Performance analysis of analog network coding based two-way amplify-and-forward system in mixed Rician and Nakagami-m fading environment
© Chaudary and Rajatheva; licensee Springer. 2012
Received: 10 December 2011
Accepted: 29 May 2012
Published: 2 July 2012
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.
KeywordsAnalog network coding (ANC) Amplify-and-forward (AF) Cumulative distribution function (CDF) Probability distribution function (PDF) Outage probability Average symbol error rate (SER) Ergodic capacity
Network coding (NC) was first introduced a decade ago , 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 . 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 researchers. Work in  presents the outage probability and average symbol error rate (SER) analysis for two-way 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  over symmetric (Nakagami-m) fading channel, and in  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-of-sight (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 . 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 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 signal-to-noise-ratio (SNR) over asymmetric (Nakagami-m and Rician) fading channels was assumed in . The asymmetric (Rayleigh and Rician) fading channels have been investigated in  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.
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.
where m is the Nakagami-m fading parameter ranging from to ∞, Γ(·) is the gamma function10, Equation 8.310.1, Γ(·,·) is the incomplete gamma function [10, Equation 8.350.2] and is the average SNR of the R→S2link. For , it exibits one-sided Gaussian distribution, for m=1, it reduces to Rayleigh distribution and it converges to a nonfading AWGN channel as m→∞.
Average symbol error rate (SER)
where is defined in . It is clear from (29) that the diversity order of the system is minm, K. The diversity order will be verified in the Section 6.
Simulation results and discussion
In this section, we analyze the performance of the analog network coded two-way relay cooperative network by plotting the analytical curves along with the simulation results and comparing them over mixed Rician and Nakagami-m fading channels. The performance of the system is analyzed by plotting the curves in terms of outage probability, average SER, ergodic capacity, and asymptotic outage probability for high SNR of the transmitted signal. We use Mathematica 7 to validate our close form analytical expressions and we build Mont-Carlo simulation using MATLAB for the system shown in Figure 1.
Figures 2, 3 and 4 show the outage probability performance of an ANC-based two-way relay network with different combinations of Nakagami-m factor values (1, 2, and 3), Rician K factor values (0, and 5 dB), and threshold SNR γthvalues (0, 5, and 10 dB). It can be observed from the figures that the increase in threshold SNR γthdegrades the performance of the system. For increasing values of K and m the performance of the system gets improved. The analytical and simulation results are in close proximity and validate the accuracy of analytical closed form expression. In high SNR region the asymptotic curves coincide with the analytical curves.
Figures 5, 6 and 7 present the average SER analysis over the mixed Rician and Nakagami-m fading channels for BPSK and QPSK modulation schemes with different Nakagami-m factor values (1, 2, and 3, respectively). The parameters for the modulation scheme are a=1,b=1 for BPSK and a=1,b=0.5for QPSK. Analytical results are obtained by substituting these parameters in (16). The results show that the performance improves with the increasing values of Rician K factor and Nakagami fading parameter m. From the examination of the slopes of SER curves, it is seen that, if we fix some value of m at the MS and change the value of K at the BS, then we can achieve a significant performance gain. In Figure 5 at average SER of 10−2, the system with m=1,K=0dB provides a performance gain of 1 dB over the system with m=1,K=5 dB for BPSK constellation. Furthermore, the system with m=1,K=10dB is generating the same performance gain over the system with m=1,K=5 dB at the average SER of 10−3. It can be shown that the diversity of system depends upon the channel conditions between the link S1 and R. Here, we have improved the quality of the link between S1and R by increasing the value of Nakagami fading parameter m from 1 to 2 as shown in Figure 6. It is observed that the system is now exhibiting a larger performance gain at high SNR regions for different values of Rician factor K. For example, when average SER = 10−3, a system with m=2,K=0dB provides a performance gain of 4 dB over the system with m=2,K=5 dB and a performance gain of 2 dB is achieved between m=3,K=5 dB and m=3,K=10 dB for BPSK modulation scheme. The same is true for m=3as shown in Figure 7, we achieved the performance gain of 5 dB between m=2,K=0 dB and m=2 and K=5 dB and a performance gain of 3 dB is achieved for the system with m=3,K=5dB over the system with m=3,K=10dB for both BPSK and QPSK modulation schemes. Moreover, the analytical closed form average SER expression is verified with Monte Carlos simulations.
Figure 8 shows the ergodic capacity for the different m and K values. The correctness of the analytical closed form expression for ergodic capacity is validated with Monte Carlos simulations. It is observed that increasing the Rician K factor or Nakagami parameter m, improves the capacity of the system.
We analyzed the performance of network coding-based two-way relay network over mixed Rician and Nakagami-m asymmetric fading channels. We derived the closed-form expressions for the outage probability, average SER using the derived CDF, and ergodic capacity using the derived PDF to predict the performance of the proposed system. The outage probability for different values of threshold SNR γth over mixed Rician and Nakagami-m fading channels was calculated, which gives a better performance with lower amount of fading (high m and K values). The average SER analysis was carried out for BPSK, and QPSK modulation schemes. It is clear from the simulation results that for higher values of m and K, better performance is achieved. In addition to that, the asymptotic outage probability for high SNR has been obtained, which provides a better understanding of the diversity order of the system.
Muhammad Hasanain Chaudary received his M.Sc. (Communications and Networks) in Computer Science and M.Sc. in Telecommunications from Bahria University, Islamabad, Pakistan and Asian Institute of Technology, Thailand respectively. He is currently working towards the PhD degree at the School of Engineering and Technology, Asian Institute of Technology, Thailand. Mr. Chaudarys research interests are in the general area of Broadband wireless networks and Signal processing for communication systems, and in particular Optimization for communication and networks, performance analysis of wireless communications systems, OFDM/OFDMA, MIMO, Network Coding and Cooperative systems.
Nandana Rajatheva received the B.Sc. degree in Electronic and Telecommunication Engineering (with first class honors) from the University of Moratuwa, Sri Lanka, and the M.Sc. and Ph.D. degrees from the University of Manitoba, Canada, in 1987, 1991, and 1995, respectively. He is an Associate Professor of Telecommunications in the School of Engineering and Technology, Asian Institute of Technology, Thailand. Currently he is a visiting Professor at the Centre for Wireless Communications, University of Oulu, Finland. He is an Editor for the International Journal of Vehicular Technology (Hindawi). His research interests include performance analysis and resource allocation for relay, Network Coding, Cognitive radio and hierarchical cellular systems.
The first author would like to thank the Higher Education Commission (HEC) of Pakistan and COMSATS Institute of Information Technology, Lahore, Pakistan for facilitating and funding this work.
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