Whitening Effects for ML-DoA Estimation using a Sparse Representation of Array Covariance

Abstract

Maximum Likelihood (ML) Direction-of-Arrival (DoA) estimation on the Vectorized Covariance Matrix Model (VCMM) exhibits improved performance in severe conditions compared to standard methods. Indeed, it benefits from the VCMM capacities summarized through the Virtual Array (VA) concept. Due to finite number of samples, the VCMM is corrupted by a coloured Gaussian noise. As a remedy, we previously introduced a pre-whitening noise transform converting the coloured noise into white Gaussian noise. Using the whitened model, we recently shown equivalence between sparse DoA estimators and the ML thereby enabling efficient implementation of ML DoA estimation under white Gaussian noise.In this work, the noise pre-whitening transform is shown to significantly improve the sparse problem conditioning by spatially decorrelating the dictionary vectors associated to sources directions thus simplifying the implementation of ML DoA estimation with a sparse representation. To this end, the expression of the spatial correlation coefficient after whitening is derived.Numerical simulations confirm the performance improvement of sparse DoA estimators after whitening for closely separated sources.