On the Performance of Cellular Two-Way Relay Systems with Analog Network Coding and Multiuser Diversity

We consider a cellular two-way relaying system in which a multi-antenna base station (BS) communicates bidirectionally with one of several single-antenna mobile stations (MSs) via a single-antenna relay using analog network coding. We employ MS selection coupled with beamforming at the BS so as to maximize the end-to-end signal-to-noise ratios. In the considered system, the target rates at the sources can generally be different owing to the asymmetric traffic flow in opposite directions. With such a general setup, we perform an overall system outage probability analysis over Rayleigh fading channels. For more insights, we derive a closed-form asymptotic expression for overall outage probability and an upper bound expression for ergodic sum-rate of the system. Based on these expressions, we show that the system achieves a performance gain, and a diversity order of minimum of the number of BS antennas and the number of MSs. Moreover, we address the problem of optimization of relay location in order to minimize the overall system outage under asymmetric traffic conditions. Finally, we provide numerical and simulation results to corroborate the theoretical analysis and the advantages offered by the proposed scheme.     

Performance Analysis of Dual-Hop AF Relay Networks in the Presence of Channel Estimation Errors and Feedback Delay

In this letter, we investigate the performance of multiple-input multiple-output two hop beamforming amplify-and-forward (AF) relay networks under imperfect channel state information (CSI) including channel estimation errors (CEE) and feedback delay (FD). To quantify the effect of imperfect CSI on our considered network, we derive the closed-form expression for the outage probability. To gain more insight, we also present an asymptotic analysis which provides the details of the diversity order and array gain. Through our works, one can see the effect of CEE and FD on the system as well as the benefits of deploying multiple antennas at the terminals. Numerical and simulation results are provided to verify the analysis and compare the performance of the considered network for two different models for channel estimation error.     

Bidirectional relaying with energy harvesting capable relay: outage analysis for Nakagami-<Emphasis Type="Italic">m</Emphasis> fading

This paper analyzes outage probability of bidirectional relaying (BDR) where two power-unconstrained single-antenna sources communicate with each other under assistance of a self-powered half-duplex single-antenna relay capable of energy harvesting and amplify-and-forward implementation. The relay harvests radio energy from both sources to power its relaying operation with the power splitting method. For outage analysis of the BDR for Nakagami-m fading, an exact formula is first proposed in closed-form. Through this formula, influences of important specifications (time switching ratio, power splitting ratio, energy conversion efficiency, fading severity, target transmission rate, transmit power of each source, distances from sources to relay) on the outage probability are then evaluated. Finally, Monte-Carlo simulations are generated to corroborate the proposed formula.     

非正交多址接入系统中的联合中继选择和用户配对算法

针对多用户NOMA中继系统,文中提出了一种联合中继选择和用户配对算法。该算法首先利用最小距离准则选择最优次级用户与主用户配对,然后进行最优中继选择来改善系统中断性能。根据系统模型的分析,推导了系统中断概率的准确表达式,并分析了高信噪比条件下的渐近中断性能。系统分集阶数的研究说明了所提NOMA中继系统相比于传统单中继NOMA系统的优越性。最后,蒙特卡洛仿真结果验证了理论分析的正确性。     

Distributed transmit-antenna selection in variable-gain relaying systems

Recently, distributed transmit-antenna selection schemes have attracted great interest, since they capture the essential benefits of multi-antenna systems while reducing their cost, complexity, delay, and feedback overhead. In those distributed schemes, the antenna selection is based on local channel-state information, in contrast to their optimal centralized counterparts, which require knowing the channel state of all links. Herein, we design two such distributed schemes for a dual-hop variable-gain amplify-and-forward relaying system with one multi-antenna source, one single-antenna relay, and one single-antenna destination. The two schemes differ in the diversity method used at the destination, namely, selection combining or maximal-ratio combining, and in the selection rule accordingly. In addition to conceiving these new schemes, we analyze their outage performance. Since an exact analysis proves intractable, we tackle the outage probability in terms of lower-bound expressions and their asymptotes at high signal-to-noise ratio. Importantly, the derived bounds turn out to be almost indistinguishable from the true performance, assessed via simulation. Our results reveal that the proposed distributed schemes achieve the same diversity order of their optimal centralized counterparts and perform closely to these, specially when the relay is near the source or destination.     

