DOA Estimation with a Rank-deficient Covariance matrix: A Regularized Least-squares approach

DOA estimation in the presence of coherent sources using a small number of snapshots faces the challenge of rank deficiency of the received signal covariance matrix. When the covariance matrix is rank deficient, only the pseudo inverse of the covariance matrix can be computed, which can give undesirable results. Traditionally, regularized least-squares (RLS) algorithms are used to tackle estimation problems in systems with ill-conditioned or rank deficient matrices. In this work, we combine the Capon beamformer with the RLS framework to develop a DOA estimation method for scenarios with rank deficient covariance matrices. Simulation results demonstrate the effectiveness of the proposed approach.