Robust Beamforming Under Channel Prediction Errors for Time-Varying MIMO System

The accuracy of acquired channel state information(CSI)for beamforming design is essential for achievable performance in multiple-input multiple-output(MIMO)systems.However,in a high-speed moving scene with time-division duplex(TDD)mode,the acquired CSI depending on the channel reciprocity is inevitably outdated,leading to outdated beamforming design and then performance degradation.In this paper,a robust beamforming design under channel prediction errors is proposed for a time-varying MIMO system to combat the degradation further,based on the channel prediction technique.Specifically,the statistical characteristics of historical channel prediction errors are exploited and modeled.Moreover,to deal with random error terms,deterministic equivalents are adopted to further explore potential beamforming gain through the statistical information and ultimately derive the robust design aiming at maximizing weighted sum-rate performance.Simulation results show that the proposed beamforming design can maintain outperformance during the downlink transmission time even when channels vary fast,compared with the traditional beamforming design.

Robust beamforming for IRS-aided SWIPT in cognitive radio networks

Intelligent reflecting surface(IRS)is widely recognized as a promising technique to enhance the system perfor-mance,and thus is a hot research topic in future wireless communications.In this context,this paper proposes a robust BF scheme to improve the spectrum and energy harvesting efficiencies for the IRS-aided simultaneous wireless information and power transfer(SWIPT)in a cognitive radio network(CRN).Here,the base station(BS)utilizes spectrum assigned to the primary users(PUs)to simultaneously serve multiple energy receivers(ERs)and information receivers(IRs)through IRS-aided multicast technology.In particular,by assuming that only the imperfect channel state information(CSI)is available,we first formulate a constrained problem to maximize the minimal achievable rate of IRs,while satisfying the harvesting energy threshold of ERs,the quality-of-service requirement of IRs,the interference threshold of PUs and transmit power budget of BS.To address the non-convex problem,we then adopt triangle inequality to deal with the channel uncertainty,and propose a low-complexity algorithm combining alternating direction method of multipliers(ADMM)with alternating optimi-zation(AO)to jointly optimize the active and passive beamformers for the BS and IRS,respectively.Finally,our simulation results confirm the effectiveness of the proposed BF scheme and also provide useful insights into the importance of introducing IRS into the CRN with SWIPT.

Robust Beamforming for Secured Wireless Power Transfer in MIMO Magnetic Resonant Coupling System:A Probabilistic Approach

Wireless power transfer(WPT) to support mobile and portable devices is an emerging wireless technique.Among all kinds of approaches,magnetic resonance coupling(MRC) is an excellent one for mid-range WPT,which provides better mobility,flexibility,and convenience due to its simplicity in hardware implementation and longer transmission distances.In this paper,we consider an MRCWPT system with multiple power transmitters,one intended power receiver and multiple unintended power receivers.We investigate the probabilistic robust beamforming designs and provide efficient algorithms to achieve the local optimums under two different criteria,i.e.,total source power minimization problem and min-max unintended receiving power restriction problem.As the problems are quite typical in robust design situations,our proposed robust beamformers can be conveniently applied to other probabilistic robust design problems,thus reduce the complexity as well as improve the beamforming performance.Numerical results demonstrate that the proposed algorithms can significantly improve the performance as well as the robustness of the WPT system.

A double constrained robust capon beamforming based imaging method for early breast cancer detection

Ultra-wideband （UWB） microwave images are proposed for detecting small malignant breast tumors based on the large contrast of electric parameters between a malignant tumor and normal breast tissue. In this study, an antenna array composed of 9 antennas is applied to the detection. The double constrained robust capon beamforming （DCRCB） algorithm is used for reconstructing the breast image due to its better stability and high signal-to-interference-plus-noise ratio （SINR）. The successful detection of a tumor of 2 mm in diameter shown in the reconstruction demonstrates the robustness of the DCRCB beamforming algorithm. This study verifies the feasibility of detecting small breast tumors by using the DCRCB imaging algorithm.

