ML-DOA estimation using a sparse representation of array covariance

Thomas Aussaguès Doctorant chez THALES Gennevilliers, et inscript en thèse à Université Paris-Saclay fera une présentation sur ces travaux de recherche.

La présentation aura lieu à l'IMT-Atlantique le 22 novembre 2024 - Petit Amphi.

Abstract.

DoA (Direction-of-Arrival) estimation is a pivotal area in numerous critical applications such as
radar or telecommunications for which a plethora of estimators has been proposed [1]. Nevertheless, classical
methods such as MUSIC [2] have limited performances in severe conditions. Although it achieves the Cramér-
Rao Lower Bound at high SNR, the Maximum Likelihood (ML) estimator [3] is rarely employed as it requires
multi-dimensional highly non-convex optimization.
In recent years, there has been a growing interest within the signal processing processing community on sparse
methods applied to DoA estimation [4] as they exhibit enhanced performances in tough scenarios. Out of the
numerous modeling of the sparse DoA estimation problem, the sparse covariance matrix representation [5] emerged as a promising choice.
For this model, the DoAs can be estimated through the minimization of a non-convex ℓ0-regularized objective
parametrized by λ the regularization parameter which is often empirically tuned. In [6], the authors proposed an
interval for the regularization parameter. However, the interval bounds depends on the sources directions thus
complexifying o-line selection of the regularization parameter.
In this work [7], we are looking for theoretical equivalence between ML and sparse estimators. We show that
under mild conditions, λ can be chosen thanks to the distribution of the minimum of the ML criterion. The
corresponding λ choice is θ-invariant, only requiring an upper bound on the number of sources. Furthermore, it
guarantees the global minimum of the sparse ℓ0-regularized criterion to be the ML solution.

[1] Hamid Krim and Mats Viberg. Two Decades of Array Signal Processing Research: The Parametric Approach. In: Signal Processing Magazine, IEEE 13 (Aug. 1996), pp. 67 94.
[2] G. Bienvenu and L. Kopp. Optimality of high resolution array processing using the eigensystem approach. In: IEEE Transactions on Acoustics, Speech, and Signal Processing 31.5 (1983), pp. 12351248.
[3] B. Ottersten et al. Exact and Large Sample Maximum Likelihood Techniques for Parameter Estimation and Detection in Array Processing. In: Radar Array Processing. Ed. by Simon Haykin, John Litva, and Terence J. Shepherd. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993, pp. 99151.
[4] Zai Yang et al. Sparse Methods for Direction-of-Arrival Estimation. 2017. arXiv: 1609.09596 [cs.IT].
[5] Joseph S. Picard and Anthony J. Weiss. Direction nding of multiple emitters by spatial sparsity and linear programming. In: 2009 9th International Symposium on Communications and Information Technology. 2009, pp. 12581262.
[6] Alice Delmer, Anne Ferréol, and Pascal Larzabal. On regularization Parameter for L0-Sparse Covariance Fitting Based DOA Estimation. In: ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). 2020, pp. 45524556.
[7] Thomas Aussaguès et al. Looking for Equivalence between Maximum Likelihood and Sparse DOA Estimators. In: 2024 32th European Signal Processing Conference (EUSIPCO). 2024.