Beamforming in the Short-Time Fourier Transform Domain via Dimensionality Reduction

Beamforming is a fundamental technique for extracting a speech signal of interest from noisy observations and is widely used in speech processing, communication, and recognition applications. Typically, microphone array beamforming is performed in the short-time Fourier transform (STFT) domain, where a distinct beamformer is designed and applied to each STFT bin. This method offers great flexibility for handling nonstationary and broadband speech signals. However, it also requires a large number of beamformers to cover all STFT subbands, making it computationally demanding, particularly for adaptive beamformers. To address this challenge, this paper proposes a dimensionality-reduction-based beamforming approach in the STFT domain. By applying the singular value decomposition (SVD) to the data matrix of signals from all channels and STFT subbands, we achieve low-dimensional representations of the observation signals. This transformation processes the speech signal components into a smaller number of dimensions, significantly reducing the number of required beamformers as compared to traditional STFT-domain methods. We provide examples of designing beamformers in this transformed domain and show through simulations that the proposed method not only reduces computational complexity but also enhances performance compared to existing techniques.