Multi-objective robust secure beamforming for cognitive satellite and UAV networks

A multi-objective optimization based robust beamforming(BF)scheme is proposed to realize secure transmission in a cognitive satellite and unmanned aerial vehicle(UAV)network.Since the satellite network coexists with the UAV network,we first consider both achievable secrecy rate maximization and total transmit power minimization,and formulate a multi-objective optimization problem(MOOP)using the weighted Tchebycheff approach.Then,by supposing that only imperfect channel state information based on the angular information is available,we propose a method combining angular discretization with Taylor approximation to transform the non-convex objective function and constraints to the convex ones.Next,we adopt semi-definite programming together with randomization technology to solve the original MOOP and obtain the BF weight vector.Finally,simulation results illustrate that the Pareto optimal trade-off can be achieved,and the superiority of our proposed scheme is confirmed by comparing with the existing BF schemes.

Joint Antenna Selection and Robust Beamforming Design in Multi-cell Distributed Antenna System

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.

Robust adaptive beamforming for constant modulus signal of interest

It is required in the diagonally loaded robust adaptive beamforming the automatic determination of the loading level which is practically a challenging problem.A constant modulus restoral method is herein presented to choose the diagonal loading level adaptively for the extraction of a desired signal with constant modulus(a common feature of the phase modulation signals).By introducing the temporal smoothing technique,the proposed constant modulus restoral diagonally loaded robust adaptive beamformer provides increased capability compared with some existing robust adaptive beamformers in rejecting interferences and noise while protecting the signal-of-interest.Simulation results are included to illustrate the performance of the proposed beamformer.

非理想CSI下IRS辅助MISO保密速率最大化方法

基于智能反射面辅助多输入、单输出的安全无线通信系统,提出一种最大化系统保密速率为目标联合主被动波束形成算法.考虑非理想信道状态信息下基站发射波束成形向量和无源智能反射面相移矩阵联合优化设计问题.为解决非凸分式规划问题,通过Charnes-Cooper变换引入两个辅助变量,将单项分式问题转化为差的形式,同时采用一种交替迭代优化联合半正定松弛方法,得到易于求解的凸问题.仿真实验结果表明,该算法相比传统算法,有效提升了系统的安全性,保密性能提升10%~30%,且在一定信道状态信息误差下保密速率下降不明显,具有较强的鲁棒性.

基于小快拍场景的联合校正稳健波束形成算法

针对传统的自适应波束形成算法在目标导向矢量失配及接收数据的协方差矩阵存在误差时,性能急剧下降的问题,提出了一种基于小快拍场景的联合协方差矩阵重构,及导向矢量优化的稳健波束形成算法。对不确定集约束求解得到干扰导向矢量,根据稀疏干扰来向的导向矢量近似正交,求出干扰导向矢量对应的干扰功率,从而完成协方差矩阵重构;对期望信号来向及其邻域进行权值求解,对加权后的数据特征分解,利用多信号分类(Multiple Signal Classification, MUSIC)谱估计算法对信号区域积分得到信号协方差矩阵,将其主特征值近似为期望信号的导向矢量完成重新估计。仿真结果表明,在无误差时,算法输出信干噪比(Signal to Interference Plus Noise Ratio, SINR)接近理论最优;在多种误差环境下输出性能随信噪比(Signal to Noise Ratio, SNR)的变化均具有较好的稳健性,并且在信号来向可精准形成波束;在小快拍时可以较快收敛至理论最优值。

阵元位置互质的线性阵列:阵列校正和波束形成

该文研究了阵元位置互质的线性阵列(CLA)的阵列校正和波束形成问题。在假设CLA天线单元部分校准的条件下,基于同时干扰定位与阵列校正(SILAC)技术,设计了一种适用于CLA的阵列校正和波束形成方法:CLA-SILAC-INCM算法。从理论上分析证明了,当CLA中包含有L_c≥3个完全校准的天线单元,使用SILAC技术可以高精度无模糊地实现干扰源角度和阵列天线幅相误差估计,并在此基础上完成干扰噪声协方差矩阵(INCM)重建和波束形成最优权向量构造。通过仿真实验验证了,提出的CLA-SILAC-INCM算法具有比其他常用算法更好的性能,尤其是信噪比接近干噪比时,CLA-SILAC-INCM算法的优势更为明显。

