基于互相关抽样分解的分布式非圆信号DOA快速估计

在非相干分布式非圆信号波达方向(DOA)估计中，针对利用信号非圆特性后输出矩阵维数扩展带来的较大运算量问题，该文提出一种基于互相关抽样分解的DOA快速估计算法。该算法仅需要从子阵间的扩展互相关矩阵中抽样出少量行元素和列元素，构成两个低维子矩阵，进而通过低秩近似分解便可快速地同时求出左右奇异矢量，即分别对应两个子阵的信号子空间，避免了计算整个互相关矩阵及其奇异值分解运算；最后利用两个子阵信号子空间的旋转不变性通过最小二乘得到DOA估计。仿真分析表明，当行列抽样数大于信源数的两倍时，所提算法与直接基于互相关矩阵奇异值分解的非相干分布式非圆信号DOA估计算法性能相近，但复杂度得到了大幅度降低；而相比于传统的低复杂度非相干分布源DOA估计算法，所提算法利用信号非圆特性具有更高的估计性能。

Fast DOA Estimation of Distributed Noncircular Sources by Cross-correlation Sampling Decomposition

In the Direction Of Arrival (DOA) estimation of incoherently distributed noncircular sources, the increase of dimension caused by array output matrix extension can cause a large computational complexity. To solve this problem, a rapid DOA estimation algorithm is proposed based on cross-correlation sampling decomposition. It only needs to calculate two low-dimensional sub-matrices, which are formed by a small number of rows and columns in the extended Cross-Correlation (CC) matrix. On the premise of the sub-matrices, the right and left singular vectors corresponding to two signal subspaces can be simultaneously obtained by the low-rank approximation decomposition, which avoids the calculation of the whole covariance matrix and its singular value decomposition. Finally, the DOA estimation can be obtained by the least squares with the rotation invariance of the signal subspaces. The simulation results show that when the number of samples in the low-dimensional sub-matrix is larger than twice the number of sources, the performance of the proposed algorithm is comparable with the DOA estimation algorithm of incoherently distributed noncircular sources based on the singular value decomposition applying to the CC matrix. Moreover, the proposed algorithm utilizes the noncircular characteristic of the signal to achieve higher estimation performance compared with the traditional low-complexity DOA estimation algorithms of the incoherently distributed sources.