Adaptive beamforming using fast low-rank covariance matrix approximations

Calculating accurate low-rank covariance estimates for sensor arrays with a large number of elements is a common task in signal processing. Many algorithms make use of the exact spectral decomposition of the empirical covariance structure-but the singular value decomposition is often too costly in practice, owing to array size or constraints on computation. Recent approaches geared toward the approximate spectral decomposition of large matrices present an appealing alternative; here we compare two recently proposed algorithms for low-rank matrix approximation and compare their performance in a beamforming covariance estimation task. Simulation results demonstrate that the latter method, explicitly designed for the efficient approximation of symmetric positive semi-definite matrices, yields performance and robustness characteristics that offer encouragement for its use in practical beamforming applications.