Distributed Beamforming for Relay Networks Based on Second-Order Statistics of the Channel State Information

In this paper, the problem of distributed beamforming is considered for a wireless network which consists of a transmitter, a receiver, and $r$ relay nodes. For such a network, assuming that the second-order statistics of the channel coefficients are available, we study two different beamforming design approaches. As the first approach, we design the beamformer through minimization of the total transmit power subject to the receiver quality of service constraint. We show that this approach yields a closed-form solution. In the second approach, the beamforming weights are obtained through maximizing the receiver signal-to-noise ratio (SNR) subject to two different types of power constraints, namely the total transmit power constraint and individual relay power constraints. We show that the total power constraint leads to a closed-form solution while the individual relay power constraints result in a quadratic programming optimization problem. The later optimization problem does not have a closed-form solution. However, it is shown that using semidefinite relaxation, this problem can be turned into a convex feasibility semidefinite programming (SDP), and therefore, can be efficiently solved using interior point methods. Furthermore, we develop a simplified, thus suboptimal, technique which is computationally more efficient than the SDP approach. In fact, the simplified algorithm provides the beamforming weight vector in a closed form. Our numerical examples show that as the uncertainty in the channel state information is increased, satisfying the quality of service constraint becomes harder, i.e., it takes more power to satisfy these constraints. Also our simulation results show that when compared to the SDP-based method, our simplified technique suffers a 2-dB loss in SNR for low to moderate values of transmit power.      

放大转发双向中继系统中降低总功率的波束成形设计

本文研究了多天线放大转发双向中继系统中在满足源节点信噪比要求条件下最小化系统总功率的波束设计问题。该问题是非凸优化问题,为了有效求解该问题,采用分层优化方法将原问题分解成发送波束成形向量优化、接收波束成形向量优化和中继波束成形矩阵优化三类子问题。发送/接收波束成形向量通过求解Rayleigh商最小化问题来获得。中继波束成形矩阵优化问题通过半正定松弛方法转化成半正定优化问题来求解。在求解这三类优化问题的基础上,提出了一种迭代波束成形算法,并采用单调有界序列定理证明了所提算法的收敛性。计算机仿真表明:所提算法经过若干次迭代即可收敛到稳定点;相比于已有算法,本文算法能显著降低系统总功率。      

Adaptive linearly constrained minimum variance beamforming for multiuser cooperative relaying using the kalman filter

In this paper, we consider a wireless communication scenario with multiple source-destination pairs communicating through several cooperative amplify-and-forward relay terminals. The relays are equipped with multiple antennas that receive the source signals and transmit them to the destination nodes. We develop two iterative relay beamforming algorithms that can be applied in real-time. In both algorithms, the relay beamforming matrices are jointly designed by minimizing the received power at all the destination nodes while preserving the desired signal at each destination. The first algorithm requires the existence of a local processing center that computes the beamforming coefficients of all the relays. In the second algorithm, each relay can compute its beamforming coefficients locally with the help of some common information that is broadcasted from the other relays. This is achieved at the expense of enforcing the desired signal preservation constraints non-cooperatively. We provide two extensions of the proposed algorithms that allow the relays to control their transmission power and to modify the quality of service provided to different sources. Simulation results are presented validating the ability of the proposed algorithms to perform their beamforming tasks efficiently and to track rapid changes in the operating environment.     

Joint Optimization of Source Power Allocation and Relay Beamforming in Multiuser Cooperative Wireless Networks

Relay beamforming techniques have been shown to significantly enhance the sum capacity of a multiuser cooperative wireless network through the optimization of the relay weights, where concurrent communications of multiple source-destination pairs are achieved via spatial multiplexing. Further optimization of the transmit power allocation over the source nodes is expected to improve the network throughput as well. In this paper, we maximize the sum capacity of a multiuser cooperative wireless network through the joint optimization of power allocation among source nodes and relay beamforming weights across the relay nodes. We consider a two-hop cooperative wireless network, consisting of single-antenna nodes, in which multiple concurrent links are relayed by a number of cooperative nodes. When a large number of relay nodes are available, the channels of different source-destination pairs can be orthogonalized, yielding enhanced sum network capacity. Such cooperative advantage is particularly significant in high signal-to-noise ratio (SNR) regime, in which the capacity follows a logarithm law with the SNR, whereas exploiting spatial multiplexing of multiple links yields capacity increment linear to the number of users. However, the capacity performance is compromised when the input SNR is low and/or when the number of relay nodes is limited. Joint optimization of source power allocation and relay beamforming is important when the input SNR and/or the number of relay nodes are moderate or the wireless channels experience different channel variances. In these cases, joint optimization of source power and distributed beamforming weights achieves significant capacity increment over both source selection and equal source power spatial multiplexing schemes. With consideration of the needs to deliver data from each source node, we further examine the optimization of global sum capacity in the presence of individual capacity requirements by maximizing sum capacity of the network subject to a minimum capacity constraint over each individual user.     

