Robust Downlink Beamforming Based on Outage Probability Specifications

A new approach to multi-antenna downlink beam- forming is proposed that provides an improved robustness against uncertainty in the downlink channel covariance matrices caused by errors between the actual and estimated channel values. The proposed method uses the knowledge of the statistical distribution of such a covariance uncertainty to minimize the total downlink transmit power under the constraint that the outage probability does not exceed a certain threshold value. Although our approach initially leads to a non-convex optimization problem, it can be reformulated in a convex form using the semidefinite relaxation technique. The resulting convex optimization problem can be solved efficiently using the well-established interior point methods. Computer simulations verify performance improvements of the proposed technique as compared to the robust transmit beamforming method based on the worst-case performance optimization with judicious selection of the upper bounds on channel covariance errors.     

星地融合网络中基于层分复用的广播和单播传输鲁棒波束赋形

星地融合网络(STIN)为解决下一代无线通信中地面基站存在的覆盖范围约束和频谱短缺瓶颈提供一种有效架构。针对该融合网络中下行广播和单播单独传输性能受限问题，该文建立基于服务质量(QoS)约束的最小化传输功率优化模型，提出基于层分复用(LDM)的鲁棒联合波束赋形传输方案。且根据最差情况准则，采用S-Procedure及半正定松弛(SDR)方法将具有无穷维约束的鲁棒优化问题转化为具有线性矩阵不等式(LMI)的确定性优化形式，并提出一种基于罚函数的迭代算法求解该问题。仿真结果表明，所提方案在传输功耗方面比传统正交时分复用(TDM)传输方案降低约6 dBm，且用户平均速率相较于非协作传输方案提升明显。     

User clustering and robust beamforming design in multicell MIMO-NOMA system for 5G communications

In this paper, we present a robust beamforming design to tackle the weighted sum-rate maximization (WSRM) problem in a multicell multiple-input multiple-output (MIMO) – non-orthogonal multiple access (NOMA) downlink system for 5G wireless communications. This work consider the imperfect channel state information (CSI) at the base station (BS) by adding uncertainties to channel estimation matrices as the worst-case model i.e., singular value uncertainty model (SVUM). With this observation, the WSRM problem is formulated subject to the transmit power constraints at the BS. The objective problem is known as non-deterministic polynomial (NP) problem which is difficult to solve. We propose an robust beamforming design which establishes on majorization minimization (MM) technique to find the optimal transmit beamforming matrix, as well as efficiently solve the objective problem. In addition, we also propose a joint user clustering and power allocation (JUCPA) algorithm in which the best user pair is selected as a cluster to attain a higher sum-rate. Extensive numerical results are provided to show that the proposed robust beamforming design together with the proposed JUCPA algorithm significantly increases the performance in term of sum-rate as compared with the existing NOMA schemes and the conventional orthogonal multiple access (OMA) scheme.     

Robust Power Allocation Designs for Multiuser and Multiantenna Downlink Communication Systems through Convex Optimization

In this paper, we study the design of the transmitter in the downlink of a multiuser and multiantenna wireless communications system, considering the realistic scenario where only an imperfect estimate of the actual channel is available at both communication ends. Precisely, the actual channel is assumed to be inside an uncertainty region around the channel estimate, which models the imperfections of the channel knowledge that may arise from, e.g., estimation Gaussian errors, quantization effects, or combinations of both sources of errors. In this context, our objective is to design a robust power allocation among the information symbols that are to be sent to the users such that the total transmitted power is minimized, while maintaining the necessary quality of service to obtain reliable communication links between the base station and the users for any possible realization of the actual channel inside the uncertainty region. This robust power allocation is obtained as the solution to a convex optimization problem, which, in general, can be numerically solved in a very efficient way, and even for a particular case of the uncertainty region, a quasi-closed form solution can be found. Finally, the goodness of the robust proposed transmission scheme is presented through numerical results. Robust designs, imperfect CSI, multiantenna systems, broadcast channel, convex optimization.     

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.     

