Partial Relaxation Approach: An Eigenvalue-Based DOA Estimator Framework

TL;DR

This paper introduces a partial relaxation approach for DOA estimation that simplifies the optimization process by relaxing interference manifold structures, leading to improved performance in low SNR and snapshot scenarios with comparable computational cost to existing methods.

Contribution

The paper presents a novel eigenvalue-based DOA estimator framework using partial relaxation, enhancing accuracy and efficiency over traditional methods like MUSIC and Capon.

Findings

Superior performance in low SNR conditions

Effective in scenarios with few snapshots

Maintains computational efficiency similar to MUSIC

Abstract

In this paper, the partial relaxation approach is introduced and applied to DOA estimation using spectral search. Unlike existing methods like Capon or MUSIC which can be considered as single source approximations 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. The conventional multidimensional optimization problem reduces, thanks to this relaxation, 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 pseudo-spectra efficiently, an iterative rooting scheme based on the rational function approximation is applied to the partial relaxation methods. Simulation results show that 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, irrespectively of any specific structure of the sensor array while maintaining a comparable computational cost as MUSIC.