Deep Alternating Projection Networks for Gridless DOA Estimation With Nested Array

Recently, deep unfolding networks with interpretable parameters have been widely utilized in direction of arrival (DOA) estimation due to the faster convergence speed and better generalization ability. However, few consider the nested array for gridless DOA estimation. In this letter, we propose a deep alternating projection network to address the problem. We first convert the covariance matrix into a measurement vector in the form of atomic norm, which can reduce the matrix dimension during projection. We then train the proposed network to alternately obtain the positive semi-definite matrix and the corresponding irregular Hermitian Toeplitz matrix, where the loss function is derived by employing the trace of network output. Finally, we apply the irregular root Multiple Signal Classification (MUSIC) method to obtain gridless DOA via nested array. We demonstrate that the proposed networks can accelerate the convergence rate and reduce computational cost. Simulations verify the performance of proposed networks in comparison with the existing methods.