A Multi-Task Deep Neural Network for Joint Estimation of Direction of Arrival and Unknown Mutual Coupling Matrix for Structured Sparse Arrays

In direction of arrival (DOA) estimation, structured sparse arrays provide improved performance over their uniformly-spaced array counterparts with the same number of elements. However, in practice when these elements are closely spaced, mutual coupling effects distort the spatial model underpinning standard DOA techniques. If the mutual coupling matrix (MCM) is not exactly known, both DOA and the MCM must be jointly estimated which results in a nonlinear problem. The advancement of neural networks and deep learning techniques offer efficient solutions to complex nonlinear and computationally intensive problems. In this paper, a neural network is trained to solve the joint DOA-MCM estimation problem and significantly reduce the computational load, making it amenable to real-time processing. We adopt a multi-task Deep-Learning (DL) approach to deal with the two-fold sets of unknowns underlying this estimation problem. The simulation results are presented for a nested sparse array.