Robust covariance matrix reconstruction algorithm for time-domain wideband adaptive beamforming

Several time-domain wideband beamformers with the response variation (RV) constraint were recently proposed to constrain the consistency of the main lobe responses over the frequency band of interest. However, when the model mismatch is severe, these beamformers may not be robust to suppress wideband interferences effectively. Instead of adding more uncertainty constraints to enhance the robustness, we attempt to remove the desired signal component from the stacked sample covariance matrix by reconstructing a wideband stacked interference-plus-noise covariance matrix (SINCM). To overcome the model mismatch for an array without calibration, we introduce a possible mismatched stacked steering vector (SSV) set, and we reconstruct the SINCM by integrating all the possible mismatched SSVs over the interference angular sector and all subbands. Then we correct the desired signal SSV using two different approaches, one is solving an optimization problem that maximizes the array output, another is the eigen-decomposition of the reconstructed stacked desired signal covariance matrix. By transforming the RV inequality constraint into a weighted part of objective function, the finite impulse response coefficient vector of the proposed wideband beamformer can be calculated in a closed form as a function of the reconstructed SINCM and the estimated SSV of the signal-of-interest. Numerical simulations show robust performance in the case of unknown SSV mismatch. An acoustic experiment is carried out on a linear hydrophone array, and the result validates that the proposed beamformer provides better performance compared with other wideband adaptive beamformers.