A Cooperative Relay Selection for Two-Way Cooperative Relay Networks in Nakagami Channels

We investigate the performance of the best-worse relay selection strategy in a two way cooperative non-regenerative relay network, where the relay is selected to maximize the worst Signal to Noise Ratio (SNR) of two links. In contrast to existing work, we aim to provide a theoretical performance analysis for this scheme under the more practical Nakagami channel. Closed-form expression of the probability density function for the SNRs of both two links is derived, based on which the outage probability of the best-worse relay selection is obtained. It is shown that the best-worse relay selection scheme achieves full diversity gain. Furthermore, the asymptotic packet error ratio with SNR increasing is also analyzed through rigorous derivations. The accuracy of our derivation is validated by computer simulations.     

Nth best relay selection with network coding in two‐way relay systems

In this paper, we propose an Nth best relay selection (Nth‐RS) scheme for analog network coding in two‐way relay systems. In traditional two‐way single‐relay selection schemes, only the best one is selected to forward network‐coded signals. However, in practical applications, the best relay may be unavailable because of the scheduling or overload constraints. In this case, we investigate a more general scheme, where the Nth best but available relay is selected. To evaluate the transmission of reliability, the expression of outage probability in exponential–integral form and its asymptotic expression in closed form are presented. Moreover, the upper bound and lower bound of outage probability are also derived. The analysis reveals that the diversity order of Nth‐RS equals to (M ? N + 1), where M is the number of relay nodes, and the results are verified by simulations. In order to improve system performance, transmit power between sources and relay is optimally allocated to minimize the upper bound of outage probability under total power constraint. Simulation results show that Nth‐RS scheme with proposed power allocation can achieve substantial improvement over equal power allocation scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

Outage analysis of opportunistic multi-antenna relay selection in decode-and-forward relay networks

This article studies the closed-form expressions of outage performance for opportunistic relay under aggregate power constraint in decode-and-forward(DF)relay networks over Rayleigh fading channels,assuming that multiple antennas are available at the relay node.According to whether instantaneous signal-to-noise ratio(SNR)or average SNR can be utilized for relay selection,two opportunistic relay schemes,opportunistic multi-antenna relay selection(OMRS)and average best relay selection(ABRS)are proposed.The performances of both two schemes are evaluated by means of theoretical analysis and simulation.It is observed that OMRS is outage-optimal among multi-antenna relay selection schemes and closely approaches the beamforming(BF)scheme known as theoretical outage-optimal.Compared with previous single-antenna opportunistic relaying(OR)scheme,OMRS brings remarkable performance improvement,which is obtained from maximum ratio combining(MRC)and beamforming techniques.It is also shown that the performance of ABRS in asymmetric channels is close to OMRS in the low and median SNR range.     

Asymptotic Analysis of Opportunistic Relaying Protocols

In this letter, we examine in detail a cooperative network with multiple relays. We investigate protocols that incorporate the opportunistic relaying technique, which selects the ?best? relay among the M available relays. We evaluate the asymptotic outage performance of incremental amplify-andforward (IAF) when it is extended to the opportunistic relaying scenario. Moreover, we propose two new protocols, namely opportunistic incremental selection AF and opportunistic joint incremental selection relaying, and derive the corresponding asymptotic outage probabilities. Finally, we compare the analytical asymptotic outage probabilities and the simulated ones. We conclude that the OJISR protocol outperforms the other protocols.     

Analysis of Network Path Selection Based on Outage Probability in Cognitive Relay Networks

This paper evaluates the outage performance of cognitive relay networks with mutual interference between secondary users and primary users under the underlay approach, while adhering to the interference constraint on the primary user. A network path selection criterion, suitable for cognitive relay networks, is provided, from which we derive the outage probability expression of cognitive relay networks. It is shown that the outage probability considering the interference to secondary user from primary user is higher than that without considering the interference to secondary user from primary user. In addition, the outage probability is affected by key network parameters. We analyze network path selection method based on outage probability and prove that the interference to secondary user from primary user has a significant effect on the network path selection and can not be ignored in practical wireless communication environments. Simulation investigation is also provided and used to verify the theoretical analysis.     

Joint Relay and Antenna Selection in MIMO PLNC Inter-vehicular Communication Systems over Cascaded Fading Channels

We investigate the joint relay and antenna selection performance in a multiple input multiple output (MIMO) Vehicle-to-Vehicle (V2V) communication system employing physical layer network coding (PLNC) with amplify-and-forward (AF) scheme at the relay antenna. Analytic results are derived under the cascaded Nakagami-m fading channel model assumption, which covers cascaded Rayleigh and conventional cellular channel models as well. We evaluate the performance of the system in terms of joint outage probability of sources and derive closed-form expressions for lower and upper bounds while an exact expression is found as a single integral form. Besides, the asymptotic diversity order is analyzed and quantified as a function of number of relays and antennas installed on the source and relay vehicles, and channel parameters. Finally, we verify the analytic derivations by computer simulations. Our results show that the outage probability performance decreases with the increasing cascading degrees of the channels but joint relay and antenna selection enhances the performance of the system superbly with the increasing number of relays and antennas. Also it is shown throughout all the simulation results, the lower bound for the joint outage probability seems to consistently be well tight for large SNR. Therefore it can be used for practical design of inter-vehicular communication systems which contain multiple relays and antennas.     

