Partially Relaxed Orthogonal Least Squares Weighted Subspace Fitting Direction-of-Arrival Estimation

Abstract

The Partial Relaxation framework has recently been introduced to address the Direction-of-Arrival (DOA) estimation problem [1]–[3]. DOA estimators under the Partial Relaxation (PR) framework are computationally efficient while preserving excellent DOA estimation accuracy. This is achieved by keeping the structure of the signal from the desired direction unchanged while relaxing the structure of the signals from the remaining undesired directions. This type of relaxation allows to compute closed-form estimates for the undesired signal part and improves the accuracy of the DOA estimates compared to conventional spectral-search methods like, e.g. MUSIC. Following a similar approach as in [4] the PR framework is combined with the Orthogonal Least Squares (OLS) technique of [5]. A novel DOA estimator is proposed that is based on Partially-Relaxed Weighted Subspace Fitting (PR-WSF) in which the DOAs are iteratively estimated. Thereby, one DOA is estimated per iteration, while accounting for both the signal contributions under the previously-determined DOAs, with full signal structure, as well as the remaining DOAs with relaxed structure. Moreover, an efficient implementation of the Partially-Relaxed Orthogonal Least Squares Weighted Subspace Fitting (PR-OLS-WSF) method is proposed that provides similar computational cost as the MUSIC algorithm. Simulation results show that the proposed PR-OLS-WSF estimator provides excellent performance especially in difficult scenarios with low Signal-to-Noise-Ratio (SNR) and closely spaced sources.