Cooperation with multiple relays in wireless sensor networks: optimal cooperator selection and power assignment

We consider the energy-minimal joint cooperator set selection and power assignment problem in a cooperation scenario with multiple relays, under transmit power constraints, while satisfying a target frame error rate (FER) at the destination receiver. We first derive the FER of a cooperative system and present a simplified calculation that also involves a simple, yet close approximation to the average bit error rate of a multiple input single output system. Our FER calculation facilitates a closed-form solution for the joint optimization problem, resulting in the Optimal Cooperator Selection and Power Assignment (O-CSPA) algorithm. Next, we devise the Distributed Cooperator Selection and Power Assignment (D-CSPA) algorithm in which the relays individually decide to become a cooperator and determine their power levels. We evaluate the performance of O-CSPA and D-CSPA algorithms under several network topologies, varying target FER levels and different power consumption models, by considering the energy dissipated in the transceiver circuits and amplifiers of all involved nodes. We show that both algorithms provide notable energy savings and conclude that the extent of the savings depends significantly on the power consumption model. D-CSPA’s performance is shown to be not only close to that of optimal solution, but also robust to errors in channel estimation.     

Precoding and decoding design for two-way MIMO AF multiple-relay system

In this paper, a joint precoding and decoding design scheme is proposed for two-way Multiple-Input Multiple-Output (MIMO) multiple-relay system. The precoding and decoding matrices are jointly optimized based on Minimum Mean-Square-Error (MMSE) criteria under transmit power constraints. The optimization problem is solved by using a convergent iterative algorithm which includes four sub-problems. It is shown that due to the difficulty of the block diagonal nature of the relay precoding matrix, sub-problem two cannot be solved with existing methods. It is then solved by converting sub-problem two into a convex optimization problem and a simplified method is proposed to reduce the computational complexity. Simulation results show that the proposed scheme can achieve lower Bit Error Rate (BER) and larger sum rate than other schemes. Furthermore, the BER and the sum rate performance can be improved by increasing the number of antennas for the same number of relays or increasing the number of relays for the same number of antennas.     

Robust Relaying Schemes for Multiple-Antenna Multi-Relay Networks

The optimal beamforming weight matrix for amplify and forward multiple-antenna multiple-relay network is investigated. It is assumed that the partial first and second hop channel state information (CSI) is available at relays. In order to minimize the mean square error (MSE) at destination, all relay weight matrices must be designed simultaneously under individual relay power constraints. Using the Lagrange dual variables, it is shown that this general vector optimization problem can be converted into a scalar optimization problem whose scalar Lagrange multipliers can be obtained numerically. This is the generalized version of the scheme suggested for complete CSI. The proposed scheme is evaluated through computer simulation with various numbers of relays and antennas to obtain MSE and bit error rate (BER) metrics. It is also shown that the resulting MSE and BER are less than those of the schemes available in the literature by a good margin depending upon the amount of the utilized relay and antennas as well as the estimation error.     

Weighted Sum Rate Maximization for Downlink Multiuser Relay Network with Direct Link

This paper investigates the joint source, relay precoder and receive filters optimization, aiming to maximize the weighted sum rate (WSR) for non-regenerative downlink multiuser MIMO relay network with source-destination direct link. The joint transceiver is developed taking both the direct link and the relay link into consideration with individual source and relay power constraints. Since the WSR problem is generally non-convex and intractable, it’s difficult to solve directly. Inspired by the recent results of relationship between the mutual information and the mean-square-error, we reformulate the WSR problem into a weighted sum mean square error minimization problem. An iterative algorithm is developed to solve the WSR problem. Simulation results demonstrate that the proposed algorithm offers significant performance gain over existing methods. In addition, we also propose a modified robust joint transceiver design against the imperfect channel state information.     

