DOA Estimation Algorithm Using Sparse Representation Theory in Coprime Arrays

This article explores the principles and applications of Direction of Arrival (DOA) estimation algorithms using sparse representation theory in coprime arrays. We begin by introducing coprime array configurations and their advantages in signal processing applications, particularly in achieving enhanced degrees of freedom with fewer physical sensors. The discussion then delves into the fundamentals of sparse representation theory, explaining how it transforms DOA estimation into an optimization problem through dictionary matrix construction and l1-norm minimization. The core implementation involves creating a spatial dictionary grid, formulating the sparse recovery problem using techniques like Basis Pursuit or LASSO, and solving it through convex optimization methods. We demonstrate practical MATLAB code examples for constructing coprime array manifolds and implementing sparse recovery algorithms. Finally, we analyze the algorithm's performance in terms of resolution, computational complexity, and robustness to noise, while discussing potential enhancements such as grid refinement techniques and off-grid compensation methods for real-world applications.