Cooperative beamforming and relay selection in cognitive radio systems

In this paper, a new scheme is suggested for cooperative beamforming (BF) and relay selection in CR networks, where a pair of secondary users communicates with each other assisted by some multiple antenna relay nodes. The goal of the algorithm is to maximize signal to interference plus noise ratio of secondary user receiver subject to limited interference caused for primary user receiver and power constraints of relay nodes. The relay selection and BF optimization problem is solved separately by employing convex semidefinite programming through rank‐one relaxation. It is shown that our proposed algorithm outperforms conventional relay selection and BF schemes. Copyright © 2014 John Wiley & Sons, Ltd.     

Optimal designs of collaborative relay‐assisted multiuser beamforming for cellular systems

With careful calculation of signal forwarding weights, relay nodes can be used to work collaboratively to enhance downlink transmission performance by forming a virtual multiple‐input multiple‐output beamforming system. Although collaborative relay beamforming schemes for single user have been widely investigated for cellular systems in previous literatures, there are few studies on the relay beamforming for multiusers. In this paper, we study the collaborative downlink signal transmission with multiple amplify‐and‐forward relay nodes for multiusers in cellular systems. We propose two new algorithms to determine the beamforming weights with the same objective of minimizing power consumption of the relay nodes. In the first algorithm, we aim to guarantee the received signal‐to‐noise ratio at multiusers for the relay beamforming with orthogonal channels. We prove that the solution obtained by a semidefinite relaxation technology is optimal. In the second algorithm, we propose an iterative algorithm that jointly selects the base station antennas and optimizes the relay beamforming weights to reach the target signal‐to‐interference‐and‐noise ratio at multiusers with nonorthogonal channels. Numerical results validate our theoretical analysis and demonstrate that the proposed optimal schemes can effectively reduce the relay power consumption compared with several other beamforming approaches. Copyright © 2012 John Wiley & Sons, Ltd.     

多小区的分布式天线系统中天线选择与鲁班性波束形的联合优化（英文）

Most of studies on Distributed Antenna System(DAS) focus on maximizing the sum capacity and perfect channel state information at transmitter(CSIT).However,CSI is inevitable imperfect in practical wireless networks.Based on the sources of error,there are two models.One assumes error lies in a bounded region,the other assumes random error.Accordingly,we propose two joint antenna selection(AS) and robustbeamforming schemes aiming to minimize the total transmit power at antenna nodes subject to quality of service(QoS) guarantee for all the mobile users(MUs) in multicell DAS.This problem is mathematically intractable.For the bounded error model,we cast it into a semidefinite program(SDP) using semidefinite relaxation(SDR) and S-procedure.For the second,we first design outage constrained robust beamforming and then formulate it as an SDP based on the Bernstein-type inequality,which we generalize it to the multi-cell DAS.Simulation results verify the effectiveness of the proposed methods.     

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.     

混合卫星-地面无线网络中的波束形成算法

针对混合卫星-地面无线通信网络的物理层安全问题,提出了一种能提升系统安全容量的波束形成算法。在混合网络中,包含窃听者的卫星网络作为主网络与地面次级网络频谱共享。首先,建立基于地面基站发射功率最小化准则,同时主用户的安全容量和次级用户的通信容量满足要求的优化问题。其次,利用约束条件转化和半正定松弛（SDR）方法得到满足凸形式的优化问题,并通过半正定规划方法求解出权矢量。最后,计算机仿真结果验证了所提出的波束形成算法的有效性及优越性。      

基于原子范数的MIMO雷达发射波形设计方法

针对现有多输入多输出(MIMO)雷达发射波形设计方法存在运算量高的问题,该文提出一种基于原子范数的MIMO雷达发射波形设计方法。根据原子范数的信号模型,该算法首先选择一个具有特殊结构的发射滤波器组以及一组正交信号,将MIMO雷达发射波形设计问题转化为原子范数最小化问题,然后采用半正定规划(SDP)对原子范数进行求解,得到(半)正定Toeplitz矩阵,并对其进行范德蒙分解实现发射滤波器组的估计,最后综合发射滤波器组与正交信号获得MIMO雷达的发射波形。理论分析与仿真结果表明,该算法满足等能量发射准则以及小的峰均功率比(PAPR)。同时,该算法相比于现有算法有较低的运算量以及良好的匹配性能。     