多用户下行链路收发机鲁棒性优化算法

该文提出了一种多用户MIMO系统中预矩阵及其匹配接收矩阵的鲁棒性优化算法。针对信道估计误差构造均方误差代价函数,在发射功率受限的约束条件下联合设计发射和接收矩阵,推导出了采用线性多用户MMSE接收时的最优收发机迭代算法。仿真表明,系统具有良好的鲁棒性。     

多中继放大转发协作通信中的功率分配和中继位置联合优化

文章研究了多中继放大转发协作分集系统中的功率分配和中继位置联合优化问题。利用信道的统计状态信息,在总功率一定的条件下,以最大化系统的信道容量为目标,推导了多中继和选择中继两种模型下基于高信噪比近似的联合优化算法的闭式解。理论分析和仿真验证表明,提出的算法大大提高了传统的等功率分配方案下系统的性能。     

上行多用户MIMO中继系统中基于不完全信道状态信息的预编码算法

论文研究了存在信道估计误差及天线相关条件下,上行多用户MIMO中继系统的预编码问题,目标是提升系统的误比特率性能。针对基于放大转发中继技术的上行多用户MIMO中继系统,考虑源-中继和中继-目的端信道中存在的信道估计误差及天线相关,提出一种基于不完全信道状态信息(Channel State Information, CSI)的预编码设计方案。首先根据最小均方误差(Minimum Mean-Squared Error, MMSE)准则设计代价函数,以发射端和中继端最大功率为约束条件,通过理论推导求得中继端和发射端的线性预编码矩阵,最后采用迭代下降法得到接收端处理矩阵的闭式解。数值仿真结果表明,在存在信道估计误差和天线相关的条件下,与现有算法相比,所提算法能有效降低系统的误比特率。     

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.     

Joint Power Allocation in Wireless Relay Networks: the Case of Hybrid Digital-Analog Transmission

In conventional digital communication systems, the quality of the received signal does not improve beyond a certain level as the channel quality increases. Such kind of quality saturation effect is caused by the unrecoverable quantization errors produced by source coding. The Hybrid Digital-Analog (HDA) transmission, where the quantization errors are transmitted in an analog mode along with the quantized data in a digital mode, has been recognized as an effective technique to combat the quality saturation effect. In this paper, we introduce HDA transmission in Wireless Relay Networks (WRNs) over Rayleigh slow-fading channels to eliminate the quality saturation effect and achieve graceful improvement for the better channel quality. Our goal is to minimize the end-to-end distortion by optimal power allocation. We note that digital-analog power allocation involved in HDA transmission is coupled with source-relay power allocation in WRNs. Therefore, the joint power allocation problem should be considered. We investigate this problem for two kinds of relays in WRNs, i.e., Amplify-and-Forward (AF) relays and Decode-and-Forward (DF) relays. In the case of AF relays, we find that the joint power problem is concave and thus derive the explicit expressions of the optimal solution. In the case of DF relays, we formulate the joint power allocation problem as a nonlinear fractional programming problem and then propose an efficient algorithm to search the optimal solution. Simulation results show that the proposed joint power allocation schemes outperform existing schemes in terms of end-to-end distortion in both WRNs with AF relays and that with DF relays under various channel conditions.     

Secrecy enhancement in two-hop DF relaying system under hardware impairment

In this paper, we investigate joint jammer selection and network coding for secrecy enhancement under transceiver hardware impairment. We propose two protocols of joint jammer selection and network coding (SCCJ-OJS and SCCJ-MiJS) to improve secrecy outage and throughput performance compared with a protocol without cooperative jamming (SCC). For performance evaluation, we derive exact closed-form expressions for the secrecy outage probability (SOP) and throughput performance of the three protocols. Our analysis is substantiated via Monte Carlo simulation. The results show that the SCC protocol is nearly in an outage state when the eavesdroppers are close to the source and/or relays, while the SCCJ-OJS and SCCJ-MiJS protocols still improve the performance compared with the SCC protocol in this strict case. In addition, transceiver hardware impairments can degrade the eavesdropping channel: the performance of the SCC protocol increases linearly with hardware impairment level, whereas SCCJ-OJS and SCCJ-MiJS protocol performance is enhanced at a low level and experience a minor decrease at a high level of hardware impairment. Finally, the theoretical results match the simulation results well.     

