Revisiting Frequency-Invariant Beamformer Design Using Weighted Spatial Response Variation

Abstract

The spatial response variation (SRV) is widely employed in frequency-invariant (FI) beamformer design, thanks to the fact that it provides more design degrees of freedom to achieve better FI performance. Recently, the weighted-SRV, a generalized form of SRV, was proposed for the FI beamformer design. It is shown that the weighted-SRV-based design outperforms the SRV-based design with mainlobe ripple and sidelobe level being able to be precisely controlled. However, the approximation error of reference beampattern in the weighted-SRV design may lead to slow convergence or even failure to converge. To address the problem, this paper reformulates the constrained weighted-SRV cost function into an unconstrained form. Under the reformulated cost function, the closed-form solutions of the weighted-SRV's weighting function are theoretically derived, and then an FI-beamformer design approach is proposed. Simulation results demonstrate the superior performance of the proposed approach.