (AF-MR) networks. This paper considers, a flat-fading channel and a relay selection scheme to select a relay with the highest Signal- to-Noise Ratio (SNR). The method aims to unify the BER calculation under low, high and optimal SNR levels. Asymptotic BER (ABER) performance at high SNR value is calculated first, and standard expressions for exact BER (EBER) performance at low and optimal SNRs are then derived. The analytic method depends on the conventional BER (CBER) approach of one-hop communication systems. The optimal SNR is obtained by balancing energy efficiency and spectral efficiency. The proposed method is found to be effective for calculating the BER of AF-MR network performance under any SNR conditions. Moreover, it improves the accuracy of ABER performance by reducing disparity computation errors between ABER and EBER performances and this allows the BER of AF-MR networks to be accurately calculated using either ABER or EBER. The outcome expressions for the method are validated by simulation results. © 2016 Elsevier B.V. All rights reserved. 1. Introduction Wireless relay networks have emerged as one of the most promising techniques for enhancing the performance of wireless networks by replacing the direct transmission link (one-hop) into two links (two-hop) [1]. They achieve considerable performance improvement in link reliability, spectral efficiency (SE) [2], Energy Efficiency (EE) [3] and BER performance [4]. The relay networks are classified into two main protocols, Amplify-and-Forward (AF) and Decode-and-Forward (DF) [5]. The AF relay acts as a repeater which amplifies input signals without any further processing, while the DF relay decodes the input signal and re-encodes it prior to retransmission [6]. The AF relay is of relatively low complexity, requires less hardware and is expected to be widely employed in future cellular ∗ Corresponding author. E-mail address: mkha232@aucklanduni.ac.nz (M.I. Khalil). networks, where a base station (or equivalent source node) can broadcast signals to mobile phones (i.e., destinations) through intermediate relay nodes [7]. It is, however, not without problems. One major problem with the AF-relay network is that it amplifies both the source signal and noise [8]. Therefore, such networks will be limited by the noise, which in turn increases error rate of the transmission signal, especially at low SNR level [1]. This paper aims to examine a new method that allows us to calculate the BER of an AF-MR network, which is defined as the number of errors in a given number of transmitted bits. Various methods have been proposed to analyze the BER performance of wireless networks. An early method was investigated by [9] to calculate the ABER of one hop communication system using various diversity techniques. In this study, a high SNR level for fading channels was adopted and different M-ary Phase Shift keying (MPSK) modulation schemes were used. It was found that the high SNR approximations are very useful for wireless performance analysis. http://dx.doi.org/10.1016/j.phycom.2016.06.002 1874-4907/© 2016 Elsevier B.V. All rights reserved.