Analysis of an ML-DoA implementation using a sparse representation of array covariance

This work analyses a sparse Direction-of-Arrival (DoA) Maximum Likelihood (ML) implementation using the Vectorized Covariance Matrix Model (VCCM). Building on the recently established equivalence between sparse and ML estimators obtained after a pre-whitening transform, an exact ML ℓ0-sparse estimator is proposed. Then, the influence of the pre-whitening transformation, introduced to ensure equivalence with the deterministic ML, is thoroughly analyzed. This procedure significantly improves the numerical conditioning of the problem. Consequently, it facilitates the implementation of the proposed estimator and enhances the resolution of closely spaced sources. Numerical results show that the pre-whitening step leads to significant performance improvements for the proposed ML sparse DoA estimator, especially in challenging scenarios involving 2 or 3 closely spaced sources observed with a small 4-element array. Furthermore, simulation results corroborate the expected optimality of the proposed estimator, inherited from the equivalence between ML and sparse estimators, by showing that it attains the Cramér–Rao lower bound (CRLB).