Partial Relaxation Approach: An Eigenvalue-Based DOA Estimator Framework

• Published in: IEEE transactions on signal processing Vol. 66; no. 23; pp. 6190 - 6203
• Main Authors: Minh Trinh-Hoang, Viberg, Mats, Pesavento, Marius
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.12.2018; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: approximate maximum likelihood; Approximation; Computer simulation; Covariance; Covariance matrices; Direction of arrival; Direction-of-arrival estimation; DOA estimation; eigenvalue decomposition; Eigenvalues; Estimators; Fitting; Iterative methods; least squares framework; Mathematical analysis; Maximum likelihood estimation; Optimization; Parameter estimation; partial relaxation; rank-one modification problem; rational function approximation; Rational functions; Sensor arrays
• ISSN: 1053-587X; 1941-0476; 1941-0476
• DOI: 10.1109/TSP.2018.2875853

In this paper, the partial relaxation approach is introduced and applied to the direction-of-arrival estimation problem using spectral search. Unlike existing spectral-based methods such as conventional beamformer, Capon beamformer, or MUSIC that can be considered as single source approximation of multi-source estimation criteria, the proposed approach accounts for the existence of multiple sources. At each considered direction, the manifold structure of the remaining interfering signals impinging on the sensor array is relaxed, which results in closed form estimates for the "interference" parameters. Thanks to this relaxation, the conventional multi-source optimization problem reduces to a simple spectral search. Following this principle, we propose estimators based on the deterministic maximum likelihood, weighted subspace fitting, and covariance fitting methods. To calculate the null-spectra efficiently, an iterative rooting scheme based on the rational function approximation is applied to the partial relaxation methods. Simulation results show that, irrespective of any specific structure of the sensor array, the performance of the proposed estimators is superior to the conventional methods, especially in the case of low signal-to-noise-ratio and low number of snapshots, while maintaining a computational cost that is comparable to MUSIC.