Linear Pre-coding in MIMO–CDMA Relay Networks

Our aim in this paper is to define a novel beamforming approach in wireless multiple-input-multiple-output (MIMO) code-division-multiple-access (CDMA) relay networks, which involves communication between multiple source-destination pairs. It is assumed that full channel state information of source-relay and relay-destination channels are available. Our design consists of a two-step amplify-and-forward protocol. The first step includes signal transmission from the sources to the MIMO relay, and the second step contains transmitting a version of the linear precoded signal to the destinations. Beamforming is investigated only in MIMO-relay node to reduce end user’s hardware complexity and save the computational power. Accordingly, the optimization problem is defined to find the MIMO relay beamforming coefficients that minimize total relay transmit power by keeping the signal-to-interference-plus-noise ratio (SINR) of all destinations above a certain threshold value. It is shown that such optimization problem is a non-convex quadratically constrained quadratic programming, which is NP-hard in general. However, by relaxing this problem to a semi-definite programming problem, the problem can be solved efficiently. Simulation results verify the performance gain implied by MIMO–CDMA relay system compared to the non-CDMA coded system.     

拥有多天线源节点的放大转发双向中继信道机会中继策略研究

We consider a two-way relay network where the Amplify-and-Forward (AF) protocol is adopted by all relays in this paper. The network consists of two multi-antenna source nodes and multiple distributed single-antenna relays. Two opportunistic relaying schemes are proposed to efficiently utilize the antennas of the source nodes and the relay nodes. In the first scheme, the best relay is selected out by a max-min-max criterion before transmitting. After that, at each source, only the antenna with the largest channel gain between itself and the best relay is activated to transmit and receive signals with full power. In the second scheme, assisted by the best relay which is selected by the typical max-min criterion, both source nodes use all their antennas to exchange data, and match filter beamforming techniques are employed at both source nodes. Further analyses show that all schemes can achieve the full diversity order, and the conclusions are not only mathematically demonstrated but numerically illustrated. System performance comparisons are carried out by numerical methods in terms of rate sum and outage probability, respectively. The beamforming assisted scheme can be found to be superior to the antenna selection scheme when accurate Channel State Information (CSI) is available at the transmitters. Otherwise, the latter is very suitable.     

频率选择性信道中的多用户分布式波束形成技术

该文研究频率选择性信道中多用户点对点分布式中继网络波束形成技术。为了均衡源节点与中继节点以及中继节点与目标节点之间的频率选择性信道,该文提出的波束形成技术在中继节点上采用有限长响应滤波器和滤波而后转发的中继数据传输方法,以最小化中继节点的发射总功率为目标,同时满足所有目标节点的服务质量(QoS)。该波束形成优化问题的直接形式由于其非凸性而难以求得最优解。该文采用半定松弛(SDP)方法将其近似为凸优化问题,进而可以用内点法高效快速求解。仿真结果表明,相较于传统的放大而后转发的波束形成技术,所提波束形成方法能有效提高频率选择性信道中多用户中继网络的性能。     

基于硬件损伤的MIMO异构网络波束成形算法

由于多输入多输出(MIMO)异构网络能够提高系统容量和实现更多的用户接入,因此受到了学术界和工业界的广泛关注,从而成为下一代通信系统的关键技术之一。然而,由于放大器非线性、相位噪声和I/Q不均衡等因素的影响,这类硬件损伤成为制约当前MIMO异构网络波束成形性能进一步提升的瓶颈。为了解决该问题,该文提前将硬件损伤考虑到MIMO异构网络波束成形算法设计当中。首先,考虑了每个基站的最大发射功率约束和每个用户的最小信干噪比约束,建立了一个含硬件损伤参数的系统总能耗最小的资源优化问题。其次,利用等价变换和半正定松弛方法,将原非凸问题转化为凸优化问题进行求解。仿真结果表明,与完美硬件条件下的波束成形算法对比,所提算法具有较好的抗硬件损伤能力和较低的中断概率。     

Beamforming for inter‐relay interference reduction in MIMO‐aided two‐path successive relaying

To effectively reduce the inter‐relay interference (IRI) in two‐path successive relaying, two beamforming schemes are proposed in this paper, utilizing multiple‐antenna relay nodes. Specifically, the two cooperation nodes perform receive combining of the source signal and transmit beamforming of the relayed signal alternately in the successive relaying process. As a result, the IRI between them can be effectively suppressed, thanks to the additional degree of freedom provided by the multiple‐input multiple‐output inter‐relay channel. In the first beamforming scheme, the source‐to‐destination signal‐to‐interference‐plus‐noise ratios (SINR) of separate paths are maximized with approximation, leading to a minimum variance distortionless response beamformer under the high SINR condition. To further improve the system performance, noting that the received SINRs of the two paths have impact on each other due to the mutual coupling of the beamformers, the sum of mean squared errors from these two transmission paths is minimized in the second scheme. Based on this performance criterion, a suboptimal beamformer design is developed numerically through cyclic minimization of the sum of mean squared error cost function. Simulation results demonstrate the superiority of both proposed beamforming schemes in terms of symbol error rate and the achievable system rate, in particular, at high IRI levels. Copyright © 2016 John Wiley & Sons, Ltd.     

