Efficient sparse parameter estimation based methods for two-dimensional DOA estimation of coherent signals

This study addresses the problem of direction-of-arrival (DOA) estimation of coherent signals via sparse parameter estimation. Since many sparse methods provide good performances regardless of signal correlations and array geometry, they can be considered as candidates for DOA estimation of coherent signals impinging on a sensor array with arbitrary geometry. However, their straightforward applications require high computational loads especially for two-dimensional (2D) DOA estimation. Two efficient methods based on sparse parameter estimation are herein presented; one is a combined approach of sparse estimation and the RELAX algorithm extended for 2D DOA estimation and the other relies on the adaptive 2D grid refinement and power update control. Numerical simulations are performed to demonstrate the efficiency of the proposed methods using a uniform circular array for both 1D and 2D DOA estimation cases. It is shown that sparse asymptotic minimum variance (SAMV)-RELAX, a combined approach of SAMV and RELAX, outperforms SAMV and multi-stage SAMV in 2D scenarios without suffering from plateau effects for off-grid signals and that its computational load is significantly lower than those of SAMV and multi-stage SAMV. In addition, SAMV-RELAX does not require the difficult selection of grid parameters for fine DOA estimation unlike the multi-stage approach.