Performance and diversity analysis of decode‐and‐forward cooperative system over Nakagami‐m fading channels

In this paper, we derive the upper bound of bit‐error rate (BER) performance and diversity gain for a decode‐and‐forward (DF) cooperative system. Either maximal‐ratio combining (MRC) or cooperative MRC (C‐MRC) is employed at the receiver in the presence of independent, non‐identical Nakagami‐m fading. Both analytical and simulation results show that C‐MRC takes advantage of spatial diversity more efficiently and thus achieves the same or better performance and diversity order as compared to MRC. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

An amplify‐and‐forward and decode‐and‐forward mixed relay communication system and its performance analysis

A kind of amplify‐and‐forward (AF) and decode‐and‐forward (DF) mixed relay communication system is proposed in this letter. The source broadcasts the signal to all the relays. Relays that can decode the signal adopt DF scheme to retransmit the signal, while the rest adopt AF scheme for retransmission. The destination employs maximum ratio combining technique to maximize the received signal‐to‐noise ratio. Another situation concerned in this letter is that when the relay cannot decode the source signal, it may retransmit the interference signal with AF scheme. Closed‐form expressions of outage probability are derived. Simulation results show that the analytical curves agree with the simulated ones very well, and the AF‐DF mixed relay system can improve the availability of the relays. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

Performance of joint transmit and receive antenna selection in dual hop amplify‐and‐forward relay network over Nakagami‐m fading channels

In this paper, performance of joint transmit and receive antenna selection in each hop of dual hop amplify‐and‐forward relay network is analyzed over flat and asymmetric Nakagami‐m fading channels. In the network, source, relay, and destination are equipped with multiple antennas. By considering relay location, we derive exact closed‐form cumulative distribution function, moment generating function, moments of end‐to‐end signal‐to‐noise ratio and closed form symbol error probability expressions for fixed and channel state information‐based relay gains. We also derive the asymptotical outage probability and symbol error probability expressions to obtain diversity order and array gain of the network. Analytical results are validated by the Monte Carlo simulations. Copyright © 2012 John Wiley & Sons, Ltd.     

Performance analysis of a variable‐gain amplify‐and‐forward relayed mixed RF‐FSO system

In this work, an amplify‐and‐forward variable‐gain relayed mixed RF‐FSO system is studied. The considered dual‐hop system consists of a radio frequency (RF) link followed by a free space optical (FSO) channel. The RF link is affected by short‐term multipath fading and long‐term shadowing effects and is assumed to follow the generalized‐K fading distribution that approximates accurately several important distributions often used to model communication channels. The FSO channel experiences fading caused by atmospheric turbulence that is modeled by the gamma‐gamma distribution characterizing moderate and strong turbulence conditions. The FSO channel also suffers path loss and pointing error induced misalignment fading. The performance of the considered system is analyzed under the collective influence of distribution shaping parameters, pointing errors that result in misalignment fading, atmospheric turbulence, and path loss. The moment‐generating function of the Signal power to noise power ratio measured end‐to‐end for this system is derived. The cumulative distribution function for the Signal power to noise power ratio present between the source and destination receiver is also evaluated. Further, we investigate the error and outage performance and the average channel capacity for this system. The analytical expressions in closed form for the outage probability, symbol and bit error rate considering different modulation schemes and channel capacity are also derived. The mathematical expressions obtained are also demonstrated by numerical plots.     

Performance analysis of selective combining decode‐and‐forward relay networks over Nakagami‐n and Nakagami‐q fading channels

In this paper, we present the performance of selective combining decode‐and‐forward relay networks in independent and non‐identically distributed Nakagami‐n and Nakagami‐q fading channels by using the best–worse and the decoding‐set approaches. The outage probability, moment generation function, symbol error probability and average channel capacity are derived in closed‐form using the signal to noise ratio (SNR) statistical characteristics. After that, we analyze the outage probability at high SNRs, and then, we optimize it. Beside the optimum method, we have proposed a sub‐optimum adaptive method. Also, we derive the outage probability for the selection‐combining case with the direct link between the source and the destination. Finally, for comparison with analytical formulas, we perform some Monte‐Carlo simulations. Copyright © 2012 John Wiley & Sons, Ltd.     

