Position-enabled complex Toeplitz LISTA for DOA estimation with unknow mutual coupling

Unfolding iterative algorithms into deep networks can increase the rate of convergence which is amenable to Direction-of-arrival (DOA) estimation problems. However, there normally exists unknown mutual coupling between antenna array elements. In this paper, a novel Position-enAbled Complex Toeplitz Learned Iterative Shrinkage Thresholding Algorithm (PACT-LISTA) is proposed which makes use of the data driven method to solve the mutual coupling problem and improve the parameter estimation performance. First, a sparse recovery (SR) model is developed to explore the inherent Topelitz structure. In order to solve the SR problem, a Complex Toeplitz LISTA (CT-LISTA) network is proposed, which integrates the Toeplitz structure into the Complex LISTA (C-LISTA) network. By ignoring the amplitude and phase information of the recovered signal, the idea of position-priority is applied to further improve the estimation accuracy. Through an innovative iteration method, the system gradually converges to the optimized stable state, which is associated with an accuracy parameter. Simulations are provided to demonstrate that the proposed approach significantly outperforms the state of art methods.