非完备杂波先验知识场景下MIMO-STAP稳健波形设计

本文考虑了色高斯干扰条件下MIMO STAP稳健波形优化问题以提高非完备杂波先验知识条件下多输入多输出（MIMO）雷达体制下空时自适应处理（STAP）最坏情况下探测性能。由于高斯干扰（包括杂波、干扰以及热噪声）场景下最大化系统输出信干噪比（SINR）等价于最大化MIMO STAP检测性能,因而在本文所建立杂波协方差估计误差的模型基础上,总功率发射以及参数不确定凸集约束下,经推导可得稳健波形优化问题。为求解得到的复杂非线性问题,本文提出了一种迭代算法以优化发射波形相关阵（WCM）从而最大化凸不确定集上最差情况下的输出SINR进而改善最差情况下MIMO STAP的检测性能。通过利用对角加载（DL）方法,所提算法中的每个迭代步骤皆可表示为能获得高效求解的半定规划（SDP）问题。与非稳健方法及非相关波形相比,数值实验验证了本文所提方法的有效性。      

Robust Cognitive Beamforming With Bounded Channel Uncertainties

This paper studies the robust beamforming design for a multi-antenna cognitive radio (CR) network, which transmits to multiple secondary users (SUs) and coexists with a primary network of multiple users. We aim to maximize the minimum of the received signal-to-interference-plus-noise ratios (SINRs) of the SUs, subject to the constraints of the total SU transmit power and the received interference power at the primary users (PUs) by optimizing the beamforming vectors at the SU transmitter based on imperfect channel state information (CSI). To model the uncertainty in CSI, we consider a bounded region for both cases of channel matrices and channel covariance matrices. As such, the optimization is done while satisfying the interference constraints for all possible CSI error realizations. We shall first derive equivalent conditions for the interference constraints and then convert the problems into the form of semi-definite programming (SDP) with the aid of rank relaxation, which leads to iterative algorithms for obtaining the robust optimal beamforming solution. Results demonstrate the achieved robustness and the performance gain over conventional approaches and that the proposed algorithms can obtain the exact robust optimal solution with high probability.      

Tomlinson-Harashima Precoding for Broadcast Channels with Uncertainty

We consider the design of Tomlinson-Harashima (TH) precoders for broadcast channels in the presence of channel uncertainty. For systems in which uplink-downlink reciprocity is used to obtain a channel estimate at the transmitter, we present a robust design based on a statistical model for the channel uncertainty. We provide a convex formulation of the design problem subject to two types of power constraints: a set of constraints on the power transmitted from each antenna and a total power constraint. For the case of the total power constraint, we present a closed-form solution for the robust TH precoder that incurs essentially the same computational cost as the corresponding designs that assume perfect channel knowledge. For systems in which the receivers feed back quantized channel state information to the transmitter, we present a robust design based on a bounded model for the channel uncertainty. We provide a convex formulation for the TH precoder that maximizes the performance under the worst-case channel uncertainty subject to both types of power constraints. We also present a conservative robust design for this type of channel uncertainty that has reduced computational complexity for the case of power constraints on individual antennas and leads to a closed-form solution for the total power constraint case. Simulation studies verify our analytical results and show that the robust TH precoders can significantly reduce the rather high sensitivity of broadcast transmissions to errors in channel state information.     

Robust Tomlinson-Harashima Precoders for Multiuser MISO Downlink with Imperfect CSI

In this paper, we consider robust non-linear precoding for the downlink of a multiuser multiple-input single-output (MISO) communication system in the presence of imperfect channel state information (CSI). The base station (BS) is equipped with multiple transmit antennas and each user terminal is equipped with a single receive antenna. We propose two robust Tomlinson-Harashima precoder (THP) designs. The first design is based on the minimization of the total BS transmit power under constraints on the mean square error (MSE) at the individual user receivers. We show that this problem can be solved by an iterative procedure, where each iteration involves the solution of a pair of convex optimization problems that can be solved efficiently. A robust linear precoder with MSE constraints can be obtained as a special case of this robust THP. The second design is based on the minimization of a stochastic function of the sum MSE under a constraint on the total BS transmit power. We formulate this design problem as an optimization problem that can be solved by the method of alternating optimization, the application of which results in a second-order cone program that can be numerically solved efficiently. Simulation results illustrate the improvement in performance of the proposed precoders compared to other robust linear and non-linear precoders in the literature.     