Optimal beamforming for two-way multi-antenna relay channel with analogue network coding

This paper studies the wireless two-way relay channel (TWRC), where two source nodes, S1 and S2, exchange information through an assisting relay node, R. It is assumed that R receives the sum signal from S1 and S2 in one timeslot, and then amplifies and forwards the received signal to both S1 and S2 in the next time-slot. By applying the principle of analogue network coding (ANC), each of S1 and S2 cancels the so-called "self-interference" in the received signal from R and then decodes the desired message. Assuming that S1 and S2 are each equipped with a single antenna and R with multi-antennas, this paper analyzes the capacity region of the ANC-based TWRC with linear processing (beamforming) at R. The capacity region contains all the achievable bidirectional rate-pairs of S1 and S2 under the given transmit power constraints at S1, S2, and R. We present the optimal relay beamforming structure as well as an efficient algorithm to compute the optimal beamforming matrix based on convex optimization techniques. Low-complexity suboptimal relay beamforming schemes are also presented, and their achievable rates are compared against the capacity with the optimal scheme.     

多跳多中继无线网络中的协作波束形成技术

针对多跳多中继无线网络中的协作波束形成技术进行研究.在基于放大转发机制的三跳协作通信系统中,对2个中继节点簇的协作波束形成矢量进行联合设计,以求在目标节点获得最大的接收信噪比.该方法首先将原始优化问题加以推导简化,然后应用半定规划方法求解获得协作波束形成矢量的次优解,并结合对分搜索算法加以改进.仿真结果表明,提出的协作波束形成方法可取得明显优于固定放大增益中继策略的接收信噪比.     

A distributed transmit beamforming synchronization strategy for multi-element radar systems

The distributed transmit beamforming has recently been discussed as an energy-effective technique in wireless communication systems. A common ground of various techniques is that the destination node transmits a beacon signal or feedback to assist source nodes to synchronize signals. However, this approach is not appropriate for a radar system since the destination is a non-cooperative target of an unknown location. In our paper, we propose a novel synchronization strategy for a distributed multiple-element beamfoming radar system. Source nodes estimate parameters of beacon signals transmitted from others to get their local synchronization information. The channel information of the phase propagation delay is transmitted to nodes via the reflected beacon signals as well. Next, each node generates appropriate parameters to form a beamforming signal at the target. Transmit beamforming signals of all nodes will combine coherently at the target compensating for different propagation delay. We analyse the influence of the local oscillation accuracy and the parameter estimation errors on the performance of the proposed synchronization scheme. The results of numerical simulations illustrate that this synchronization scheme is effective to enable the transmit beamforming in a distributed multi-element radar system.     

Robust hybrid beamforming design for millimeter-wave massive MIMO systems

Hybrid analog-digital beamforming is recognized as a promising solution for a practical implementation of massive multiple-input multiple-output(MIMO) systems based on millimeter-wave(mmWave) technology. In view of the overwhelming hardware cost and excessive power consumption and the imperfection of the channel state information(CSI), a robust hybrid beamforming design is proposed for the mmWave massive MIMO systems, where the robustness is defined with respect to imperfect knowledge or error of the CSI at the transmitter due to limited feedback and/or imperfect channel estimation. Assuming the errors of the CSI are bounded, the optimal hybrid beamforming design with robustness is formulated to a mean squared error(MSE) minimization problem. An iterative semidefinite programming(SDP) based algorithm is proposed to obtain the beamforming matrices. Simulation results show that the proposed robust design can provide more than 4 dB performance gain compared to that of non-robust design.     

Joint Clustering Relay Selection and Beamforming in Cooperative Cognitive Radio Networks

This paper proposes a joint clustering relay selection and beamforming method for a more realistic cooperative cognitive radio network, in which a secondary network of multiple secondary links and a relay network coexist with a primary network of one primary link. We aim to improve performance of the system in terms of maximizing the received signal power of the secondary destinations, subject to the constraint of received interference plus noise power of the primary destination using the proposed method. Since different relays cooperate differently towards the signals at the secondary and primary destinations, the proposed method can improve the performance of the system and enables the relay network to simultaneously transmit signals of all secondary links toward the destinations by clustering the relays. Results of simulations confirm validity of the method and improve the system performance compared to the existing cooperative beamforming and Zero-Forcing beamforming, in which no relay selection strategy is used.