Iterative receiver for amplify‐and‐forward relay networks with unknown noise correlation

For amplify‐and‐forward relay networks, we propose an iterative scheme to estimate channel and detect information symbols for the multi‐antenna destination in spatially correlated noise. The equivalent channel coefficients and noise covariance are estimated by expectation–maximization algorithm. In addition, we discuss the initialization of iteration and analyze the modified Cramér–Rao bound to show the performance of the proposed iterative estimation. Moreover, on the basis of the structure of the proposed iterative estimator, a joint channel estimation and detection receiver is also provided. Finally, simulation results show that the proposed channel estimator and receiver can achieve the optimal performances in amplify‐and‐forward relay networks with unknown noise correlation. Copyright © 2012 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.     

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.     

基于导频信号的MIMO-AF协作中继信道估计

提出一种在2个时隙内对MIMO-AF协作两跳中继信道进行估计的方法.重点研究在信源发送功率和中继发送功率受限的约束条件下,运用MMSE准则构建信源至中继节点信道估计的优化问题,采用矩阵分解的方法将信号分解成酉分量和对角分量,简化代价函数.最后用二分法求出最佳的导频信号和中继放大系数.仿真结果表明,本方法能够得到确定的、精度较高的信道估计值,并分析了信道相关性、天线数目对信道估计的影响.     

Nelder‐Mead–based power optimization for secrecy enhancement in amplify‐and‐forward cooperative relay networks

Cooperative communication based on relaying nodes has been considered as a promising technique to increase the physical layer security (PLS) performance in wireless communications. In this paper, an optimal power allocation (OPA) scheme based on Nelder‐Mead (NM) algorithm is proposed for improving the secrecy rate of amplify‐and‐forward (AF) cooperative relay networks employing cooperative jamming (CJ) scheme. The proposed hybrid jamming scheme allows the source and selected relay to transmit the jamming signal along with the information to confound the eavesdropper. The path selection probability of ant colony optimization (ACO) algorithm is used for selecting the relay for transmission. The performance based on secrecy rate is evaluated for “n” trusted relays distributed dispersedly between the source and destination. Gradient‐based optimization and three‐dimensional exhaustive search methods are used as benchmark schemes for comparison of the proposed power optimization algorithm. The secrecy performance is also compared with conventional AF scheme and CJ scheme without power optimization (EPA). The impact of single and multiple relays on secrecy performance is also evaluated. Numerical results reveal that, compared with the gradient method and exhaustive search algorithm, the proposed power allocation strategy achieves optimal performance. Also, the derived OPA results show a significantly higher secrecy rate than the EPA strategy for both CJ and AF schemes.     

MMSE‐based transceiver design for distributed MIMO amplify‐and‐forward cooperative networks in correlated channels

In this paper, the source‐precoder, multiple‐relay amplifying matrices, and destination‐equalizer joint optimization is investigated in distributed MIMO amplify‐and‐forward multiple‐relay networks with direct source–destination transmission in correlated fading channels. With the use of taking both the direct link and spatial correlation between antenna elements into account, the cooperative transceiver joint design is developed based on the minimum mean‐squared error criterion under individual power constraints at the source and multiple‐relay nodes. Simulation results demonstrate that the cooperative transceiver joint design architecture for an amplify‐and‐forward MIMO multiple‐relay system outperforms substantially the noncooperative transceiver design techniques on the BER performance under the spatial‐correlation channels.Copyright © 2012 John Wiley & Sons, Ltd.     

Novel noncoherent detection for multi‐hop amplify‐and‐forward relaying systems

Because of the multiplication of fading gains and noise, the actual distributions of the received signals in multi‐hop amplify‐and‐forward relaying systems are no longer Gaussian. In this work, they are fitted with the t location‐scale distribution and the logistic distribution. Using these distributions, two novel noncoherent detectors are proposed based on the maximum likelihood method. Numerical results show that both new detectors outperform the conventional energy detector. The performance gain increases when the signal‐to‐noise ratio increases or when the hop number decreases. Importantly, the bit error rate of the conventional energy detector reaches an error floor while the bit error rates of the new detectors do not. Copyright © 2015 John Wiley & Sons, Ltd.     

