DOA Estimator for 2D Coherently Distributed Source Via Sparse Representation with Nested Array

Considering two-dimensional (2D) coherently distributed (CD) sources, an estimator under a proposed nested array has been presented in this work. A hole-free virtual array is firstly generated by difference operation on the coordinates of elements in nested array. Then close expression of sensor positions of the virtual array is derived. Next, rational invariance relationships between rows in general steering matrix is deduced. Afterwards, sparse representation for DOA estimation with the proposed nested array is established on the basis of rational invariance relationship of the virtual array. The estimation algorithm is resolved by converting the l1-norm constraint of the sparse representation into second order cone constraints and a residual error constraint. The performances of the proposed estimator are examined through simulations considered to be undermined as well as paying attention to diverse factors. Simulations shows that the proposed estimator has better performances in comparison with uniform arrays composed of similar number of sensors.