Acoustic vector-sensor beamforming and Capon direction estimation

We consider beamforming and Capon direction of arrival (DOA) estimation using arrays of acoustic vector sensors. We derive an expression for the Cramer-Rao bound (CRB) on the DOA parameters of a single source. Using this, we give conditions that minimize the lower bound on the asymptotic mean-square angular error, and conditions that ensure it is isotropic. The asymptotic performance of the Capon (1969, 1971) and beamforming estimators is analyzed and compared with a scalar-sensor array. The vector-sensor array is seen to have improved performance due to its elements´ directional sensitivity. Large sample approximations for the mean-square error (MSE) matrices of the estimators are derived. Throughout, we compare vector-sensor arrays with their scalar-sensor counterparts