Performance comparison of dual‐hop hybrid decode‐or‐amplify‐forward relay schemes for M‐ary quadrature amplitude modulation burst transmission over Rayleigh fading channels

This paper shows the analytical performance expressions of M‐ary quadrature amplitude modulation burst symbol transmission for hybrid decode‐or‐amplify‐forward (HDAF) relay schemes over quasi‐static Rayleigh‐fading channels. First, we derive the probability density function of the received instantaneous signal‐to‐noise ratio as the simplified form, which is related to all the possible occurrence probabilities of error‐events for M‐ary quadrature amplitude modulation burst transmission. On the basis of the derived probability density function, we express average bit error probability, average symbol error probability, and average burst error rate as closed forms, which can be also applied to both amplify‐and‐forward and adaptive decode‐and‐forward (ADF) schemes. The analysis and simulation results show that HDAF scheme for burst transmission can achieve the performance of ADF scheme with symbol‐by‐symbol transmission, which is the achievable lower bound. Furthermore, the outage probability, the normalized channel capacity, and the goodput performance are also derived as closed forms. The analysis shows the superiority of HDAF scheme to ADF scheme. Comparison with simulations confirms that the derived analytical expressions are accurate over all signal‐to‐noise ratio regions and for different numbers of relays and modulation orders.     

Conventional and modified TAS/OSTBC schemes in dual‐hop fixed‐gain amplify‐and‐forward relaying systems with imperfect feedback

Modified transmit antenna selection (TAS)/orthogonal space‐time block coding (OSTBC) (M‐TAS/OSTBC) schemes have been shown to achieve superior error performance together with a reduced‐rate feedback channel in the presence of feedback errors (FEs) when compared with the conventional TAS/OSTBC (C‐TAS/OSTBC) schemes. This paper focuses on the bringing of fixed‐gain amplify‐and‐forward (FGAF) relaying schemes that employ M‐TAS/OSTBC schemes at both hops that provides reduced feedback‐rate and robust error performance in the presence of erroneous‐feedback channels. The exact expressions of the outage and error probabilities for both dual‐hop FGAF relaying schemes in Nakagami‐m fading channels have been derived and validated via Monte Carlo simulations. Additionally, with the help of high signal‐to‐noise ratio (SNR) (i.e., asymptotic) approaches and some analytical approximations, the asymptotic diversity order analysis has been carried out. Besides, by providing a simulation‐based examination on the inclusion of power allocation within the modified scheme, the additional advantages on the performance have been exhibited. The extensive investigation and comparisons to the conventional schemes have shown that M‐TAS/OSTBC schemes employed at each transmission link provide full diversity order and considerable error performance as the C‐TAS/OSTBC scheme in ideal feedback cases and also achieve more robust error performance in the presence of FEs. Thus, by using M‐TAS/OSTBC schemes, the overall performances of the dual‐hop FGAF relaying schemes have been enhanced, which would result in reductions on the average SNR requirements to achieve a specified error rate constraint. Copyright © 2015 John Wiley & Sons, Ltd.     

Quadrature space shift keying performance with dual‐hop AF relay over mixed fading

Quadrature space shift keying (QSSK) modulation combined with cooperative relaying improves the reliability in communication and enhances the overall spectral efficiency. Here, QSSK scheme is analyzed for multiple‐input multiple‐output (MIMO) wireless communication system with dual‐hop amplify‐and‐forward (AF) relaying systems over asymmetric mixed Rayleigh/Rician and symmetric Nakagami‐m/Nakagami‐m fading channels. Analytical expressions for cumulative distribution function (CDF) of the end‐to‐end signal‐to‐noise ratio are derived and used to evaluate the average bit error probability (ABEP) of QSSK modulation in mixed asymmetric and symmetric fading channels. The obtained ABEP expression is in the form of Whittaker function, which can be numerically evaluated using its numerical or series representation. Numerical and simulation results are presented to illustrate the impact of fading parameters on the system performance.     

Performance analysis and power allocation for decode‐and‐forward cooperative communications over Rician fading channel

This paper derives the asymptotic symbol error rate (SER) and outage probability of decode‐and‐forward (DF) cooperative communications over Rician fading channels. How to optimally allocate the total power is also addressed when the performance metric in terms of SER or outage probability is taken into consideration. Analysis reveals the insights that Rician factor has a great impact on the system performance as compared with the channel variance, and the relay–destination channel quality is of importance. In addition, the source–relay channel condition is irrelevant to the optimal power allocation design. Simulation and numerical evaluation substantiate the tightness of the asymptotic expressions in the high‐SNR regions and demonstrate the accuracy of our theoretical analysis. Copyright © 2011 John Wiley & Sons, Ltd.     