Solution of the multiuser downlink beamforming problem with individual SINR constraints

We address the problem of joint downlink beamforming in a power-controlled network, where independent data streams are to be transmitted from a multiantenna base station to several decentralized single-antenna terminals. The total transmit power is limited and channel information (possibly statistical) is available at the transmitter. The design goal: jointly adjust the beamformers and transmission powers according to individual SINR requirements. In this context, there are two closely related optimization problems. P1: maximize the jointly achievable SINR margin under a total power constraint. P2: minimize the total transmission power while satisfying a set of SINR constraints. In this paper, both problems are solved within a unified analytical framework. Problem P1 is solved by minimizing the maximal eigenvalue of an extended crosstalk matrix. The solution provides a necessary and sufficient condition for the feasibility of the SINR requirements. Problem P2 is a variation of problem P1. An important step in our analysis is to show that the global optimum of the downlink beamforming problem is equivalently obtained from solving a dual uplink problem, which has an easier-to-handle analytical structure. Then, we make use of the special structure of the extended crosstalk matrix to develop a rapidly converging iterative algorithm. The optimality and global convergence of the algorithm is proven and stopping criteria are given.     

非理想信道状态信息下RIS辅助的安全通信

利用可重构智能表面(Reconfigurable Intelligent Surface, RIS)辅助无线发射机,可提高多用户无线网络的安全传输能力。在非理想信道状态信息(Channel State Information, CSI)下提出了鲁棒波束形成优化方法来提高系统对抗干扰和窃听攻击的能力。具体地,使用RIS辅助发射机,对RIS的相位波束形成和基站的传输功率进行联合优化,在分别满足有界CSI的最坏情况速率约束和统计CSI的速率中断概率约束来最小化系统的总传输功率。由于存在CSI误差,针对有界CSI和统计CSI误差约束,分别利用S-procedure来松弛保密速率约束和大偏差不等式(Large Deviation Inequality, LDI)来松弛保密速率中断概率约束。仿真结果表明,相比于无源反射法和传统波束形成方案,该方法可分别降低约88%和93%总传输功率,同时提高约15 dBm和12 dBm的干扰容限。     

多小区蜂窝网络波束成形优化策略

为了克服多小区的邻小区干扰问题,该文在多小区蜂窝网络中,研究了多小区多用户下行协同传输技术。该文提出一种联合优化基站和中继的波束成形权重的迭代算法,在基站和中继总功率限制下最大化最差用户接收信干噪比(Signal-to-Interference-and-Noise Ratio, SINR)。该文提出的联合优化波束成形策略,可以应用半正定松弛技术(Semi-Definite Relaxation, SDR)得到有效的解决。仿真表明,在多小区通信系统中,该文提出的迭代算法只需要少量的迭代次数就可以达到近似最优性能,并且在性能和资源消耗之间给出一种折中的传输策略。     

Robust Waveform Design for MIMO Radar with Imperfect Prior Knowledge

Waveform optimization for multi-input multi-output radar usually depends on the initial parameter estimates (i.e., some prior information on the target of interest and scenario). However, it is sensitive to estimate errors and uncertainty in the parameters. Robust waveform design attempts to systematically alleviate the sensitivity by explicitly incorporating a parameter uncertainty model into the optimization problem. In this paper, we consider the robust waveform optimization to improve the worst-case performance of parameter estimation over a convex uncertainty model, which is based on the Cramer–Rao bound. An iterative algorithm is proposed to optimize the waveform covariance matrix such that the worst-case performance can be improved. Each iteration step in the proposed algorithm is solved by resorting to convex relaxation that belongs to the semidefinite programming class. Numerical results show that the worst-case performance can be improved considerably by the proposed method compared to that of uncorrelated waveforms and the non-robust method.     

Downlink Throughput Maximization for Interference Limited Multiuser Systems: TDMA versus CDMA

We consider the downlink throughput maximization problem for interference limited multiuser systems. Our goal is to characterize the optimum base station transmission strategy, i.e., whether the base station transmits to one-user (TDMA) or multiple users (CDMA). Specifically, we aim at determining the optimum number of users to be scheduled and finding the corresponding power allocation. We model the interference by the aid of the orthogonality factor, and determine the throughput maximizing transmission strategy for a range of the values of the orthogonality factor, and the channel gains, subject to a total power constraint. Although the resulting optimization problem may turn out to be non-convex, we show that valuable observations regarding the structure of the optimum solution can be obtained by examining the performance metric from an individual user's point of view. We propose an exact and a near-exact algorithm to determine whether one-user-transmission is the optimum strategy, or more than one user should be transmitted to. Numerical results to support our analysis, as well as the modifications to the proposed algorithms in the presence of individual power constraints are presented.     

