A 2D Nested Array Based DOA Estimator for Incoherently Distributed Sources via Sparse Representation Utilizing L1-Norm

Nested arrays are sparse arrays composed of subarrays with nonuniform sensor spacing. Compared with traditional uniform arrays, nested arrays have more degree of freedoms (DOFs) and larger apertures. In this paper, a nested array has been proposed as well as a direction-of-arrival (DOA) estimation method for two-dimensional (2D) incoherently distributed (ID) sources. A virtual array is firstly obtained through vectorization of the cross-correlation matrix of subarrays. Sensor positions of the virtual array and the optimal configuration of the nested array are derived next. Then rotational invariance relationship for generalized steering matrix of the virtual array with respect to nominal azimuth is deduced. According to the rotational invariance relationship, sparse representation model under l(1)-norm constraint is established, which is resolved by transferring the objective function to second-order cone constraints and combining a estimation residual error constraint for receive vector of the virtual array. Simulations are conducted to investigate the effectiveness of the proposed method in underdetermined situation and examine different experiment factors including SNR, snapshots, and angular spreads as well as sensor number of subarrays. Results show that the proposed method has better performance than uniform parallel arrays with the same number of sensors.