基于上下行对偶性的多用户MIMO下行链路鲁棒收发机设计

针对多用户多天线(MIMO)下行链路信道状态信息(CSI)非理想的条件,该文研究SINR平衡问题及功率最小化问题的收发机设计。在信道误差受限情况下,该文建立worst-case SINR上下行链路对偶性,并基于该对偶性,为两种鲁棒收发机提出新的设计策略。该策略避免了凸优化内点迭代算法,从而大大降低复杂度。仿真结果显示,所提算法与现有的凸优化算法性能一致。     

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.     

Joint Power Allocation and Interference Mitigation Techniques for Cooperative Spread Spectrum Systems with Multiple Relays

This paper presents joint power allocation and interference mitigation techniques for the downlink of spread spectrum systems which employ multiple relays and the amplify and forward cooperation strategy. We propose a joint constrained optimization framework that considers the allocation of power levels across the relays subject to an individual power constraint and the design of linear receivers for interference suppression. We derive constrained minimum mean-squared error (MMSE) expressions for the parameter vectors that determine the optimal power levels across the relays and the linear receivers. In order to solve the proposed optimization problem efficiently, we develop joint adaptive power allocation and interference suppression algorithms that can be implemented in a distributed fashion. The proposed stochastic gradient (SG) and recursive least squares (RLS) algorithms mitigate the interference by adjusting the power levels across the relays and estimating the parameters of the linear receiver. SG and RLS channel estimation algorithms are also derived to determine the coefficients of the channels across the base station, the relays and the destination terminal. The results of simulations show that the proposed techniques obtain significant gains in performance and capacity over non-cooperative systems and cooperative schemes with equal power allocation.     

Robust Transceiver Optimization in Downlink Multiuser MIMO Systems

We study robust transceiver optimization in a downlink, multiuser, wireless system, where the transmitter and the receivers are equipped with antenna arrays. The robustness is defined with respect to imperfect knowledge of the channel at the transmitter. The errors in the channel state information are assumed to be bounded, and certain quality-of-service targets in terms of mean-square errors (MSEs) are guaranteed for all channels from the uncertainty regions. Iterative algorithms are proposed for the transceiver design. The iterations perform alternating optimization of the transmitter and the receivers and have equivalent semidefinite programming representations with efficient numerical solutions. The framework supports robust counterparts of several MSE-optimization problems, including transmit power minimization with per-user or per-stream MSE constraints, sum MSE minimization, min-max fairness, etc. Although the convergence to the global optimum cannot be claimed due to the intricacy of the problems, numerical examples show good practical performance of the presented methods. We also provide various possibilities for extensions in order to accommodate a broader set of scenarios regarding the precoder structure, the uncertainty modeling, and a multicellular setup.      

Resource allocation scheme in two-way multi-relay OFDM system

A joint optimization scheme for power allocation and subcarrier pairing under high SNR in two-way multi-relay OFDM system was proposed.Unlike those schemes in which relays use subcarriers separately,all the relays were allowed to forward signal on each subcarrier pair for providing much space diversity.With the constraint of total system power,the proposed scheme firstly allocated each relay power with Cauchy inequality with the assuming that the total relay power was fixed.Then the dichotomy was used to calculate the power allocation between the source node and the relay node by maximizing the equivalent channel gain for different subcarrier pairs.Lastly,the power of different subcarrier pairs was allocated by convex programming,and the subcarriers were paired by Hungarian algorithm to obtain the maximum system capacity.There was no optimal power allocation method with low complexity because of the complexity of the power allocation algorithm in two-way multi-relay networks.This algorithm greatly reduces the complexity of power allocation and simulation results show that the proposed scheme outperforms the relay selection scheme and the relays use subcarriers separately scheme.     

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.     