可重构智能反射面辅助太赫兹通信系统鲁棒波束赋形算法

太赫兹通信作为6G的关键技术之一,被认为是能够解决频谱资源短缺、提升系统容量的有效手段。然而,由于路径损耗极高和分子的吸收作用,太赫兹容易被障碍物阻挡导致通信中断。为了解决该问题,该文将可重构智能反射面(RIS)引入到太赫兹通信系统中,且考虑信道不确定性对传输稳定性的影响,基于用户服务质量约束、基站发射功率约束及RIS离散相移约束,建立多用户能效最大化波束赋形模型。利用丁克尔巴赫、连续凸近似、S-程序、半正定松弛、相位映射和块坐标下降将原非凸优化问题转化为凸优化问题进行求解。仿真结果表明,与传统非鲁棒波束赋形对比,所提算法能效提升了15.4%,中断概率减小了15.48%。

多维阵列张量模型的鲁棒波束成形方法

传统波束成形算法在应对维数较高的多维阵列时,训练快拍数难以满足远大于信号维数这一要求,从而导致波束成形器性能急剧下降。针对这一问题,本文给出了多维阵列输出数据的张量模型,基于多维阵列子维度的可分离性,引入张量波束成形方法,分析了其在训练快拍数需求上具有的优势。然后,基于张量波束成形中子维度干扰协方差矩阵的模型,通过直接估计干扰协方差矩阵实现了一种鲁棒张量波束成形方法。分析表明:该方法可更好地应对非均匀杂波环境以及相干干扰,并得到更高的输出信干噪比,以给出的二维极化敏感阵列为例,所提方法的训练快拍数需求为传统方法的1/3,相干干扰下输出信干噪比提高了约2.5 dB,仿真验证了分析的有效性。

基于列车先验信息的RIS-MIMO系统鲁棒波束成形算法

针对高移动性场景中完美信道状态信息(CSI)难以获取导致的智能超表面多输入多输出(RIS-MIMO)系统主被动波束成形算法性能恶化的问题,构建了RIS辅助的高铁毫米波MIMO中继通信模型。首先,在列车位置信息不完全的情况下,估计并推导了RIS-车载移动中继(MRN)之间视线战略(LOS)路径角度估计误差的统计特性;其次,对毫米波MIMO系统的中断性能进行了研究,给出了以信道容量作为中断判决的中断概率表达式;最后,将优化问题建模为5G基站(gNB)发射功率约束的中断概率最小化问题,提出了一种基于黎曼共轭梯度下降的复圆流形优化算法并求解该问题。仿真结果表明,与现有算法和传统的无RIS系统以及RIS随机相位调节下的高铁通信系统相比,所提算法具有更快的收敛速度和更高的系统鲁棒性。

基于不完美CSI的低轨卫星通信系统鲁棒资源分配算法

为了解决低轨卫星通信系统因资源受限导致的能量与速率不平衡的问题,同时考虑信道不确定性对实际卫星通信系统性能衰退的影响,该文提出一种基于最大化最小能效的鲁棒资源分配算法。首先,考虑每个用户中断速率约束、功率分配系数约束和最大发射功率约束,基于高斯信道不确定性,构建了联合优化卫星波束成形向量与功率分配因子的鲁棒资源分配模型。所描述的问题是一个含参数摄动的非凸、非确定性多项式难问题,很难直接求解。为此,基于丁克尔巴赫、伯恩斯坦不等式、半正定松弛和交替优化等方法将其转化为等价的凸优化问题,并提出一种基于迭代的混合鲁棒波束成形与功率分配算法。仿真结果表明,该文算法具有较好的能效和较强的鲁棒性。

一种非平滑相干干扰鲁棒的自适应波束形成器

针对文献报道的鲁棒自适应波束形成(robust adaptive beamforming,RAB)算法,分析了在存在相干干扰时其性能严重下降甚至失效的原因:通过将接收信号协方差矩阵分解为阵列流形矩阵左和共轭右乘一个矩阵P的描述形式,在存在相干干扰时,P为非对角阵,其非对角元素表征了信号与干扰间的互相关,该成分造成了RAB算法的失效;另表明:快拍数有限可视为特殊的相干干扰情况。为此,提出了一种构建P为对角阵的协方差矩阵拟合方法;并据拟合的协方差矩阵,给出了对非平滑相干干扰RAB方法。仿真验证了分析的有效性,所提方法在相干干扰时仍能实现非相干干扰时的性能,且收敛速度优于报道方法。

