ESPRIT-like Direction of Arrival Estimation Algorithm Based on Gradient Descent for Co-prime Linear Array

The problem of direction-of-arrival (DOA) estimation is investigated for co-prime linear array, where the co-prime linear array incorporates two uniform linear arrays (ULAs) with adjacent spacing larger than half wavelength. In this paper, we propose an ESPRIT-like DOA estimation method based on gradient descent for co-prime linear array. First, we decompose the entire co-prime array into several subarrays regarding each sensor as a subarray and derive the property of rotational invariance between manifold matrixs of any two subarrays. Then, this paper uses the gradient descent to iterative search the rotational invariance matrix and obtain direction information of the incident signals. The proposed method can achieve full DOFs, and there is no grid search in the range of directions. Simulation results corroborate the effectiveness and superiority of the proposed method, compared with the total spectral search method (TSS) and MUSIC for ULA with the same sensor number.