Performance analysis of analog network coding based two-way amplify-and-forward system in mixed Rician and Nakagami-m fading environment

Chaudary and Rajatheva EURASIP Journal on Wireless Communications and Networking 2012, 2012:209 http://jwcn.eurasipjournals.com/content/2012/1/209 R ESEA R CH Open Access Performance analysis of analog network coding based two-way amplify-and-forward system in mixed Rician and Nakagami-m fading environment Muhammad Hasanain Chaudary* and Nandana Rajatheva Abstract This paper presents the performance analysis of analog network coding-based two-way amplify-and-forward relaying under mixed Rician and Nakagami-m fading environment. Closed form expressions for both the cumulative distribution function and probability distribution function of the instantaneous end-to-end SNR are derived. Using those, the closed form expressions for the first moment, second moment, and the symbol error rate (SER) for M-PSK modulated signals are obtained. The performance of the system is analyzed in terms of outage probability, average SER, and ergodic capacity. In addition, we investigate the outage probability for high SNR scenario to identify more details of the system performance in depth. Simulations are performed to verify the correctness of our theoretical analysis. Keywords: Analog network coding (ANC), Amplify-and-forward (AF), Cumulative distribution function (CDF), Probability distribution function (PDF), Outage probability, Average symbol error rate (SER), Ergodic capacity Introduction Network coding (NC) was first introduced a decade ago [1], owing to its potential for improving the performance of a wireless network. In a wireless relay network, the application of network coding at the physical layer has been shown to increase the network throughput [2]. This network throughput is achieved by reducing the number of time slots required to exchange information between two source nodes S1 and S2 via a relay node R, from four to two. Four time slots have been used traditionally. We can divide the prior related research into two main categories. The first category deals with the performance analysis over the symmetric fading channels for the relay networks (two-way, dual-hop, multi-hop, and multi-cast) [3-7]. The second category deals with the performance of relay networks over asymmetric fading channels [8,9]. In the past years, the performance of relay networks (two-way, dual-hop, multi-hop, and multi-cast) over symmetric fading channels is being carried out by many *Correspondence: Telecommunications, School of Engineering & Technology, Asian Institute of Technology, Pathumthani, 12120 Thailand researchers. Work in [3] presents the outage probability and average symbol error rate (SER) analysis for twoway amplify-and-forward relaying over the symmetric (Nakagami-m) fading channel and in [4,5] authors consider the symmetric (Rayleigh) fading channel. Along with network coding (NC) for two-way relaying the performance is studied in terms of outage probabaility and ergodic sum-rate in [6] over symmetric (Nakagami-m) fading channel, and in [7] the optimal transmission scheme analysis is carried out by computing the outage probability over symmetric (Rayleigh) fading channel. In a relay network two sources are communicating with each other by using a single relay. Considering a practical scenario, relay network may have a line-ofsight (LOS) communication in one of the sides (source to relay link) and on the other side it may have only multipath communication (relay to destination link), and vice versa [8]. In such scenario using asymmetric fading channel is a promising solution. Recently, there is an increasing research interest on the performance of relay networks over asymmetric fading channels, and some recent examples of that are [8,9]. For the dual-hop © 2012 Chaudary and Rajatheva; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Chaudary and Rajatheva EURASIP Journal on Wireless Communications and Networking 2012, 2012:209 http://jwcn.eurasipjournals.com/content/2012/1/209 amplify-and-forward relay transmission system, the performance in terms of deriving the closed form analytical expressions for cumulative distribution function (CDF) and probability density function (PDF) of end-end signalto-noise-ratio (SNR) over asymmetric (Nakagami-m and Rician) fading channels was assumed in [8]. The asymmetric (Rayleigh and Rician) fading channels have been investigated in [9] by deriving the exact and lower bound expressions for the outage probability and average bit error probability. None of these works have focused on the ergodic capacity analysis. To the best of our knowledge the performance analysis over mixed Rician and Nakagami-m asymmetric fading channels with analog network coding (ANC)-based two-way amplify-and-forward relay system has not been investigated before. Hence, in this paper we have adopted ANC-based two-way amplify-and-forward system in a mixed Rician and Nakagami-m asymmetric fading environment. We have assumed source nodes S1 and S2 to be a base station (BS) and a mobile station (MS), respectively. We have used Rician fading channel between BS and relay node R as they are assumed to have LOS communication and we have used Nakagami-m fading channel between MS and relay node R as they are considered to have only multipath communication. This particular setup is shown in Figure 1. We will analyze the performance by evaluating the closed form expressions for outage probability, average SER (using the derived CDF), and ergodic capacity (using the derived PDF). We have plotted the analytical results using these derived close form expressions. Additionally, we investigate the outage probability for high SNR regime for a more comprehensive analysis of the system performance. At high SNR, the asymptotic outage probability that is obtained is very close to the exact outage probability. Remainder of the paper is organized as follows. Section 2 presents the system model. Performance and capacity analysis are discussed in Sections 3 and 4, respectively. Section 5 provides the asymptotic analysis. Results are given in Section 6, and Section 7 concludes the paper. System Model We consider a network coding-based two-way relaying system model in mixed Rician and Nakagami-m fading Page 2 of 10 environment as shown in Figure 1. Two source nodes S1 and S2 communicate through relay node R. The Rician fading (line-of-sight) environment is employed between the S1 → R link, where as Nakagami-m fading environment is employed between the S2 → R link. The communications between the nodes is accomplished in two time slots. During the first time slot, both source nodes S1 and S2 transmit simultaneously to relay node R. During the second time slot, relay node R normalizes the received signal-based on its transmit power constraint and broadcasts t (...truncated)