A Temporal–Spatial Joint High-Gain Beamforming Method in the STFT Domain Based on Kronecker Product Filters

Superdirective beamformers are highly appealing for their superior directivity and effectiveness in suppressing diffuse noise. However, their sensitivity to sensor noise and array imperfections poses significant challenges in practice. Achieving higher robustness often necessitates a trade-off in directivity, thereby reducing their ability to suppress directional and diffuse noises. A key concern, therefore, is how to improve noise suppression while maintaining robustness. To address this, we propose in this paper a novel temporal-spatial joint high-gain beamforming method based on a Kronecker product decomposition, making use of the inter-frame correlation to improve performance. The signal model in the proposed work uses recent pairs of time frames and employs the Kronecker product of the steering vector with a frequency- and angle-dependent inter-frame correlation vector. The high-gain beamformers are formulated as Kronecker product filters, where the temporal filter is optimized to maximize the white noise gain (WNG) and the spatial filter is optimized to enhance the directivity factor (DF). With accurate estimation of the correlation vector, Kronecker product high-gain beamformers can simultaneously improve both WNG and DF. The proposed method offers flexibility and can be extended to design other types of beamformers, with a maximum WNG (MWNG) beamformer presented as an example within the same framework. This paper also explores three approaches to estimating the correlation vector: time-invariant, time-varying, and data-driven estimations. Simulation results show notable improvements in noise suppression performance across various scenarios, highlighting the practical effectiveness of the proposed method.