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.