基于矩阵填充的二维自适应波束形成算法

2D adaptive beamforming algorithm based on matrix completion

针对基于矩阵填充的二维自适应波束形成问题,提出一种基于奇异值门限(SVT)的特征分解线性约束最小方差(SVT-ELCMV)算法。首先建立二维自适应波束形成矩阵填充模型,其次验证接收信号矩阵满足零空间性质(NSP),并分析最小可恢复阵元数,最后以SVT算法将稀疏阵列信号恢复为完整信号,并通过修正的特征分解线性约束最小方差(LCMV)形成有效波束。算法解决了稀疏阵列平均副瓣大幅度上升的缺陷,且在平面阵列部分阵元无法正常工作时依然有效。计算机仿真表明:SVT-ELCMV算法可使稀疏阵列具有与完整阵列相同的二维波束形成能力,并可有效抑制干扰信号,验证了算法的有效性和优越性。

The two-dimensional（2D）adaptive beamforming based on matrix completion is considered,and a singular value threshold（SVT）based-eigenvalues decomposition linearly constrained minimum variance（SVT-ELCMV）algorithm is proposed.Firstly,a signal model of two-dimensional adaptive beamforming is established based on the matrix completion.And then,the received signal is proved to satisfy the null space property（NSP）.Furthermore,the minimum number of array elements to recover the sparse matrices has been analyzed.Finally,the sparse signal is recovered to full signal by SVT algorithm and an effective beam is formed based on the modified LCMV algorithm.This algorithm overcomes the problem that the average sidelobes increases significantly in sparse array,and it keeps valid in the situation when some elements of the sparse array do not work.Computer simulation shows that the SVT-ELCMV algorithm makes the sparse array have the same beamforming capability with the full array.Moreover,the proposed algorithm can restrain the interference signals effectively,so the superiority of the algorithm is verified.