基于JADE-斜投影的鲁棒波束形成算法

针对矩阵重构类波束形成算法对阵列幅相误差敏感的问题,提出一种基于盲源信号分离和斜投影的矩阵重构鲁棒波束形成算法。首先,依靠盲源分离技术得到接收信号和混合矩阵,结合期望信号先验信息完成混合矩阵中信号导向矢量的搜索。然后,利用盲源分离得到的信号协方差矩阵完成阵列幅相误差估计。最后,基于幅相误差校准的混合矩阵和斜投影思想,构建各干扰的斜投影算子,将接收数据分别向干扰斜投影空间进行投影,得到对应的干扰信号,完成干扰噪声协方差矩阵重构。仿真结果表明,所提方法对阵列幅相误差具有较好的鲁棒性,验证了算法的有效性。

一种基于MVDR的改进型麦克风阵列语音增强算法

传统的最小方差无失真响应(Minimum Variance Distortionless Response,MVDR)波束形成算法不能很好地跟踪信号统计特征的变化,适应时变环境的能力较差.本文对其进行改进,提出一种实时估计环境噪声及干扰的相关矩阵的方法,使用时变遗忘因子更新相关矩阵,遗忘因子根据目标语音的存在概率变化,最后引入对角加载技术更新滤波器权向量,以保证波束形成的质量.实验结果显示,相比传统的MVDR算法,改进后的MVDR波束形成算法具有更好的降噪效果,能获得更高的分段信噪比和PESQ得分.

基于深度展开ADMM网络的稳健自适应波束形成

阵列通道间的幅相误差导致导向矢量失配,会严重退化自适应波束形成的性能。现有稳健自适应波束形成(RAB)方法通过引入最差导向矢量失配误差约束或联合估计幅相误差和波束形成器权值矢量,以改善波束形成性能,但这些方法的计算复杂度高,且在有限快拍下性能有限。为此,文中在深度展开框架下提出一种基于交替方向乘子法(ADMM)的RAB网络,以快速实现幅相误差和干扰协方差矩阵的联合估计。首先,建立存在阵列通道幅相误差时的干扰信号稀疏表示模型;然后,根据基于ADMM的幅相误差和干扰稀疏表示系数联合估计算法,设计一种深度展开ADMM(DU-ADMM)网络,该网络的输入为接收到达的干扰信号,输出为幅相误差和干扰稀疏表示系数;最后,利用该网络的输出重构出干扰加噪声协方差矩阵,并生成稳健自适应波束形成器。仿真结果表明,DU-ADMM网络可在单快拍场景下实现RAB,且能够以较少的网络层数更精确地估计出幅相误差,有效降低了计算量,同时可获得更高的输出信干噪比。

基于智能反射面的无线携能认知网络鲁棒传输设计

针对智能反射面辅助的无线携能认知网络,提出了一种基于用户非完美信道状态信息的波束成形方案,提高网络的频谱和能量收集效率。在假设用户信道误差范数有界的条件下,建立了以信息接收用户最小可达速率最大化为目标函数,以满足信息接收用户和能量接收用户需求、主用户干扰阈值和基站最大发射功率为约束条件的优化问题。针对此非凸问题,提出利用三角不等式、交替方向乘子法和交替优化的迭代算法,以较低的计算复杂度求解得到基站的有源波束成形权矢量和智能反射面的无源波束成形矩阵。最后,仿真验证了所提方案相较于随机相位方案能够有效提高系统的性能,证明了在携能认知网络中引入智能反射面的可行性和有效性。

智能反射面辅助的星地认知网络多播传输鲁棒优化设计

针对智能反射面(Intelligent reflecting surface,IRS)辅助的星地认知网络(Cognitive satellite and terrestrial networks,CSTN),提出了一种基于用户非完美信道状态信息的鲁棒多播传输算法,进一步提高了系统频谱效率。卫星采用多播技术服务多个主用户,同时共享频谱资源的地面基站(Base station,BS)通过空分多址和智能反射面分别服务直达用户和遮挡用户。然后,以地面网络发射功率最小化为优化目标,同时将地面用户的中断概率和主用户所受的最大干扰功率作为约束条件,提出联合优化问题。针对此非凸问题,首先借助指数分布的累积分布函数将非凸的中断概率约束转化为可解形式。接着,提出了一种结合交替优化与半正定松弛的鲁棒波束成形算法,以获得较优性能的解。计算机仿真结果证明了所提算法的鲁棒性和优越性。