Successive relaying for large MIMO amplify‐and‐forward relay networks

In this paper, we consider a large relay network with one source, K relays and M users, where the source and relays are equipped with W and N antennas, respectively. We propose an amplify‐and‐forward successive relaying protocol in which the relays are divided into 2 groups to successively help transmission to M users. Achievable sum rate of the proposed protocol is derived and found to scale as when N and M are fixed and K→∞ . On the other hand, when M and K are fixed and N→∞, the achievable sum rate scales as . Therefore, the scaling law of the achievable sum rate coincides with the capacity scaling law of the considered network. Then, both precoding at the source and grouping of the relay nodes are jointly optimized to further improve the proposed protocol. Numerical results show that the proposed successive relaying protocol can outperform the conventional 2‐slot relaying protocol and the proposed joint optimization scheme for source precoding and relay grouping bring considerable rate gain.     

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 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.     

Performance of fixed‐gain amplify‐and‐forward nonlinear relaying with hardware impairments

In this paper, a fixed‐gain amplify‐and‐forward relaying under non‐ideal hardware is analyzed. The relaying system is impaired because of relay's power amplifier (PA) nonlinearity and in‐phase and quadrature‐phase (IQ) imbalance at a destination. Closed‐form expressions for outage probability as well as ergodic capacity approximation and its upper bound are derived. Also, the outage probability and the ergodic capacity asymptotic expressions in the high signal‐to‐noise ratio are deduced. For the first time, the joint influence of PA nonlinearity and IQ imbalance on the system in terms of outage probability, symbol error rate, and ergodic capacity is investigated. The results are compared with the respect to soft envelope limiter and traveling‐wave tube amplifier at the relay. Based on the analytical and the numerical results, important insights into the impact of IQ imbalance and nonlinearity of the aforementioned PA models on the system performance are gained as well as valuable information on the performance of practically deployed fixed‐gain amplify‐and‐forward relaying system. Copyright © 2015 John Wiley & Sons, Ltd.     

Performance analysis of MIMO cognitive amplify‐and‐forward relay networks with orthogonal space–time block codes

In this paper, we study the performance of multiple‐input multiple‐output cognitive amplify‐and‐forward relay networks using orthogonal space–time block coding over independent Nakagami‐m fading. It is assumed that both the direct transmission and the relaying transmission from the secondary transmitter to the secondary receiver are applicable. In order to process the received signals from these links, selection combining is adopted at the secondary receiver. To evaluate the system performance, an expression for the outage probability valid for an arbitrary number of transceiver antennas is presented. We also derive a tight approximation for the symbol error rate to quantify the error probability. In addition, the asymptotic performance in the high signal‐to‐noise ratio regime is investigated to render insights into the diversity behavior of the considered networks. To reveal the effect of network parameters on the system performance in terms of outage probability and symbol error rate, selected numerical results are presented. In particular, these results show that the performance of the system is enhanced when increasing the number of antennas at the transceivers of the secondary network. However, increasing the number of antennas at the primary receiver leads to a degradation in the secondary system performance. Copyright © 2014 John Wiley & Sons, Ltd.     

基于压缩感知的放大转发双向中继信道估计

为了更有效地对放大转发双向中继信道进行估计,对级联卷积信道的稀疏特性进行了分析,并基于其稀疏性,采用压缩感知技术,通过合理地设计导频将合成级联卷积信道分解成2个独立的级联卷积信道分别进行信道估计。研究分析和仿真结果表明,级联卷积信道具有稀疏性且其稀疏度在一定范围内变化。所提的方案只需在端节点对级联卷积信道进行估计就可以完成双向信息的交换,提高了频谱效率,降低了信道估计误差,并且无需信道稀疏度的先验信息。     

Distributed simultaneous wireless information and power transfer in multiuser amplify‐and‐forward ad hoc wireless networks

This paper studies the problem of stable node matching for distributed simultaneous wireless information and power transfer in multiuser amplify‐and‐forward ad hoc wireless networks. Particularly, each source node aims to be paired with another node that takes the role of an amplify‐and‐forward relay to forward its signal to the destination, such that the achievable rate is improved, in return of some payment made to the relaying node. Each relaying node splits its received signal from its respective source into two parts: one for information processing and the other for energy harvesting. In turn, a matching‐theoretic solution based on the one‐to‐one stable marriage matching game is studied, and a distributed polynomial‐time complexity algorithm is proposed to pair each source node with its best potential relaying node based on the power‐splitting ratios, such that their utilities or payments are maximized while achieving network stability. For comparison purposes, an algorithm to enumerate all possible stable matchings is also devised to study the impact of different matchings on the source and relay utilities. Simulation results are presented to validate the proposed matching algorithm and illustrate that it yields sum‐utility and sum‐payment that are closely comparable to those of centralized power allocation and node pairing, with the added merits of low complexity, truth telling, and network stability.     

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.     

