针对常规均匀线阵DOA估计中可估计信源数目不足的问题, 提出了一种基于虚拟孔径扩展的非均匀稀疏阵DOA估计算法。该算法首先对非均匀稀疏阵接收信号协方差矩阵进行向量化处理, 通过Khatri-Rao积运算得到新的协方差矩阵; 然后利用任意阵列下的空间平滑算法恢复新协方差矩阵的秩;最后通过对新协方差矩阵进行特征值分解实现DOA估计。与传统MUSIC算法相比, 该算法可以在阵元数目小于信源数目的条件下实现DOA估计, 大大增加了可估计信源数目, 同时在低信噪比、小快拍条件下仍能得到DOA估计结果。仿真结果证明了算法的有效性。

In the Direction of Arrival (DOA) estimation of uniform linear array, the number of the sources that can be estimated is inadequate. To solve the problem, a DOA estimation algorithm based on virtual aperture expansion is presented. Firstly, vectorization processing is made to the received signal covariance matrix of non-uniform sparse matrix, and a new covariance matrix is obtained by Khatri-Rao integral operation. Then, the rank of new covariance matrix is restored by using spatial smoothing algorithm for arbitrary array. Finally, the DOA estimation is implemented by the eigenvalue decomposition of the covariance matrix. Compared with the traditional MUSIC algorithm, the DOA estimation can implement DOA estimation under the condition that the number of array elements is less than the source number, and can greatly increase the estimated source number. Meanwhile, it can obtain DOA estimation results under low SNR and small snapshot conditions. Simulation results demonstrate the effectiveness of the proposed algorithm.