能量收集认知多跳中继网络中断性能分析及优化

针对能量收集认知无线网络中的多跳中继传输问题,该文构建了一种新的具有主网络干扰的功率信标(PB)辅助能量收集认知多跳中继网络模型,并提出单向传输方案。在干扰链路统计信道状态信息场景下,推导了次网络精确和渐近总中断概率闭合式。针对精确总中断概率表达式的复杂性和非凸性,采用自适应混沌粒子群优化(ACPSO)算法对次网络总中断性能进行优化。仿真结果表明,PB功率、干扰约束、次网络跳数、能量收集比率、主接收端数目和信道容量阈值等参数对中断性能影响显著,所提算法能快速和有效地对网络中断性能进行优化。     

Exact SEP and performance bounds for orthogonal space‐time block codes in cooperative multiantenna AF relaying networks

In this paper, we derive a moment generating function (MGF) for dual‐hop (DH) amplify‐and‐forward (AF) relaying networks, in which all nodes have an arbitrary number of antennas, with orthogonal space‐time block code (OSTBC) transmissions over Rayleigh fading channels. We present an exact error rate expression based on the derived MGF and another analytical approach to derive achievable performance bounds as closed‐forms of symbol error rate, outage probability, and normalized channel capacity. Furthermore, we derive the asymptotic behavior of symbol error rate and outage probability. From this asymptotic behavior, it is shown that the diversity order and its dependence on antenna configurations can be explicitly determined. Simulation results are also presented to verify their accuracy by comparing with numerical results and to provide an insight to the relationship between relaying networks' antenna configuration and diversity order. It is confirmed that the transmit antenna gain of the source node and the receive antenna gain of the relay node can be obtained only when the relay is close to the destination, and then, the transmit antenna gain of the relay node and the receive antenna gain of the destination node can be obtained only when the relay is close to the source.     

Three-phase two-way relaying with imperfect channel estimation and asymmetric traffic requirements: performance analysis and optimization

We study the effect of imperfect channel estimation (ICE) and asymmetric traffic requirements (ATRs) on the performance of bidirectional relaying with a direct link by employing three-phase analog network coding under Nakagami-m fading. Under such a realistic scenario, a tight lower bound on the overall outage probability is derived in closed-form, while a useful expression is presented for the asymptotically low outage regime. We also deduce the tight closed-form expression for the ergodic sum-rate. Furthermore, we formulate and solve analytically three optimization problems viz., relay power allocation under fixed location of the relay, relay position with fixed relay power allocation, and joint optimization of relay power allocation and location. Our results reveal that for given ICE, the optimal relay location offers significant system performance enhancement under ATRs, whilst the optimal relay power allocation has a more noticeable impact under symmetric traffic. It is also shown that the joint optimization of relay power allocation and location can further enhance the system performance, regardless of ATRs and ICE. Above all, based on the direct link quality, we show that the considered scheme outperforms its two-phase counterpart, even in the low signal-to-noise ratio regime.

     

多中继与多用户选择的中继系统安全性能分析

为了考察使用多中继选择与多用户选择的放大转发（AF）中继系统的物理层安全性能,推导了其在瑞利衰落信道上和联合发送天线选择/接收最大比合并天线分集下的非零安全容量概率和安全中断概率的精确表达式以及在高信噪比下的渐近安全中断概率解析表达式。AF中继系统的非零安全容量概率和安全中断概率的数值计算和仿真结果相吻合,验证了以上理论分析的正确性;分析结果表明,其安全分集增益为源节点发射天线数、最优中继节点接收天线数、中继节点数的三者乘积与最优中继节点发射天线数、最优用户接收天线数、用户数三者乘积之间的最小值,且与窃听信道无关。     

Performance Analysis and Enhancement for Opportunistic Analog Network Coding with Imperfect CSI

Imperfect channel state information (CSI) is among the main factors that affect system performance in wireless networks. In this paper, we investigate the impact of imperfect CSI on the performance of analog network coding (ANC) for a two-way relaying system based on opportunistic relay selection (ORS). An exact and generalized closed-form expression for system outage probability is presented in a Rayleigh flat-fading environment. To provide more insights, the closed-form asymptotic expression is then obtained. It is shown that the presence of channel estimation error causes outage probability maintain a fixed level even when a noiseless channel is adopted. Therefore, to mitigate the negative impact of imperfect CSI, we deduce the power allocation to minimize the system outage probability based on the knowledge of instantaneous channel information. Numerical results validate the accuracy of the derived expressions and highlight the effect of proposed power allocation algorithm compared with conventional uniform power allocation.     

