N-m衰落下双跳多中继协作通信系统的性能分析

An exact average symbol error rate analysis for the distributed dual-hop relay cooperative network with multiple relays in a Nakagami-m fading environment is presented. In the derivation of the moment generation function of receiver Signal-to-Noise Ratio(SNR), the sectional integral method is used, instead of the cumulative density function method which is ordinarily used by the deduction of the outage probability of S-R-D link. The accurate symbol error rate of a dual-hop relay cooperative network is obtained with the closed-form Moment Genoration Function (MGF) expression. The correctness of the symbol error rate is verified through numerical simulations and is compared with other analytical methods. These deductions clearly show that the distributed cooperative diversity network presented has strong superiorities in overcoming severe fading and can achieve full diversity order.     

Exact symbol error probability of a Cooperative network in a Rayleigh-fading environment

In a distributed spatial diversity wireless system, not all antennas are located at one station as in classical transmit diversity systems, but are dispersed at different, possibly mobile, stations in the network. Transmit diversity is created when the selected stations assist a sender by relaying its information signal to the destination. In this letter, we present an exact average symbol error rate analysis for the distributed spatial diversity wireless system with K amplifying relays in a Rayleigh-fading environment. The average symbol error rate formula allows us to clearly illustrate the advantage that the distributed diversity system has in overcoming the severe penalty in signal-to-noise ratio caused by Rayleigh fading. Using simple bounds on the probability of error, we show that the cooperative network presented in this letter achieves full diversity order.     

Distributed space-time coding scheme with differential detection and power allocation for cooperative relay network

By introducing orthogonal space-time coding (STC) scheme in wireless cooperative relay network, two distributed differential STC (DSTC) schemes based on the amplify-and-forward (AF) and decode-and- forward (DF) methods are, respectively, developed. The scheme performance is investigated in symmetric and asymmetric wireless relay networks. The presented schemes require no channel information at both relay terminals and destination terminal, and have linear decoding complexity when compared with the existing scheme. Moreover, they are suitable for the application of different constellation modulations and DSTC schemes, and thus provide more freedoms of design. Besides, the power allocations between source and relay terminals are jointly optimized to minimize the system pairwise error probability for symmetric and asymmetric networks, and two practical methods are presented to solve the complicated optimized problem from asymmetric network. Simulation results show that the scheme with DF method has better performance than that with AF method due to no amplification of noise power, but the performance superiority will decrease at high SNR due to the error propagation of decoding at the relays. Furthermore, the distributed DSTC schemes with optimal power allocation have better performance than those with conventional fixed power allocation.     

Relay ordering in a multi-hop cooperative diversity network

In this paper, we first propose an optimum relay ordering algorithm for the multi-branch multi-hop cooperative diversity networks. This optimum algorithm has a high complexity that makes it hard to implement. Therefore, a suboptimum relay ordering algorithm, which considerably reduces the complexity, is then developed. Furthermore, for a cooperative network with two relays, we analytically evaluate the performance of the suboptimum algorithm by using an approximate end-to-end signal-to-noise ratio expression. Specifically, an approximate probability of wrong selection and an approximate expression of the symbol error rate are derived. The analysis and the numerical results demonstrate that the suboptimum algorithm performs very well as the optimum one at a much lower complexity.     

Symbol error rate of selection amplify-and-forward relay systems

Cooperative diversity schemes significantly improve the performance of wireless networks by transmitting the same information through several nodes. The amplify-and-forward (AF) relaying method is one of the most attractive cooperative diversity schemes due to its low complexity. Selection AF relaying has recently been proven to achieve the same diversity order as and lower outage probability than all-participate relays. In this letter, we present an asymptotic analysis of the symbol error rates of a selection AF network, and compare it with the conventional all-participate scheme     

Asymptotic performance analysis of amplify-and-forward cooperative networks in a nakagami-m fading environment

This letter analyzes the performance of repetitionbased cooperative wireless networks using amplify-and forward relaying. The network consists of a source, R parallel relays, and a destination, and the channel coefficients are distributed as independent, non-identical, Nakagami-m. The approximated average symbol error rate (SER) is investigated. For sufficiently large SNR, this letter derives a close-form average SER when m is an integer. The simplicity of the asymptotic results provides valuable insights into the performance of cooperative networks and suggests means of optimizing them. We also use simulation to verify the analytical results. Results show that the derived error rates are tight approximations particularly at medium and high SNR.     

