Average SNR and Ergodic Capacity Analysis for Opportunistic DF Relaying with Outage over Rayleigh Fading Channels

In the paper, we deal with a single-selection opportunistic relaying with the decode-and-forward (DF) protocol over Rayleigh fading channels. The exact end-to-end average signalto- noise ratios (SNR) and ergodic capacities of both proactive and reactive opportunistic relaying are derived as a closed-form for arbitrary link SNR. In addition, the effective ergodic capacity satisfying the minimum required data rate without outage is also identified for both relaying schemes. The analysis results are used to demonstrate which relaying scheme outperforms the other for given system parameters.     

Outage Probability of Decode‐and‐Forward Relaying Systems with Efficient Partial Relay Selection in Nakagami Fading Channels

Recently, efficient partial relay selection (e‐PRS) was proposed as an enhanced version of PRS. In comparing e‐PRS, PRS, and the best relay selection (BRS), there is a tradeoff between complexity and performance; that is, the complexity for PRS, e‐PRS, and BRS is low to high, respectively, but vice versa for performance. In this paper, we study the outage probability for e‐PRS in decode‐and‐forward (DF) relaying systems over non‐identical Nakagami‐m fading channels, where the fading parameter m is an integer. In particular, we provide closed‐form expressions of the exact outage probability and asymptotic outage probability for e‐PRS in DF relaying systems. Numerical results show that e‐PRS achieves similar outage performance to that of BRS for a low or medium signal‐to‐noise ratio, a high fading parameter, a small number of relays, and a large difference between the average channel powers for the first and the second hops.     

物理层网络编码机会中继及中断性能分析

该文研究了频率非选择性瑞利衰落信道中的物理层网络编码系统容量问题。基于放大转发机制提出了一种基于最大最小互信息准则的机会中继策略。在瑞利衰落信道环境下,从双向通信的角度,通过理论分析得出其中断概率解析式,同时推导了理想物理层网络编码和传统直接传输系统的中断概率解析式。通过理论分析,发现在某些节点发射功率条件下,系统中断概率将完全取决于单向链路。在此基础上完成了数值仿真实验,结果表明所提策略的中断性能与理想物理层网络编码和传统直接传输相比有了显著的提高。     

Power allocation for bidirectional AF relaying over rayleigh fading channels

This letter presents two novel power allocation schemes for bidirectional amplify-and-forward (AF) relaying over Rayleigh fading channels through the exploitation of channel mean strength. The first scheme aims to maximize the upper bound of average sum rate, and the other aims to achieve the trade-off of outage probability between two terminals. Numerical results show considerable performance improvement in comparison with conventional power allocation approaches.     

Closed-Form Solution of Outage Capacity for Cooperative DF and AF Relay Network

Cooperative relaying permits one or more relays to transmit a signal from the source to the destination, thereby increasing network coverage and spectral efficiency. The performance of cooperative relaying is often measured as outage probability. However, appropriate measure for the channel quality is outage capacity. Although the outage probability for cooperative relaying protocol has been analyzed before, very little research has been addressed for the outage capacity. This paper is the first of its kind to derive a closed-form analytical solution of outage capacity using fixed decode and forward relaying and amplify and forward relaying in independent but non identically distributed (i.n.i.d.) Rayleigh fading channels, considering channel coefficients known to the receiver side. The analytical results show a tradeoff between the SNR and the number of relays for a specific outage capacity. A comparison between decode and forward relaying and amplify and forward relaying shows that decode and forward relaying outperforms amplify and forward relaying for a large number of relays.     

Transactions Letters - Outage Capacity and Optimal Power Allocation for Multiple Time-Scale Parallel Fading Channels

In this paper, we address the optimal power allocation problem for minimizing capacity outage probability in multiple time-scale parallel fading channels. Extending ideas from the work of Dey and Evans (2005), we derive the optimal power allocation scheme for parallel fading channels with fast Rayleigh fading, as a function of the slow fading gains. Numerical results are presented to demonstrate the outage performance of this scheme for lognormal slow fading on two parallel channels.     

Performance analysis of spectrally efficient amplify‐and‐forward opportunistic relaying scheme for adaptive cooperative wireless systems

In this paper, we propose an adaptive amplify‐and‐forward (AF) relaying scheme that selects the best relay among the available relay nodes opportunistically to cooperate with a source node for improvement of the spectral efficiency. This improvement can be achieved by introducing a policy that gives the useful cooperative regions and defines a switching threshold signal‐to‐noise ratio that guarantees the bit error rate (BER) of cooperative transmission is below the target. We model all links as independent non‐identically distributed Rayleigh fading channels. We then derive closed‐form expressions for the average spectral efficiency, average BER, and outage probability when an upper bound for the signal‐to‐noise ratio of the end‐to‐end relay path is applied and adaptive discrete rate is considered. Numerical and simulation results show that the proposed scheme, compared with the outage‐based AF incremental relaying, AF fixed relaying, and the conventional direct transmission, can achieve the maximum average spectral efficiency while maintaining the average BER and outage probability. Copyright © 2013 John Wiley & Sons, Ltd.     