Outage Probability Based Robust Distributed Beam-Forming in Multi-User Cooperative Networks with Imperfect CSI

In this paper, a new robust problem is proposed for relay beamforming in relay system with stochastic perturbation on channels of multi user and relay network. The robust problem aims to minimize the transmission power of relay nodes while the imperfect channel information (CSI) injects stochastic channel uncertainties to the parameters of optimization problem. In the power minimization framework, the relays amplification weights and phases are optimized assuming the availability of Gaussian channel distribution. The power sum of all relays is minimized while the outage probability of the instantaneous capacity (or SINR) at each link is above the outage capacity (or SINR) for each user. The robust problem is a nonconvex SDP problem with Rank constraint. Due to the nonconvexity of the original problem, three suboptimal problems are proposed. Simulation and numerical results are presented to compare the performance of the three proposed solutions with the existing worst case robust method.     

Two-way cooperative communications with statistical channel knowledge

We consider the problem of distributed beamforming for a two-way relay network which consists of two transceivers and multiple relay nodes. The main assumption in this work, which differentiates it from previously reported results, is that one of the transceivers is assumed to have only statistical information about channels between the other transceiver and the relay nodes. This assumption imposes less stringent restrictions on the bandwidth required to obtain channel state information via training. Based on this statistical modeling, we propose to use a chance-constrained programming approach to design a distributed beamforming algorithm. In this approach, we aim to minimize the total transmit power (consumed in the entire network) as perceived by one of the transceivers, subject to two probabilistic constraints. These constraints guarantee that the outage probability of the transceivers' received SNRs, as perceived by the master transceiver, is not less than certain given thresholds. We prove rigorously that such an approach leads to a relay selection algorithm where the relay with the strongest channel coefficient to the master transceiver participates in relaying and the remaining relays are shut off. As such, the optimal distributed beamforming algorithm is simplified to a power control solution. Closed-form solution to this problem is obtained and its performance is evaluated through numerical examples.     

On the Diversity–Multiplexing Tradeoff in Multiple-Relay Network

This paper studies the setup of a multiple-relay network in which $K$ half-duplex multiple-antenna relays assist in the transmission between either one or several multiple-antenna transmitter(s) and a multiple-antenna receiver. Each two nodes are assumed to be either connected through a quasi-static Rayleigh-fading channel, or disconnected. We propose a new scheme, which we call random sequential (RS), based on the amplify-and-forward relaying. We prove that for general multiple-antenna multiple-relay networks, the proposed scheme achieves the maximum diversity gain. Furthermore, we derive diversity–multiplexing tradeoff (DMT) of the proposed RS scheme for general single-antenna multiple-relay networks. It is shown that for single-antenna two-hop multiple-access multiple-relay $(K > 1)$ networks (without direct link between the transmitter(s) and the receiver), the proposed RS scheme achieves the optimum DMT. However, for the case of multiple-access single-relay setup, we show that the RS scheme reduces to the naive amplify-and-forward (AF) relaying and is not optimum in terms of DMT, while the dynamic decode-and-forward (DF) scheme is shown to be optimum for this scenario.      

Power Allocation Schemes for Amplify-and-Forward MIMO-OFDM Relay Links

We consider a two-hop MIMO-OFDM communication scheme with a source, an amplify-and-forward relay, and a destination. We examine the possibilities of power allocation (PA) over the subchannels in frequency and space domains to maximize the instantaneous rate of this link if channel state information at the transmitter (CSIT) is available. We consider two approaches: (i) separate optimization of the source or the relay PA with individual per node transmit power constraints and (ii) joint optimization of the source and the relay PA with joint transmit power constraint. We provide the optimal PA at the source (or the relay) with a node transmit power constraint that maximizes the instantaneous rate for a given relay (or source) PA. Furthermore, we show that repeating this separate optimization of the source and the relay PA alternately converges and improves the achievable rate of the considered link. Since the joint optimization of the source and the relay PA is analytically not tractable we use a high SNR approximation of the SNR at the destination. This approximation leads to rates which are quite tight to the optimum.