Low-Rank Robust Superdirective Beamforming Using Multidimensional Kronecker Products

Superdirective beamformers exhibit high spatial directivity and can therefore effectively suppress spatially isotropic noise, playing a key role in speech communication, far-field pickup, and other scenarios. However, because they are highly sensitive to array imperfections and self-noise, the lack of robustness limits their practical applications. To improve their robustness, a trade-off between high directivity and robustness is typically required, such as using diagonal loading factors to constrain white noise gain. However, as the number of microphones increases, conventional robust superdirective beamformers become less efficient owing to excessive parameter redundancy. Kronecker product beamforming offers a computationally efficient solution that enhances the robustness of beamformers while reducing parameter size. Existing studies, however, are mostly constrained to two-dimensional formulations, with limited research on higher-dimensional decomposition structures and the effects of different decomposition modes on beamformer performance. To address the above issues, we extend the existing two-dimensional Kronecker product method to a multidimensional form and propose a low-rank robust superdirective beamforming method based on multidimensional Kronecker product. This method improves design flexibility by decomposing the beamformer into a Kronecker product form of multiple sets of short filters. Under a distortionless constraint, the method alternately iterates to solve for the multiple sets of short filters with the goal of maximizing the directivity factor. Experimental results show that for different array structures, the proposed method achieves comparable performance to traditional methods with fewer parameters(number of filter coefficients)and lower matrix inversion dimensions across different decomposition modes. Therefore, it exhibits higher efficiency in practical systems. Furthermore, by analyzing the impact of different decomposition approaches on beamforming performance, the effectiveness and computational advantages of the proposed method were verified.