Subspace Perturbation Bounds with an Application to Angle of Arrival Estimation using the MUSIC Algorithm

This paper explores how angle of arrival (AoA) estimation using the multiple signal classification (MUSIC) algorithm is affected by estimation errors in the space-time covariance matrix. In particular, we explore how this estimation error perturbs the signal-plus-noise and noise-only subspaces of the matrix, and how this subsequently affects the performance of MUSIC for AoA estimation. This subspace perturbation is shown to depend on the space-time covariance matrix itself, the sample size over which it is estimated, as well as the distance of the smallest signal-related eigenvalue to the noise floor. We link a bound on this perturbation to a bound on MUSIC performance, and demonstrate its utility for AoA estimation in simulations.