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.     

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.     

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.     

MMSE based joint Tomlinson-Harashima source and linear relay precoder design in non-regenerative MIMO relay system

This paper proposes a joint nonlinear transceiver design scheme based on minimum mean square error(MMSE) criterion for non-regenerative multiple input multiple output(MIMO) relay system.The proposed scheme decomposes the error covariance matrix,reformulates the original joint design problem as two separate optimization problems,and then provides a closed-form solution with only local channel state information(CSI) available at the source and destination.Performance evaluation shows that the proposed scheme significantly outperforms linear schemes,and has a competitive performance compared with existing global CSI based nonlinear schemes,both iterative and non-iterative.     

Statistically robust design of linear filter for non-regenerative MIMO relay systems

This paper addresses the robust linear filter design issues for non-regenerative multiple input multiple output (MIMO) relay systems with imperfect channel state information (CSI) in both or partial hops. By considering statistical Kronecker channel model involving channel mean and antenna correlation, the robust linear processing schemes in imperfect CSI scenario for both hops are first derived based on mean squared error (MSE) criterion. In addition to this, the result is also extended to two practical scenarios, i.e. imperfect CSI for relay link with perfect CSI for access link and imperfect CSI for access link with perfect CSI for relay link. Simulation results show that the proposed scheme is capable of mitigating the performance degradation caused by the imperfect CSI.     

Two‐pilot channel estimation scheme for amplify‐and‐forward relay networks

In amplify‐and‐forward relay networks, the equivalent channel to the destination node is not independent of equivalent noise and the equivalent noise does not follow a Gaussian distribution. Therefore, it is difficult to directly estimate the equivalent channel based on traditional optimal rules. In this paper, we propose a two‐pilot estimation (TPE) scheme that decomposes a non‐Gaussian noise channel estimation problem into two channel estimation problems in Gaussian noise. In TPE scheme, the relay‐destination channel is first estimated by one pilot and the other pilot is used to estimate the equivalent channel with the aid of the estimated relay‐destination channel. Simulation results show that the TPE scheme can achieve less estimation error and larger system throughput than other existing channel estimators in slow fading case. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

QoS‐driven jointly optimal subcarrier pairing and power allocation for OFDM amplify‐and‐forward relay systems

In this paper, we investigate the quality‐of‐service (QoS) driven subcarrier pairing and power allocation for two‐hop amplify‐and‐forward OFDM relay systems. By integrating the concept of effective capacity, our goal is to maximize the system throughput subject to a given delay QoS constraint. We propose a jointly optimal subcarrier pairing and power allocation scheme, which can be implemented with two separate steps. First, pair the subcarriers over the source‐relay channel and relay‐destination channel by the descending order of the subcarriers’ channel gains. Second, by making use of the derived equivalent end‐to‐end channel gains of the subcarrier pairs, optimally allocate power over the subcarrier pairs, and then optimally partition the power of the subcarrier pairs between the source and the relay. The simulation results show that our proposed scheme can efficiently provide different levels of delay QoS guarantees, even if under stringent delay QoS constraints. The simulation results also verify that our proposed scheme shows significant superiorities over the other existing schemes. 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.     

Optimal precoder design for non‐regenerative multiple‐input multiple‐output cognitive relay systems with perfect and imperfect channel state information

This paper studies optimal precoder design for non‐regenerative multiple‐input multiple‐output (MIMO) cognitive relay systems, where the secondary user (SU) and relay station (RS) share the same spectrum with the primary user (PU). We aim to maximize the system capacity subject to the transmit power constraints at the SU transmitter (SU‐Tx) and RS, and the interference power constraint at the PU. We jointly optimize precoders for the SU‐Tx and RS with perfect and imperfect channel state information (CSI) between the SU‐Tx/RS and PU, where our design approach is based on the alternate optimization method. With perfect CSI, we derive the optimal structures of the RS and SU‐Tx precoding matrices and develop the gradient projection algorithm to find numerical solution of the RS precoder. Under imperfect CSI, we derive equivalent conditions for the interference power constraints and convert the robust SU‐Tx precoder optimization into the form of semi‐definite programming. For the robust RS precoder optimization, we relax the interference power constraint related with the RS precoder to be convex by using an upper bound and apply the gradient projection algorithm to deal with it. Simulation results demonstrate the effectiveness of the proposed schemes. Copyright © 2013 John Wiley & Sons, Ltd.     

An architecture for amplify‐and‐forward cooperative systems with real modulations

This paper proposes a simple architecture for half‐duplex cooperative systems which use amplify‐and‐forward (AF) as a relay strategy and one‐dimensional modulations for source messages. The proposed solution uses the two orthogonal channels of quadrature modulation in order to allow a node to behave simultaneously as a source and a relay. We demonstrate that the new scheme has a similar performance to the conventional orthogonal amplify‐and‐forward protocol without suffering from bandwidth loss, and avoids error propagation problems of previously reported AF superposition schemes. The proposed technique is suitable for applications with low spectral efficiencies and practical adaptive systems where real modulations are implemented based on a quadrature modulation core. Copyright © 2009 John Wiley & Sons, Ltd.     

基于MMSE准则的MIMO多中继系统线性收发机设计

本文以放大转发MIMO多中继系统为研究对象,研究其联合线性收发机的优化设计问题,其基本思想是在中继的总发射功率约束下,最小化系统的均方误差(MSE).为降低系统复杂度,本文首先引入了乘积矩阵的奇异值分解,把收发机的设计简化为以奇异值向量和酉矩阵为优化变量的优化问题;接着利用变量替换并引入罚项,将简化后的问题转化成只有酉矩阵约束的优化问题.在此基础上,通过引入替换变量的欧氏梯度,设计了新的黎曼欧氏最陡下降算法,从而有效地处理酉矩阵约束.仿真结果表明,与传统的设计方法相比,本文提出的方案性能最优,最接近MSE下界.     

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.     

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.     

MIMO中继下行通信系统中的多目标优化设计

针对通信系统中系统功率消耗和接收信号均方误差(MSE)存在冲突关系,无法同时达到性能最优的情况,采用多目标优化(MOO)框架联合优化系统功率消耗和接收信号MSE.文中考虑两跳的多入多出(MIMO)放大转发(AF)中继下行通信系统.联合优化形成的多目标优化问题是非凸且难以直接求解的,为此,提出一种基于帕累托最优策略的资源分配方法,该方法采用加权切比雪夫法,并引入中继预编码矩阵的一般结构和Schur补引理将优化问题转化为SDP问题.仿真结果验证了所提出方法的有效性,表明其具有更好的性能,同时也给出了系统功耗和MSE性能之间的帕累托最优边界.     

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.     

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 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.     

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.