同频干扰环境下双向AF中继性能分析及参数优化

双向中继（two-way relaying, TWR）作为提高中继网络频谱效率的一种有效手段,近年来受到广泛关注。本文研究同频干扰环境下三时隙TWR策略的中断概率性能,中继采用放大转发（amplify-and-forward, AF）策略。首先,理论推导了策略中断概率下界的闭合表达式和高信噪比下的渐进表达式。仿真表明,理论结果能够匹配策略的实际中断概率性能。根据理论结果,以最小化中断概率为目标对中继节点功率分配和中继位置参数进行优化。提出三种优化问题,即（1）给定中继位置,中继功率分配优化问题,（2）给定中继功率分配方案,中继位置优化问题,（3）联合优化中继功率分配和中继位置。仿真结果表明,联合优化能够实现最优的中断概率性能。      

Nakagami-m信道下全双工解码转发中继中断概率分析

研究存在残余自干扰（residual self-interference, RSI）条件下全双工解码转发中继的中断概率性能。在Nakagami-m信道下,推导了多跳解码转发（multi-hop decode-and-forward,MH-DF）策略和选择解码转发（selected decode-and-forward,SDF）策略的端到端中断概率闭合表达式和渐近表达式,分析了两种策略的可达分集度。结果显示,MH-DF策略的可达分集度为0,SDF策略的可达分集度由信道成型因子和中继功率伸缩方案决定。相比于MH-DF策略,SDF策略具有更优的中断概率性能和抗自干扰能力。      

Cognitive amplify‐and‐forward relay networks with beamforming under primary user power constraint over Nakagami‐m fading channels

In this paper, we analyze the performance of cognitive amplify‐and‐forward (AF) relay networks with beamforming under the peak interference power constraint of the primary user (PU). We focus on the scenario that beamforming is applied at the multi‐antenna secondary transmitter and receiver. Also, the secondary relay network operates in channel state information‐assisted AF mode, and the signals undergo independent Nakagami‐m fading. In particular, closed‐form expressions for the outage probability and symbol error rate (SER) of the considered network over Nakagami‐m fading are presented. More importantly, asymptotic closed‐form expressions for the outage probability and SER are derived. These tractable closed‐form expressions for the network performance readily enable us to evaluate and examine the impact of network parameters on the system performance. Specifically, the impact of the number of antennas, the fading severity parameters, the channel mean powers, and the peak interference power is addressed. The asymptotic analysis manifests that the peak interference power constraint imposed on the secondary relay network has no effect on the diversity gain. However, the coding gain is affected by the fading parameters of the links from the primary receiver to the secondary relay network. Copyright © 2012 John Wiley & Sons, Ltd.     

Outage Analysis of Cognitive AF Relay Networks with Multiple Primary Users and Heterogeneous Non-identical Parameters

In this paper, we investigate outage performance of dual-hop cognitive AF relay networks with multiple primary users (PUs) and heterogeneous non-identical parameters, including non-identical Rayleigh fading channels, non-identical interference power constraints of PUs, and non-identical noise powers in signals. To overcome the analysis complexity resulted from the consideration of heterogeneous non-identical parameters completely, we conduct our analysis in two steps. In the first step, we focus on networks with non-identical Rayleigh fading channels but with identical interference power constraints and identical noise powers. As analysis results, both the exact closed-form expression and asymptotic closed-form expression of the cumulative distribution function of equivalent end-to-end signal-to-noise ratio of the network are obtained. Then in the second step, we propose a method for transforming networks with heterogeneous non-identical parameters into new networks with identical interference power constraints and identical noise powers meanwhile guaranteeing that outage performance of the two networks before and after the transformation are identical. Hence, outage performance of networks with heterogeneous non-identical parameters can be obtained by applying the analysis results in the fist step to the corresponding transformed networks. Numerical simulations validate the correctness of our analysis, and the simulations also indicate that taking multiple PUs and the diversity of the parameters into consideration is of key importance in obtaining a more accurate estimation of outage performance of such networks.