Off-grid DOA estimation of correlated sources for nonuniform linear array through hierarchical sparse recovery in a Bayesian framework and asymptotic minimum variance criterion

This paper provides a method to solve off-grid direction-of-arrival (DOA) estimation for nonuniform linear array (NLA) correlated source condition through hierarchical sparse recovery and asymptotic minimum variance (AMV) criterion. In this method, space is firstly divided into a discretized grid. Most rows and columns of the signal covariance matrix modeled on this grid are zero vectors because the number of sources is considerably smaller than that of grid points. Hence, the vectorized signal covariance matrix is regarded as a block-sparse vector, and active blocks are sparse vectors. Based on this, a hierarchical sparse prior is then assigned on the vectorized signal covariance matrix to encourage the sparsity between and within blocks. Finally, the variational Bayesian inference is applied to estimate the vectorized signal covariance matrix. Furthermore, first-order Taylor series expansion is applied to approximate the steering vector as a function of the grid error between the true DOA and the closest grid point. Grid error is estimated under the AMV criterion and applied to modify the grid iteratively, thus alleviating the basis mismatch. Simulation results show that the proposed method achieves high estimation accuracy for the NLA correlated source condition.