Riemannian Covariance Fitting for Direction-of-Arrival Estimation

作     者：Picard, Joseph S. Bar, Amitay Talmon, Ronen 

作者机构：The Viterbi Faculty of Electrical and Computer Engineering Technion - Israel Institute of Technology Haifa32000 Israel 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2024年

核心收录：

主　　题：Beamforming 

摘      要：Covariance fitting (CF) is a comprehensive approach for direction of arrival (DoA) estimation, consolidating many common solutions. Standard practice is to use Euclidean criteria for CF, disregarding the intrinsic Hermitian positive-definite (HPD) geometry of the spatial covariance matrices. We assert that this oversight leads to inherent limitations. In this paper, as a remedy, we present a comprehensive study of the use of various Riemannian metrics of HPD matrices in CF. We focus on the advantages of the Affine-Invariant (AI) and the Log-Euclidean (LE) Riemannian metrics. Consequently, we propose a new practical beamformer based on the LE metric and derive analytically its spatial characteristics, such as the beamwidth and sidelobe attenuation, under noisy conditions. Comparing these features to classical beamformers shows significant advantage. In addition, we demonstrate, both theoretically and experimentally, the LE beamformer’s robustness in scenarios with small sample sizes and in the presence of noise, interference, and multipath channels. Copyright © 2024, The Authors. All rights reserved.