Energy efficiency and spectral efficiency tradeoff in downlink OFDMA systems with imperfect CSI

In this paper, we investigate the tradeoff between energy efficiency (EE) and spectral efficiency (SE) in downlink orthogonal frequency division multiplexing access (OFDMA) systems, whilst considering the channel estimation cost and the corresponding effect of imperfect channel state information (CSI) on SE and EE. The problem is formulated as a multi-objective optimization to determine the optimal pilot transmission power, data transmission power and subcarrier assignment, and then transformed into a single-objective optimization problem, which is a non-convex mixed-integer nonlinear programming (NCMINP) and NP-hard. To address it, we propose an efficient algorithm by adopting alternating optimization and convex optimization methods in lower power region as well as approximate conversion and branch-and-bound methods in high power region. Simulation results analyze and validate the performance of EE-SE tradeoff.     

非准确先验知识下认知雷达低峰均比稳健波形设计

针对目标和杂波先验知识不准确时认知雷达的检测波形设计问题,同时兼顾功率放大器对低峰均比(PAR)波形的需求,该文提出一种信号相关杂波背景下认知雷达低PAR稳健波形设计方法。首先,在目标和杂波不确定集范围内,基于极大极小化准则构造关于输出信干噪比(SINR)的优化模型;然后将不确定性参数代入该模型,给出最差SINR下对应杂波协方差矩阵和目标Toeplitz矩阵的取值;在此基础上,利用半正定松弛,将非凸的优化模型转化为关于发射波形半正定矩阵的凸问题进行求解;最后,通过秩1近似法结合最近邻方法,进一步从波形的最优矩阵解中提取出最优向量解。分析表明,在稳健性能相同的情况下,与现有方法相比该算法具有更低的运算量,仿真结果验证了所提方法的有效性和稳健性。     

Multiuser MIMO Transceiver Design for Uplink and Downlink with Imperfect CSI

This paper considers a joint linear transmitter and receiver design for multi-user multiple-input multiple-output (MU-MIMO) systems using total mean square error (TMSE) criterion, subject to a total transmit power constraint assuming imperfect channel state information. Both the uplink and downlink MU-MIMO systems, which is employed with improper constellations such as binary phase shift-keying and $M$ -ary amplitude shift-keying are considered. A minimum TMSE design is formulated as a nonconvex optimization problem under a total transmit power constraint and the closed-form optimum linear precoder and decoder for both the downlink and uplink MU-MIMO systems with improper modulation are determined by solving this nonconvex optimization problem. A novel contribution in this paper is to derive a closed-form optimum linear precoder and decoder for both the downlink and uplink MU-MIMO systems with improper modulation by solving the nonconvex optimization problem under total power constraint. The simulation results show that the performance of the proposed design is improved over the previous design.     

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.      

Optimum Downlink Power Control of a DS-CDMA System via Convex Programming

An optimum downlink power control that maximizes the user-capacity of a Direct Sequence-Code Division Multiple Access (DS-CDMA) cellular system is proposed based on a convex programming method. First, the downlink beamforming weights for the base-station antenna-array are designed based on the maximum Signal-Interference-Ratio (SIR) criterion. Then by optimizing the downlink power subject to a fixed total transmit power constraint, we further increase the Signal-Interference-Noise-Ratio (SINR) at the mobile terminal, thus increasing the capacity of the system. With the same methodology, we can also minimize the required transmit power while satisfying the SINR threshold constraints. Additionally, a robust downlink power control approach for mitigating the performance degradation due to channel estimates error is also proposed. Computer simulations are given to demonstrate the improvement of downlink capacity, received SINR, robustness, and the minimization of the required transmit power for a DS-CDMA system with antenna-array at the base-station.     

Uniform power allocation in MIMO channels: a game-theoretic approach

When transmitting over multiple-input-multiple-output (MIMO) channels, there are additional degrees of freedom with respect to single-input-single-output (SISO) channels: the distribution of the available power over the transmit dimensions. If channel state information (CSI) is available, the optimum solution is well known and is based on diagonalizing the channel matrix and then distributing the power over the channel eigenmodes in a "water-filling" fashion. When CSI is not available at the transmitter, but the channel statistics are a priori known, an optimal fixed power allocation can be precomputed. This paper considers the case in which not even the channel statistics are available, obtaining a robust solution under channel uncertainty by formulating the problem within a game-theoretic framework. The payoff function of the game is the mutual information and the players are the transmitter and a malicious nature. The problem turns out to be the characterization of the capacity of a compound channel which is mathematically formulated as a maximin problem. The uniform power allocation is obtained as a robust solution (under a mild isotropy condition). The loss incurred by the uniform distribution is assessed using the duality gap concept from convex optimization theory. Interestingly, the robustness of the uniform power allocation also holds for the more general case of the multiple-access channel.