Real-Valued Deep Unfolded Networks for Off-Grid DOA Estimation via Nested Array

Xiaolong Su, Zhen Liu, Junpeng Shi, Panhe Hu, Tianpeng Liu, Xiang Li

Abstract: Recently, deep unfolded networks have been widely utilized in direction of arrival (DOA) estimation due to the reduced computational complexity and improved estimation accuracy. However, few consider the nested array for off-grid DOA estimation, where the estimated DOAs are not on the prespecified grids. In this article, we propose a deep unfolded FOCal underdetermined system solver network and a deep unfolded alternating direction method of multiplies to address the problem, which respectively aim to improve estimation accuracy and further reduce computational complexity. We first apply first-order Taylor expansion and vectorize the covariance matrix into a real-valued single snapshot for network input. We then train the proposed networks to obtain <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">on-</small> grid DOA spatial spectrum and off-grid values, where the <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">off-</small> grid DOA estimation is calculated by the peaks of <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">off-</small> grid DOA spatial spectrum and corresponding <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">off-</small> grid values. We demonstrate that the proposed networks with interpretable parameters can accelerate the convergence rate and achieve better generalization. Simulations verify the performance of proposed networks in comparison with the existing methods.