基于低管秩张量分解的互质阵列自适应波束成形算法  

Coprime array-adaptive beamforming based on low-tubal-rank tensor decomposition

作　　者：程耘 刘天鹏 师俊朋 苏晓龙 刘振 Yun CHENG;Tianpeng LIU;Junpeng SHI;Xiaolong SU;Zhen LIU(College of Electronic Science and Technology,National University of Defense Technology,Changsha 410073,China)

机构地区：[1]国防科技大学电子科学学院,长沙410073

出　　处：《中国科学：信息科学》2023年第2期402-416,共15页Scientia Sinica(Informationis)

基　　金：国家自然科学基金创新研究群体(批准号:61921001);国家自然科学基金(批准号:61801488,62022091,62071476);湖南省科技创新计划(批准号:2020RC2041,2021RC3079,2021RC3080);中国博士后科学基金(批准号:2020M683728,2021T140788);国防科技大学学校科研计划(批准号:ZK20-33)资助项目。

摘　　要：互质阵列因其大阵列孔径和高自由度特性在波束成形领域受到广泛关注.为了充分利用该特性,近年来学者们提出了基于孔洞填充的算法,有效提高了互质阵列波束成形的性能.然而,这些算法存在计算量大、噪声鲁棒性弱等缺点,难以适应复杂多变的实际环境.为此,本文利用张量的多维结构在参数估计上的性能优势,提出了一种基于低管秩张量分解的互质阵列自适应波束成形算法.首先将互质阵列的多采样虚拟信号矩阵重排为张量形式,利用其低管秩特性补全缺失的互相关信息;然后从补全后的张量数据中提取信号参数,并与目标先验进行匹配,最终得到波束成形权矢量.本算法分别利用ADMM和Tucker分解提高了张量补全和分解的运算效率;所设计的目标匹配方案也有效控制了算法误差.仿真结果展示了本算法在性能和计算复杂度相对于现有方法的优势,尤其是在低信噪比和少采样数的情况下.The coprime array(CPA)has attracted extensive attention in the field of adaptive beamforming(ABF)because of its large array aperture and high degree of freedom.To make full use of this characteristic,several algorithms based on hole filling have been proposed to improve the performance of ABF.However,these algorithms have disadvantages in computation and noise robustness,which are difficult to adapt to complex and changeable environments.To solve this problem,this paper proposes a CPA-ABF algorithm based on lowtubal-rank tensor decomposition.First,the multi-sampling virtual signal matrix of the CPA is rearranged into a tensor form,and the missing cross-correlation information is completed using its low tubal rank.Then,signal parameters are extracted from the completed tensor data and matched with the target a priori.Finally,the ABF weight vector is obtained.The algorithm uses ADMM and Tucker decomposition to improve the efficiency of tensor completion and decomposition.The designed target matching scheme also effectively controls the algorithm error.The simulation results show the advantages of the algorithm in performance and computational complexities compared with existing methods,especially in the case of low signal-to-noise ratios and a small number of samples.

关 键 词：自适应波束成形 互质阵列 张量分解 自由度 参数估计 

分 类 号：TN911.7[电子电信—通信与信息系统]