DOA矩阵方法及其性能分析

为了在小样本、低信噪比以及高信源相关性的条件下都能对波达方向（direction of arrival，DOA）进行精确估计，基于压缩感知理论，利用目标信号空间分布的稀疏性，提出了基于加权l₁范数稀疏信号表示的DOA估计算法.该算法对l₁-奇异值分解（singular value decomposition，SVD）算法进行改进，对接收矩阵进行预处理，根据子空间的正交性确定加权矩阵，以加权l₁范数作为最小化的目标函数进行优化得到稀疏信号，进而得到信号的DOA.仿真结果表明，通过加权处理的l₁范数下稀疏信号重构方法能有效抑制偏差，在低信噪比下能够准确稳定地估计出DOA，并且能够提高估计精度.

DOA matrix method and its performance analysis

To accurately estimate the direction of arrival (DOA) under conditions of small samples, low signal-to-noise ratio and high correlations of sources, according to the compressive sensing theory, DOA estimation based on weighted l₁ norm sparse signal representation was proposed by using the sparse distribution of the spatial signal source bearing. The l₁-SVD algorithm was improved by this algorithm, the receiving matrix was proposed, the weighting matrix was determined according to the orthogonality of the subspace, and the sparse vector was obtained by the optimization using the weighted 1 norm as target function for minimization. Then, the DOA of the signal was obtained. Simulations demonstrate that the proposed algorithm can effectively suppress the deviation by sparse signal reconstruction method under weighted processing l₁ norm. At the low SNR, DOA can be estimated accurately and steadily, and the precision of DOA estimation can be improved effectively.