Effect of imperfect channel state information and co‐channel interferences on two‐hop fixed gain amplify‐and‐forward relay networks with beamforming

This letter investigates the joint effects of imperfect channel state information and co‐channel interferences on a two‐hop fixed gain amplify‐and‐forward (AF) relay network with beamforming. Specifically, the analytical expressions of the outage probability and the average symbol error rate for the AF relaying are derived. Moreover, the asymptotic analysis at high signal‐to‐noise ratio is also presented to reveal the diversity order and array gain of the considered AF relay system. Finally, computer simulations are given to confirm the validity of the analytical results. Copyright © 2014 John Wiley & Sons, Ltd.     

Ergodic capacity analysis of cooperative amplify‐and‐forward relay networks over generalized fading channels

This paper presents two new methods for evaluating the ergodic channel capacities of cooperative non‐regenerative multirelay networks in a myriad of fading environments and under three distinct source‐adaptive transmission policies: (i) optimal rate adaptation with a fixed transmit power; (ii) optimal joint power‐and‐rate adaptation; and (iii) truncated channel inversion with fixed rate. In contrast to the previous related works, our proposed unified analytical frameworks that are based on the moment generating function and/or the cumulative distribution function of end‐to‐end signal‐to‐noise ratio allow us to gain insights into how power assignment during different transmission phases, relay node placement, fade distributions, and dissimilar fading statistics across the distinct communication links impact the ergodic capacity, without imposing any restrictions on the channel fading parameters. Copyright © 2013 John Wiley & Sons, Ltd.     

Performance analysis of Alamouti scheme with transmit antenna selection in non‐identical Nakagami‐m fading channels

In this paper, error performances of multiple‐input multiple‐output systems that employ Alamouti‐coded transmission with transmit antenna selection are examined for binary phase‐shift keying, binary frequency‐shift keying, M‐ary phase‐shift keying, and M‐ary quadrature amplitude‐modulation signals in independent but non‐identically distributed flat Nakagami‐m fading channels. Exact symbol error rate expressions are derived by using the moment‐generating function‐based analysis method. Upper bound expressions have been obtained in order to examine the asymptotic diversity order of transmit antenna selection/Alamouti scheme. Also, outage probability analysis of investigated systems has been given in order to examine the system capacity. Monte Carlo simulations have validated the analytical symbol error rate performance results. Copyright © 2011 John Wiley & Sons, Ltd.     

SEP calculations for coherent M‐ary FSK in different fading channels with MRC diversity

In this paper, the authors derive symbol error probability (SEP) expressions for coherent M‐ary frequency shift keying (MFSK) modulation schemes in multipath fading channels. The multipath or small‐scale fading process is assumed to be slow and frequency non‐selective. In addition, the channel is also subjected to the usual degradation caused by the additive white Gaussian noise (AWGN). Different small‐scale fading statistics such as Rayleigh, Rician (Nakagami‐n), Hoyt (Nakagami‐q), and Nakagami‐m have been considered to portray diverse wireless environments. Further, to mitigate fading effects through space diversity, the receiver front‐end is assumed to be equipped with multiple antennas. Independent and identically distributed (IID) as well as uncorrelated signal replicas received through all these antennas are combined with a linear combiner before successive demodulation. As the detection is coherent in nature and thus involves phase estimation, optimum phase‐coherent combining algorithms, such as predetection maximal ratio combining (MRC), may be used without any added complexity to the receiver. In the current text, utilizing the alternate expressions for integer powers (1≤n≤4) of Gaussian Q function, SEP values of coherent MFSK are obtained through moment generating function (MGF) approach for all the fading models (with or without MRC diversity) described above. The derived end expressions are composed of finite range integrals, which can be numerically computed with ease, dispenses with the need of individual expressions for different M, and gives exact values up to M=5. When the constellation size becomes bigger (M≥6), the same SEP expressions provide a quite realistic approximation, much tighter than the bounds found in previous literatures. Error probabilities are graphically displayed for each fading model with different values of constellation size M, diversity order L, and for corresponding fading parameters (K, q, or m). To validate the proposed approximation method extensive Monte‐Carlo simulations were also performed, which show a close match with the analytical results deduced in the paper. Both these theoretical and simulation results offer valuable insight to assess the efficacy of relatively less studied coherent MFSK in the context of the optimum modulation choice in wireless communication. Copyright © 2010 John Wiley & Sons, Ltd.     

