DOA Estimation of Coherent Sources via Low-Rank Matrix Decomposition

In this letter, we propose an effective algorithm for estimating the direction of arrival (DOA) of coherent sources using an overlapped coprime array (OCA). Unlike the existing coprime configuration, the proposed OCA is utilized to enhance the consecutive lags of the difference coarray without increasing the number of sensors, which provides a more simplified configuration and reduces hardware complexity. A noise-free covariance matrix obtained from the OCA is first vectorized. A longer virtual uniform linear array (ULA) is constructed by interpolating zeros into the holes of the coarray. Subsequently, a Toeplitz matrix is defined. Finally, we proposed a low-rank matrix reconstruction model based on the Schatten-p norm for the output generated by the interpolated virtual array. Utilizing matrix decomposition minimization as a substitute for rank minimization. The optimization problem is solved by proximal alternating linearized minimization (PALM). The DOAs of coherent sources are estimated by integrating subspace-based spectral estimation algorithms. Therefore, the proposed algorithm can achieve lower computational complexity and higher estimation accuracy. Simulation results demonstrate the superiority of the proposed algorithm over several existing methods.