The existing robust narrowband beamformers based on probability-constrained optimization have an excellent performance as compared to several state-of-the-art robust beamforming algorithms. However, they always assume that the steering vector errors are small enough. Without this assumption, we extend the probability-constrained approach to a wideband beamformer. In addition, a novel robust wideband beamformer with frequency invariance constraints is proposed by introducing the response variation (RV) element. Our problems can be reformulated in a convex form as the iterative second order cone programming (SOCP) problem and solved effectively using well-established interior point method. Compared with existing robust wideband beamformers, a more efficient control over the beamformer's response against the steering vector errors is achieved with an improved output signal-to-interference-plus-noise ratio (SINR).
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