Efficient iterative DOA estimation using a rectangular array in presence of data loss

Direction of Arrival (DOA) estimation is a fundamental aspect of signal processing, particularly in array processing applications. This study explores the use of iterative techniques for DOA estimation within a uniform rectangular array (URA) framework, leveraging complex Least Mean Squares (LMS) and complex Recursive Least Squares (RLS) algorithms. DOA estimation involves determining the directions from which signals arrive at an array of microphones, but this process is often challenged by data loss. To address this issue, we propose the complex TNNM-LMS (Truncated Nuclear Norm Minimization - LMS) and complex TNNM-RLS methods, which enhance DOA estimation in the presence of data loss using a rectangular array. The approach formulates the problem as a low-rank matrix recovery task, where missing data is reconstructed before applying complex LMS/RLS algorithms for DOA estimation. By integrating low-rank matrix recovery techniques, we aim to restore missing entries in the array signal matrix, leading to improved estimation accuracy. Through extensive simulations, we validate the effectiveness of the proposed algorithms in accurately estimating DOA even under data loss conditions. Additionally, we introduce a computationally efficient approach for obtaining the spatial spectrum using a 2D Fourier domain method.