Robust adaptive beamforming with random steering vector mismatch

In this paper, random steering vector mismatches in sensor arrays are considered and probability constraints are imposed for designing a robust minimum variance beamformer (RMVB). To solve the resultant design problem, a Bernstein-type inequality for stochastic processes of quadratic forms of Gaussian variables is employed to transform the probabilistic constraint to a deterministic form. With the use of convex optimization techniques, the deterministic problem is reformulated to a semidefinite programming (SDP) problem which can be efficiently solved. In order to overcome the degradation caused by the presence of the signal-of-interest (SOI) in the training snapshots, two methods with different application conditions to interference-plus-noise covariance matrix (INCM) construction are also introduced. Additionally, the uncertainty of the sample covariance matrix is taken into account to improve the robustness when the INCM-based approaches are not feasible. Numerical examples are presented to demonstrate the performances of the proposed robust beamformers in different scenarios.