A Nyström-based low-rank unitary MVDR beamforming scheme

Abstract

A Nyström-based scheme is devised to approximate the real symmetrical covariance matrix of the popular unitary MVDR (U-MVDR) beamformer with low-rank kernel matrix, based on which a novel lightweight and robust Nyström-based U-MVDR (NU-MVDR) beamformer is developed. Subsequently, the full-dimensional Nyström covariance matrix estimator’s signal subspace can be calculated by eigenvalue decomposition (EVD) of two reduced-dimensional matrices, which will save a significant amount of computing load at the EVD stage. This scheme has obvious computational efficiency and lightweight storage overheads. Meanwhile, we derive the effect of the Nyström covariance matrix’s rank on the output signal-to-interference-plus-noise ratio (SINR). Numerical results demonstrate that the proposed beamformer performs well in less snapshots and steering vector errors cases.