Pré-Publication, Document De Travail Année : 2025

ML-DoA Estimation using a Sparse Representation of Array Covariance with a non-standard noise

Résumé

Maximum Likelihood (ML) Direction-of-Arrival (DoA) on the vectorized covariance matrix model (VCMM), relying on a Virtual Array (VA) of antennas, exhibits enhanced ability to separate closely spaced sources. Due to the finite number of snapshots, the VCMM observation is corrupted by a non-white and non-circular Gaussian noise resulting in an intricate ML criterion. To address this issue, this paper introduces a novel two-stage transform that turns the initial non-white and non-circular Gaussian noise into a real and white Gaussian noise. Following this, the ML estimator is formulated for the transformed model and the corresponding Cramér-Rao Lower Bound (CRLB) is derived. Unfortunately, the ML implementation involves intractable multi-dimensional and highly non-linear non-convex optimization. This paper introduces a novel sparse DoA estimator that implements the ML using the proposed two-stage transform. This transform is shown to significantly simplify the sparse estimator implementation. To quantify the transform effects, the problem conditioning is derived and shown to be consequently improved after the transform. Numerical simulations showcase performance improvements of the sparse DoA estimator after the two -stage transform in severe scenarios with 2 and 3 closely spaced sources using a 4-elements array.
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hal-04920380 , version 1 (30-01-2025)

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  • HAL Id : hal-04920380 , version 1

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Thomas Aussaguès, Anne Ferréol, Alice Delmer, Pascal Larzabal. ML-DoA Estimation using a Sparse Representation of Array Covariance with a non-standard noise. 2025. ⟨hal-04920380⟩
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