Joint sensing and transmission for cognitive amplify‐and‐forward two‐way relay networks

In this paper, we propose a cognitive transmission scheme for Amplify‐and‐Forward (AF) two‐way relay networks (TWRNs) and investigate its joint sensing and transmission performance. Specifically, we derive the overall false alarm probability, the overall detection probability, the outage probability of the cognitive TWRN over Rayleigh fading channels. Furthermore, based on these probabilities, the spectrum hole utilization efficiency of the cognitive TWRN is defined and evaluated. It is shown that smaller individual or overall false alarm probability can result in less outage probability and thus larger spectrum hole utilization efficiency for cognitive TWRN, and however produce more interference to the primary users. Interestingly, it is found that given data rate, more transmission power for the cognitive TWRN does not necessarily obtain higher spectrum hole utilization efficiency. Moreover, our results show that a maximum spectrum hole utilization efficiency can be achieved through an optimal allocation of the time slots between the spectrum sensing and data transmission phases. Finally, simulation results are provided to corroborate our proposed studies. Copyright © 2016 John Wiley & Sons, Ltd.     

Exact capacity analysis of multi‐relay multiuser cooperative networks based on two‐step selection

This paper advocates the capacity analysis of an amplify‐and‐forward cooperative communication system model in multi‐relay multiuser networks. A two‐step selection scheme is adopted, and both relay and user selection are based on the outdated channel state information. Exact expression of channel capacity for independent, but not necessarily identically distributed, Rayleigh fading channels is derived. Finally, simulations are carried out to verify the correctness of theoretical analysis and illustrate the effect of parameters on the performance. Results show that although the performance of our scheme is inferior to the optimal joint selection scheme, it is still a practical scheme because its complexity is much lower than that of the optimal scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

Decode‐and‐forward with partial relay selection

Exact expressions for outage probability and symbol error rate are presented for a decode‐and‐forward cooperative network with partial relay selection. An independent but not identically distributed Nakagami‐m fading environment is considered. Numerical and simulated results show the validity of the analytical results. Copyright © 2010 John Wiley & Sons, Ltd.     

Cooperative amplify‐and‐forward partial relay selection with outdated channel information in spectrum‐sharing systems

Recently, cooperative relaying techniques have been integrated into spectrum‐sharing systems in an effort to yield higher spectral efficiency. Many investigations on such systems have assumed that the channel state information between the secondary transmitter and primary receiver used to calculate the maximum allowable transmit secondary user transmit power to limit the interference is known to be perfect. However, because of feedback delay from the primary receiver or the time‐varying properties of the channel, the channel information may be outdated, which is an important scenario to cognitive radio systems. In this paper, we investigate the impact of outdated channel state information for relay selection on the performance of partial relay selection with amplify and forward in underlay spectrum‐sharing systems. We begin by deriving a closed‐form expression for the outage probability of the secondary network in a Rayleigh fading channel along with peak received interference power constraint and maximum allowable secondary user transmit power. We also provide a closed‐form expression for the average bit‐error rate of the underlying system. Moreover, we present asymptotic expressions for both the outage probability and average bit‐error rate in the high signal‐to‐noise ratio regime that reveal practical insights on the achievable diversity gain. Finally, we confirm our results through comparisons with computer simulations. Copyright © 2016 John Wiley & Sons, Ltd.     

A two‐hop equalize‐and‐forward relay scheme in OFDM‐based wireless networks over multipath channels

Relay communications have attracted increasing research attentions as a cost‐effective technique to improve spatial diversity, service coverage, and energy efficiency in wireless networks. However, existing relay schemes (e.g., amplify‐and‐forward and decode‐and‐forward (DF) schemes) still face several major challenges, particularly the accumulation of multipath channels effect in AF and long processing latency in DF. To address these issues, we propose a novel equalize‐and‐forward (EF) relay scheme to enhance the retransmission reliability while maintaining low processing delay at the relay node. In particular, the proposed EF relay estimates and equalizes the channel between source and relay to eliminate the channel accumulation effect without signal regeneration. To further reduce the relay processing time, the channel estimation and equalization in the proposed EF design are performed in parallel. The proposed equalization is realized by presetting the equalizer coefficients with the current channel response that is predicted in parallel using multiple past channel responses. Numerical results show that the proposed EF relay scheme can achieve comparable symbol error rate performance as the DF relay with much less relay latency. In addition, the EF relay exhibits low outage probability at the same data rate as compared with traditional amplify‐and‐forward and DF schemes. schemes. Copyright © 2015 John Wiley & Sons, Ltd