Two-Dimensional Underdetermined DOA Estimation of Quasi-Stationary Signals using Parallel Nested Array

In this paper, a two dimensional underdetermined direction of arrival estimation (DOA) of quasi-stationary signals using a parallel nested array structure is investigated. The quasi-stationary signals have the statistical property that they remain locally static over one frame but exhibit differences from one time frame to others. The special time domain property enables us to perform underdetermined direction-of-arrival estimation in time domain. By exploiting the temporary diversity of the quasi-stationary signals and effective difference coarray virtual array aperture provided inherently in the parallel nested array, more degrees of freedom can be used to resolve DOA estimation. The Khatri-Rao operation for the cross covariance matrix of the subarrays received data is adopted to convert the 2-D DOA estimation problem into two separate one-dimensional DOA estimation problems. Then, a subspace-based estimation of signal parameters via rotational invariance technique and a sparsity-based sparse Bayesian learning are proposed to realize the according one-dimensional DOA estimation. And the estimated azimuth and elevation angles can be properly automatically paired. Simulation results are carried out to demonstrate the effectiveness of the proposed algorithms for the 2-D underdetermined DOA estimation.