Performance analysis of cooperative network over Nakagami and Rician fading channels

This paper presents an analysis on the performance of single‐relay and multiple fixed‐relay cooperative network. The relay nodes operate in amplify‐and‐forward (AF) mode and transmit the signal through orthogonal channels. We consider maximal‐ratio combining at the destination to get the spatial diversity by adding the received signals coherently. The closed‐form moment‐generating function (MGF) for the total equivalent signal‐to‐noise ratio (SNR) is derived. The exact expressions of symbol‐error rate, outage capacity, and outage probability are obtained using the closed‐form MGF for single‐relay and multiple‐relay cooperative network with M‐ary phase shift keying (M‐PSK) and M‐ary quadrature amplitude modulation (M‐QAM) over independent and non‐identical Nakagami‐m channels and Rician fading channels. The approximated closed‐form expression of ergodic capacity is derived for both Nakagami‐m and Rician fading channels. The performance of the system is analyzed at various relay locations. The theoretical results are then compared with the simulation results obtained for binary PSK, quadrature PSK, and 16‐QAM modulation schemes to verify the analysis. Here, the expressions derived can be easily and more efficiently used to compute the performance parameters than doing Monte Carlo simulations. It is shown that cooperation is significant only for low K values for Rician by plotting cooperation gain versus K. The results show that the cooperative network performs best when the relay is located in the middle of source to destination link, at lower SNR values, and the performance of the system is worst if the relay is located closer to the source than to the destination. Copyright © 2013 John Wiley & Sons, Ltd.     

MRC分集接收的MQAM在Nakagami信道上的性能分析

Nakagami信道是一种适应性较强的信道模型，MQAM(M-ary quadrature amplitude modulation)是一种频谱利用率较高的调制方式。在存在多径影响的无线通信环境中，最大比合并(maximum ratio combining)方式的分集接收是克服衰落的有效方法。本文利用适用范围更广的Nakagami信道模型，在多径衰落的情况下对最大比合并分集接收的MQAM系统误符号率性能作了分析。仿真结果对分析实际信道下具体系统的性能具有一定的参考价值。     

Performance analysis of channel estimation in amplify‐and‐forward multi‐hop direct forwarding wireless networks

In this paper, we study the performance of a training‐based least square (LS) and linear minimum mean‐square‐error (LMMSE) channel estimation for both hop‐by‐hop and multi‐hop direct forwarding wireless sensor networks over frequency‐selective fading channels. Specifically, to investigate the properties of the channel estimation, we accomplish a theoretical analysis of MSE in terms of various link parameters. From the performance evaluation, we analytically present the effects of the number of hops on the MSE performance for channel estimations in both multi‐hop networks. Interesting observations of MSE behaviors under various conditions are discussed, and the receiver complexity and channel equalization performance are also analyzed. Finally, through the computer simulations, the analytical results and detection performance are demonstrated. Copyright © 2014 John Wiley & Sons, Ltd.     

OFDM-MQAM在相关Nakagami-m衰落信道上的性能分析

本文研究频率选择性相关Nakagami衰落信道上采用最大比合并(MRC)分集接收的正交频分多路复用M进制正交幅度调制(OFDM-MQAM)系统.使用矩生成函数(MGF)方法和高斯超几何函数、Appell超几何函数或Lauricella函数,推导任意衰落参数频率选择性相关Nakagami衰落信道上MRC分集接收的OFDM-MQAM系统的误符号率(SER)性能,获得了OFDM-MQAM误符号率的一个新的解析表达式.数值计算结果阐明了多径路径数、Nakagami衰落参数和信道脉冲响应抽头间的相关系数对OFDM-MQAM误符号率性能的影响.     

Outage analysis of opportunistic‐based hybrid decode‐amplify‐forward relaying in polar code environment

Outage analysis plays a vital role in wireless systems to determine reliable transmission and effective communication. Incremental hybrid decode‐amplify‐forward (IHDAF) relay offers a way of meeting the challenges of capacity and coverage improvement with great potential in cooperative communication networks. Therefore, opportunistic incremental hybrid relaying must be integrated with coding schemes to achieve full diversity. In this paper, the outage behavior of polar coded and distributed coded cooperative relaying schemes is analyzed. Simulation results show that opportunistic incremental HDAF using polar code offers an outage capacity of 17 b/s/Hz for 4 × 4 multiantenna and 45 b/s/Hz in 8 × 8 multiantenna systems with an outage of 10^?8 and 10^?13, respectively. Moreover, the polar coded opportunistic IHDAF system in 8 × 8 MIMO achieves 2 and 6 dB higher gains compared with amplify‐and‐forward (AF) and decode‐and‐forward (DF) relaying schemes. The closed‐form expression for outage probability has been derived through Marcum‐Q approximations and processed through Monte Carlo simulations.