Recursive Steering Vector Estimation and Adaptive Beamforming under Uncertainties

The accurate determination of the steering vector of a sensor array that corresponds to a desired signal is often hindered by uncertainties due to array imperfections, such as the presence of a direction-of-arrival (DOA) estimation error, mutual coupling, array sensor gain/phase uncertainties, and sensor position perturbations. Consequently, the performance of conventional beamforming algorithms that use the nominal steering vector may be significantly degraded. A new method for recursively correcting possible deterministic errors in the estimated steering vector is proposed here. It employs the subspace principle and estimates the desired steering vector by using a convex optimization approach. We show that the solution can be obtained in closed form by using the Lagrange multiplier method. As the proposed method is based on an extended version of the conventional orthonormal PAST (OPAST) algorithm, it has low implementation complexity, and moving sources can be handled. In addition, a robust beamformer with a new error bound that uses the proposed steering vector estimate is derived by optimizing the worst case performance of the array after taking the uncertainties of the array covariance matrix into account. This gives a diagonally loaded Capon beamformer, where the loading level is related to the bound of the uncertainty in the array covariance matrix. Numerical results show that the proposed algorithm performs well, especially at high signal-to-noise ratio (SNR) and in the presence of deterministic sensor uncertainties.