Vandermonde Decomposition Reconstruction for DOA Estimation with Sparse Arrays

In this work, we propose a novel direction-of-arrival (DOA) estimation algorithm for sparse linear array via Vandermonde decomposition reconstruction. Unlike virtual array interpolation algorithms, the suggested method performs interpolation directly on the physical array, that is, Nyquist spatial filling. By utilizing the Vandermonde decomposition of the covariance matrix of a uniform linear array (ULA), this filling process is formulated as a structured matrix completion problem via matrix factorization, where the factor matrix is encouraged to exhibit a Vandermonde structure. Subsequently, an iterative approach is developed to solve the resultant problem using the alternating direction method of multipliers (ADMM). Finally, DOAs are retrieved from the reconstructed covariance matrix using subspace-based algorithms. Simulation results demonstrate the superiority of our algorithm over the existing methods.