PL approximation of DBPSK in DF-based cooperative FSO network with pointing error

In this paper, we utilize piecewise linear (PL) approximation to analyze the performance of cooperative free space optical (FSO) network employing differentially modulated binary phase shift keying (DBPSK) data with multiple decode-and-forward (DF) relays. The maximum-likelihood (ML) decoding rule at the destination is approximated by PL approximation which considers the possibility of erroneous relaying and performs very similar to the ML decoder with reduced decoding complexity. The atmospheric fading optical links are modeled by Gamma–Gamma distribution subject to both types of detection techniques, i.e., heterodyne detection and intensity modulation/direct detection (IM/DD) with pointing error. We analytically formulate the probability of error for the multiple-DF relay-based FSO network. However, the novel unified expression of average bit error rate (BER) of PL decoder with single relay and single source to destination pair is derived. Further, we also derive the asymptotic approximate BER of DF-FSO network with multiple relays at high signal-to-noise ratio (SNR) of source to relay links considering heterodyne detection with negligible pointing error. In addition, the unified closed-form expressions of outage probability with single and multiple DF relays are derived in terms of Meijer G function. The expression of outage probability is examined at high SNR in order to obtain analytical diversity order. The impact of different power distribution techniques on outage probability is determined by utilizing power distribution parameters. The derived analytical results are validated through simulation.     

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.     

Decode-to-cooperate: a sequential alamouti-coded cooperation strategy in dual-hop wireless relay networks

An optimal cooperation strategy, decode-to-cooperate, is proposed and investigated for performance improvements in dual-hop wireless relay networks. Based on decode-and-forward (DF) strategy with multiple relay selection, we design a novel scheme such that the source node keeps transmitting sequentially and the selected relays cooperate by transmitting the decoded signal using distributed Alamouti coding. We exploit the multipath propagation effect of the wireless channel to achieve lower probability of error and introduce optimum power allocation and relay positioning. We analyze the scenario when the source to destination direct link is not available and derive a closed form expression for symbol error rate (SER), its upper bound and an asymptotically tight approximation to exploit the performance gain by selecting the optimum relays in a multiple-relay cooperation scheme. Moreover, asymptotic optimum power allocation (based on the SER approximation) and optimal relay positioning are also considered to further improve the SER. The proposed relay selection scheme outperforms cooperative (DF) and non-cooperative schemes by more than 2 dB.     

Performance analysis of repetition-based cooperative networks with partial statistical CSI at relays

This letter analyzes the performance of repetitionbased cooperative diversity wireless networks using amplifyand forward relaying, in which each relay has only statistical knowledge of the source-relay link. The network channels are modeled as independent, non-identical, Rayleigh distributed coefficients. The exact symbol error rate is derived using the moment generating function (MGF). We derive the probability density function and MGF of the total SNR. Then, the MGF is used to determine the symbol error rate (SER). The diversity order of the amplify-and-forward cooperation with partial statistical channel state information is also found via the asymptotic behavior of the average SER, and it is shown that the cooperative network achieves full diversity. Our analytical results are confirmed by simulations.     

