Beamforming with Random Projections: Upper and Lower Bounds

2025-07-08

AI Summary

In distributed microphone arrays, conventional beamformers struggle to simultaneously achieve high white noise gain and effective interference suppression. To address this trade-off, this paper proposes a hybrid beamforming framework based on random projection. The method employs a data-driven approach to project high-dimensional array observations onto a lower-dimensional subspace, explicitly modeling computational complexity as an adjustable design parameter. We theoretically derive tight upper and lower bounds on the output power of the compressed-domain beamformer, thereby enhancing adaptivity to underlying signal structure. By integrating random projection, minimum-variance distortionless response (MVDR) beamforming, signal subspace analysis, and statistical signal processing, the proposed framework achieves superior SNR and SINR gains over conventional MVDR while significantly reducing computational cost—enabling real-time operation without compromising robustness.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Beamformers often trade off white noise gain against the ability to suppress interferers. With distributed microphone arrays, this trade-off becomes crucial as different arrays capture vastly different magnitude and phase differences for each source. We propose the use of multiple random projections as a first-stage preprocessing scheme in a data-driven approach to dimensionality reduction and beamforming. We show that a mixture beamformer derived from the use of multiple such random projections can effectively outperform the minimum variance distortionless response (MVDR) beamformer in terms of signal-to-noise ratio (SNR) and signal-to-interferer-and-noise ratio (SINR) gain. Moreover, our method introduces computational complexity as a trade-off in the design of adaptive beamformers, alongside noise gain and interferer suppression. This added degree of freedom allows the algorithm to better exploit the inherent structure of the received signal and achieve better real-time performance while requiring fewer computations. Finally, we derive upper and lower bounds for the output power of the compressed beamformer when compared to the full complexity MVDR beamformer.

Problem

• Trade-off between noise gain and interferer suppression in beamforming
• Dimensionality reduction in distributed microphone array processing
• Balancing computational complexity with beamformer performance

Innovation

• Uses multiple random projections for dimensionality reduction
• Mixture beamformer outperforms MVDR in SNR and SINR
• Introduces computational complexity as design trade-off