Statistical channel knowledge-based optimum power allocation for relaying protocols in the high SNR regime

We are concerned with transmit power optimization in a wireless relay network with various cooperation protocols. With statistical channel knowledge (in the form of knowledge of the fading distribution and the path loss information across all the nodes) at the transmitters and perfect channel state information at the receivers, we derive the optimal power allocation that minimizes high signal-to-noise ratio (SNR) approximations of the outage probability of the mutual information (MI) with amplify-and-forward (AF), decode-and-forward (DF) and distributed space-time coded (DSTC) relaying protocols operating over Rayleigh fading channels. We demonstrate that the high SNR approximation-based outage probability expressions are convex functions of the transmit power vector, and the nature of the optimal power allocation depends on whether or not a direct link between the source and the destination exists. Interestingly, for AF and DF protocols, this allocation depends only on the ratio of mean channel power gains (i.e., the ratio of the source-relay gain to the relay-destination gain), whereas with a DSTC protocol this allocation also depends on the transmission rate when a direct link exists. In addition to the immediate benefits of improved outage behavior, our results show that optimal power allocation brings impressive coding gains over equal power allocation. Furthermore, our analysis reveals that the coding gain gap between the AF and DF protocols can also be reduced by the optimal power allocation     

Performance Analysis of the Dual-Hop Asymmetric Fading Channel

In real wireless communication environments, it is highly likely that different channels associated with a relay network could experience different fading phenomena. In this paper, we investigate the end-to-end performance of a dualhop fixed gain relaying system when the source-relay and the relay-destination channels experience Rayleigh/Rician and Rician/Rayleigh fading scenarios respectively. Analytical expressions for the cumulative distribution function of the end-to-end signal-to-noise ratio are derived and used to evaluate the outage probability and the average bit error probability of M-QAM modulations. Numerical and simulation results are presented to illustrate the impact of the Rician factor on the end-toend performance. Furthermore, these results confirm that the system exhibits an improved performance in a Rician/Rayleigh (source-relay link/relay-destination link) environment compared to a Rayleigh/Rician environment.     

Decouple-and-Forward Relaying for Dual-Hop Alamouti Transmissions

In this letter, decouple-and-forward (DCF) relaying for dual-hop Alamouti transmissions is proposed as enhanced amplify-and-forward (AF) relaying to achieve spatial diversity gain especially provided by a two-antenna relay. DCF relaying that consists of decoupling, re-encoding and amplifying needs a little more complicated relay than AF relaying but a less complicated one than decode-and-forward (DF) relaying. Assuming uncorrelated Rayleigh fading channels, we derive a probability density function (PDF) of end-to-end signal-to-noise ratio (SNR) for the DCF system and provide its bit error rate (BER) performance. Numerical investigation shows that the analysis provided in this letter is exact and in dual-hop Alamouti transmissions, DCF achieves BER close to DF and even better BER when SNR is low.     

基于发射分集的多点中继合作通信系统性能研究

为了降低合作通信系统中的误码率和中断概率,本文研究了多点中继合作通信系统.采用矩母函数(Moment Generating Function)分析方法,通过引入超几何函数,详尽推导出Rayleigh衰落信道下的平均符号错误率和中断率的精确表达式.通过蒙特卡洛仿真,验证了表达式的正确性,其性能优于单点中继合作通信系统.     

增强合作中继系统在多径阴影联合衰落信道下的性能分析

针对数字通信系统在多径阴影联合衰落信道下不易获得性能闭式解的问题,运用MG（mixture Gamma）模型近似了NL（Nakagami-lognormal）衰落信道模型,在各跳具有独立不同衰落分布下研究和推导了增强合作中继系统的误码率和中断性能,数值和仿真分析验证了理论分析的正确性。结果表明运用MG近似NL模型有助于合作中继系统在多径阴影联合衰落信道下的性能研究。     

Cooperative multiple relay system for frequency selective environment: outage analysis and power allocation

In this paper, we propose a novel cooperative relaying scheme with multiple relays for frequency selective wireless environment. In our proposed scheme, the frequency selective wireless channel is divided into flat fading sub‐channels. Cooperative relaying is then employed over each sub‐channel to improve the system diversity order. We then investigate the asymptotic behavior of the outage probability and show that the proposed scheme achieves full diversity order in both amplify and forward (AF) and adaptive decode and forward (ADF) relaying scenarios. Furthermore, we propose a power allocation strategy to minimize the system outage probability. Simulation results confirm our analysis and show that the proposed power allocation method outperforms uniform power allocation. Copyright © 2010 John Wiley & Sons, Ltd.     