Opportunistic Relaying for MIMO Amplify-and-Forward Cooperative Networks

We consider a wireless relay network with multiple antenna terminals over Rayleigh fading channels, and apply distributed space-time coding (DSTC) in amplify-and-forward (A&F) mode. The A&F scheme is used in a way that each relay transmits a scaled version of the linear combination of the received symbols. It turns out that, combined with power allocation in the relays, A&F DSTC results in an opportunistic relaying scheme, in which only the best relay is selected to retransmit the source’s space-time coded signal. Furthermore, assuming the knowledge of source-relay CSI at the source node, we design an efficient power allocation which outperforms uniform power allocation across the source antennas. Next, assuming M-PSK or M-QAM modulations, we analyze the performance of the proposed cooperative diversity transmission schemes in a wireless relay networks with the multiple-antenna source and destination. We derive the probability density function (PDF) of the received SNR at the destination. Then, the PDF is used to determine the symbol error rate (SER) in Rayleigh fading channels. We derived closed-form approximations of the average SER in the high SNR scenario, from which we find the diversity order of system R min{N _s , N _d }, where R, N _s , and N _d are the number of the relays, source antennas, and destination antennas, respectively. Simulation results show that the proposed system obtain more than 6 dB gain in SNR over A&F MIMO DSTC for BER 10^?4, when R = 2, N _s  = 2, and N _d  = 1.     

Performance analysis of selective cooperation in amplify‐and‐forward relay networks over identical Nakagami‐m channels

In cooperative communications, multiple relays between a source and a destination can increase the diversity gain. Because all the nodes must use orthogonal channels, multiple‐relay cooperation becomes spectrally inefficient. Therefore, a bestrelay selection scheme was recently proposed. In this paper, we analyzed the performance of this scheme for a system with the relays operating in amplify‐and‐forward mode over identical Nakagami‐m channels using an exact source–relay–destination signal‐to‐noise ratio (SNR).We derived accurate closed‐form expressions for various system parameters including the probability density function of end‐to‐end SNR, the average output SNR, the bit error probability, and the channel capacity. The analytical results were verified through Monte Carlo simulations. Copyright © 2011 John Wiley & Sons, Ltd.     

Non-coherent distributed space–time coding techniques for two-way wireless relay networks

To overcome the overhead involved with channel estimation, several non-coherent distributed space–time coding (DSTC) strategies for two-way wireless relay networks (TWRNs) using the amplify-and-forward and the decode-and-forward protocol have been recently proposed that do not require channel state information (CSI) at any node to decode the information symbols. In this paper, novel differential DSTC strategies for TWRNs using the two- and three-phase protocol are proposed. In our transmission schemes, the relays do not waste power to transmit information known at the respective destination nodes. This is achieved by combining the symbols from both terminals received at the relays into a single symbol of the unaltered constellation. Furthermore, in our strategies, the direct link between the communicating terminals can be naturally incorporated to further improve the diversity gain. Simulations show a substantially improved performance in terms of bit error rate (BER) of the proposed strategies as compared to the existing strategies.     

Performance analysis of multiuser diversity in cooperative multi-relay networks under rayleigh-fading channels

In multiuser cooperative relay networks, cooperative diversity can be obtained with the help of relays, while multiuser diversity is an inherent diversity in multiuser systems. In this letter, the performance analysis of multiuser diversity in cooperative multi-relay networks is presented. Both the case of all relay participating and the case of relay selection are considered. We first derive asymptotic expressions of outage probability and symbol error probability for amplify-and-forward (AF) and decode-and-forward (DF) protocols with joint multiuser and cooperative diversity. Then, the theoretical analysis are validated by Monte Carlo simulations. Both the theoretical analysis and simulations show that a multiuser diversity order of K and a cooperative diversity order of M+ 1 can be achieved simultaneously for both AF and DF protocols (where K is the number of accessing users and M is the number of available relays). These demonstrate that the multiuser diversity can be readily combined with the cooperative diversity in multiuser cooperative relay networks.     

Performance of differential modulation with wireless relays in Rayleigh fading channels

We propose a new amplify-and-forward scheme amenable to differential modulation for cooperative systems with wireless relays. We derive closed-form expressions of the probability density function (PDF) of the signal-to-noise ratio (SNR) and average bit-error rate (BER) for the proposed scheme and the analytical results are confirmed with numerical simulations. An asymptotic analysis reveals that the proposed cooperative scheme with one relay offers a diversity order approaching two in Rayleigh fading channels as the average SNR increases.     

