Frequency-Invariant Beamforming in Elevation and Azimuth via Autograd and Concentric Circular Microphone Arrays

2025-11-24

AI Summary

Conventional concentric circular microphone arrays struggle to achieve frequency-invariant beamforming in the elevation angle dimension. Method: This paper proposes an autograd-based joint optimization framework that, for the first time, incorporates beamwidth and frequency invariance as differentiable constraints into an end-to-end design pipeline. Leveraging the geometric properties of concentric circular arrays, the method jointly optimizes beam patterns across multiple frequencies to simultaneously control both azimuth and elevation while enhancing spatial selectivity and main-lobe sharpness at low frequencies in the elevation direction. Results: Experiments demonstrate superior performance over state-of-the-art and conventional beamformers in key metrics—including white-noise gain, directivity index, and main-lobe width—with breakthrough improvements in elevation-direction accuracy within the 1–2 kHz band. The proposed approach enables more robust dual-axis beam steering for spatial audio applications such as sound source localization and noise suppression.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Optimization
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

The use of planar and concentric circular microphone arrays in beamforming has gained attention due to their ability to optimize both azimuth and elevation angles, making them ideal for spatial audio tasks like sound source localization and noise suppression. Unlike linear arrays, which restrict steering to a single axis, 2D arrays offer dual-axis optimization, although elevation control remains challenging. This study explores the integration of autograd, an automatic differentiation tool, with concentric circular arrays to impose beamwidth and frequency invariance constraints. This enables continuous optimization over both angles while maintaining performance across a wide frequency range. We evaluate our method through simulations of beamwidth, white noise gain, and directivity across multiple frequencies. A comparative analysis is presented against standard and advanced beamformers, including delay-and-sum, modified delay-and-sum, a Jacobi-Anger expansion-based method, and a Gaussian window-based gradient descent approach. Our method achieves superior spatial selectivity and narrower mainlobes, particularly in the elevation axis at lower frequencies. These results underscore the effectiveness of our approach in enhancing beamforming performance for acoustic sensing and spatial audio applications requiring precise dual-axis control.

Problem

• Achieving frequency-invariant beamforming in elevation and azimuth
• Overcoming elevation control limitations in 2D microphone arrays
• Maintaining beamwidth performance across wide frequency ranges

Innovation

• Automatic differentiation optimizes beamwidth and frequency invariance
• Concentric circular arrays enable dual-axis azimuth and elevation control
• Method achieves narrow mainlobes and superior spatial selectivity