不对称放大转发双向中继功率分配及中继位置选择

该文研究基于放大转发中继的不对称双向中继系统容量问题。首先,在瑞利衰落信道环境下,从双向通信的角度,通过理论分析得出其中断概率精确表达式和渐进表达式。理论分析发现节点发射功率和源节点目标速率共同决定系统中断概率,并且在大多数业务下系统中断性能仅取决于单向链路,而与另一链路无关。基于此,以优化系统中断性能为目标,提出一种基于业务知识的节点功率分配算法和中继位置选择算法。数值仿真实验结果表明,通过功率分配和中继位置选择可以显著提高不对称放大转发双向中继系统的中断性能。     

Bit error probability of distributed Turbo coded relay systems over quasi-static Rayleigh fading channels

As is known, distributed Turbo coding (DTC) performs close to the theoretic outage probability bound of a relay channel when correct decoding is assumed at the relay. However, decoding error is inevitable in practical fading channels due to the error-prone feature of radio channels, and the decoding error propagation in DTC scheme will severely degrade the error performance of the relay system. As a result, it is necessary to evaluate the error performance of the DTC scheme in multi-hop relaying wireless systems in practical fading channels. Moreover, the theoretical method of analysis provides an effective tool for obtaining the error performance besides lengthy simulations. In this article, the concept of equivalent signal-to-noise ratio (SNR) of the two-hop relay channel and the method of computing equivalent SNR are developed, and then the upper bound on the bit error probability (BEP) of DTC relay systems is analyzed by use of Turbo code's distance spectrum, the concept of uniform interleaver, the limit-before-averaging technique, and the union bound method. Both theoretical analysis and numerical simulation are implemented for relay systems with DTC scheme over quasi-static Rayleigh fading channels. The results show that the upper bound approaches the simulation results in the medium to high SNR region.     

Cooperative Fading Regions for Decode and Forward Relaying

Cooperative transmission protocols over fading channels are based on a number of relaying nodes to form virtual multi-antenna transmissions. Diversity provided by these techniques has been widely analyzed for the Rayleigh fading case. However, short range or fixed wireless communications often experience propagation environments where the fading envelope distribution is meaningfully different from Rayleigh. The main focus in this paper is to investigate the impact of fading distribution on performances of collaborative communication. Cooperative protocols are compared to co-located multi-antenna systems by introducing the concept of cooperative fading region. This is the collection of fading distributions for which relayed transmission can be regarded as a competitive option (in terms of performances) compared to multi-antenna direct (noncooperative) transmission. The analysis is dealt with by adopting the information theoretic outage probability as the performance metric. Cooperative link performances at high SNR are conveniently expressed here in terms of diversity and coding gain as outage parameters that are provided by the fading statistics of the channels involved in collaborative transmission. Advantages of cooperative transmission compared to multi-antenna are related to the propagation environment so that the analysis can be used in network design.      

Power Allocation for Amplify-and-Forward Relaying with Correlated Shadowing

Power allocation is a key technique to exploit the benefits of cooperative relaying. In this paper, we investigate the effect of shadowing on the power allocation of amplify-and-forward cooperative relaying systems. Considering the joint effects of path loss, correlated shadowing and flat Rayleigh fading, the approximate outage probability at high signal-to-noise ratio (SNR) is first derived. Then we solve the power allocation problem by minimizing the approximate outage probability subject to a total power constraint. It is shown by the analytical results that the correlation coefficients and the standard deviations of shadowing have significant impacts on the power allocation. The simulation results show that the proposed power allocation scheme yields about 2 dB SNR gain compared to the equal power allocation in the high SNR regime.     

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。      

Performance analysis of single relay selection in rayleigh fading

We provide closed-form expressions for the outage and bit error probability (BEP) of uncoded, threshold-based opportunistic relaying (OR) and selection cooperation (SC), at arbitrary signal to noise ratios (SNRs) and number of available relays, assuming decode-and-forward relays and Rayleigh fading channels. Numerical results demonstrate that SC performs slightly better in terms of outage probability; in terms of BEP, both systems may outperform one another, depending on the SNR threshold that determines the set of relays that participate in the forwarding process.     

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.