Performance analysis of AF OFDM system using multiple relay in presence of nonlinear‐PA over inid Nakagami‐m fading

In this paper, performance of an orthogonal frequency division multiplexing–based variable‐gain amplify and forward cooperative system using multiple relay with relay selection is analyzed over independent but not necessarily identically distributed frequency selective Nakagami‐m fading channels. For the analysis, nonlinear power amplifier is considered at the relay, and selection combining is adopted at destination node. Closed‐form expressions of the outage probability for various threshold signal‐to‐noise ratio (SNR) values and average symbol error rate for M‐ary quadrature amplitude modulation techniques are derived for the considered system. Further, the outage probability analysis is performed in high SNR regime to obtain the diversity order. Furthermore, impact of different fading parameters, multiple relay, and nonlinear power amplifier is highlighted on the outage probability and asymptotic outage probability for various threshold SNRs and on the average symbol error rate for various quadrature amplitude modulation constellations. The derived analytical expressions are generalized for various fading environments while considering the integer‐valued fading parameters. Finally, all the analytical results are verified through the Monte Carlo simulations for various SNR levels and system configurations.     

放大转发中继网络中的一种中继选择方案

提出了一种放大转发网络中的中继选择方案,假设目的节点配置多个天线,源节点和所有中继节点都配置单个天线,方案选择一组中继同时在相同的频带上放大转发接收到的源节点信息以最大化接收信噪比。与只择一个最优中继的方案相比,方案在保持满分集阶数的情况下获得了更高的中断容量和更优的误符号率性能。与只选择一个最优中继的方案相比,在0.000 01的误符号率水平上,少需要发射功率1.6 dB。     

The Amplify-and-Forward Half-Duplex Cooperative System: Pairwise Error Probability and Precoder Design

In this paper, an exact asymptotic pairwise error probability (PEP) is derived for a half-duplex cooperative system employing an amplify-and-forward (AF) protocol. When compared with the PEP of a traditional multiple-input multiple-output (MIMO) system, the "diversity gain" for the cooperative system is no longer just a simple exponential function of the signal-to-noise ratio (SNR), rather, it involves the logarithm of the SNR. The term diversity gain function is used to designate this characteristic of the PEP. The coding gain, on the other hand, is found similar to that for the MIMO system and is proportional to the determinant of the autocorrelation of the error matrix. Based on our analysis and observations, we propose a design of unitary precoder for the cooperative system to achieve the full diversity gain function. For the case of a 4-QAM signal being transmitted, we further optimize the coding gain and arrive at a closed-form optimum precoder. Simulations indicate that our proposed precoder designs greatly improve the performance of the cooperative system     

异步协同系统频选信道下基于线性预处理的DSTC结构设计

在协同中继系统中,应用分布式空时码(Distributed Space Time Coding, DSTC),可以在有效提高系统效率的同时获得全协同分集。但是,各中继节点的异步传输和节点间的多径衰落会破坏空时码字的结构,使之不能获得全分集。本文针对两中继的异步协同系统,提出了一种频率选择性信道下的基于线性预处理的DSTC传输结构。在此传输结构中,源节点对发送数据块进行预处理后发送给中继节点,中继节点对接收信号进行简单的共轭重排等处理,使得在目的节点形成DSTC的结构。其中,为抵抗异步传输和多径衰落引入的符号间干扰(Inter-symbol Interference, ISI),在源节点处和中继节点处均加入循环前缀(Cyclic Prefix, CP)。于是目的节点对接收到的信号进行DFT处理后,可以运用ML算法对数据信息进行检测。理论分析和仿真表明,当存在定时误差和节点间为频率选择性信道时,目的节点运用ML检测算法该传输结构可获得全空间分集和全多径分集。然后,本文考虑了信道各径延迟为整数倍符号周期的情况,并且证明了该传输结构的分集增益只与节点间信道的有效信道长度有关。      

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.