Spatial Power Estimation via Riemannian Covariance Matching

TL;DR

This paper introduces SERCOM, a Riemannian geometry-based algorithm for spatial power spectrum estimation that improves accuracy and robustness over traditional methods, especially in challenging conditions.

Contribution

The paper presents a novel Riemannian-aware covariance matching algorithm using JBLD divergence, which is computationally efficient and more robust than existing approaches.

Findings

SERCOM outperforms existing methods in DOA and power estimation.

SERCOM is robust to spectral distortions and low SNR conditions.

The JBLD divergence allows efficient computation without eigen-decomposition.

Abstract

We propose a new method for spatial power spectrum estimation in array processing that leverages the Riemannian geometry of Hermitian positive definite (HPD) matrices. We show that conventional approaches minimize variants of the Euclidean distance between the sample covariance matrix and a model covariance matrix, without considering the fact that covariance matrices lie on the Riemannian manifold of HPD matrices. By exploiting this manifold, we present a Riemannian-aware covariance matching algorithm, termed SERCOM, using the Jensen-Bregman LogDet (JBLD) divergence, which, unlike other Riemannian distances, can be evaluated efficiently without eigen-decomposition. We theoretically compare the JBLD divergence to other Euclidean- and Riemannian-based distances, demonstrating robustness to spectral distortions. Experimental results demonstrate that SERCOM consistently outperforms existing methods in direction-of-arrival (DOA) and power estimation, particularly in challenging scenarios with low SNR, limited number of snapshots, and correlated sources.