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A Directional-Derivative-Constrained Method for Continuously Steerable Differential Beamformers with Uniform Circular Arrays

Tiantian Xiong, Yongyi Deng, Kunlong Zhao, Jilu Jin, Xueqin Luo, Gongping Huang, Jingdong Chen, Jacob Benesty

Abstract

Differential microphone arrays offer a promising solution for far-field acoustic signal acquisition due to their high spatial directivity and compact array structure. A key challenge lies in designing differential beamformers that are continuously steerable and capable of enhancing target signals arriving from arbitrary directions. This paper studies the design of differential beamformers for circular arrays and proposes a novel framework that incorporates directional derivative constraints. By constraining the first-order derivatives of the beampattern at the desired steering direction to zero and assigning suitable values to higher-order derivatives, the beamformer is ensured to achieve its maximum response in the target direction and provide sufficient beam steering. This approach not only improves steering flexibility but also enables a more intuitive and robust beampattern design. Simulation results demonstrate that the proposed method produces continuously steerable beampatterns.

A Directional-Derivative-Constrained Method for Continuously Steerable Differential Beamformers with Uniform Circular Arrays

Abstract

Differential microphone arrays offer a promising solution for far-field acoustic signal acquisition due to their high spatial directivity and compact array structure. A key challenge lies in designing differential beamformers that are continuously steerable and capable of enhancing target signals arriving from arbitrary directions. This paper studies the design of differential beamformers for circular arrays and proposes a novel framework that incorporates directional derivative constraints. By constraining the first-order derivatives of the beampattern at the desired steering direction to zero and assigning suitable values to higher-order derivatives, the beamformer is ensured to achieve its maximum response in the target direction and provide sufficient beam steering. This approach not only improves steering flexibility but also enables a more intuitive and robust beampattern design. Simulation results demonstrate that the proposed method produces continuously steerable beampatterns.
Paper Structure (5 sections, 21 equations, 5 figures)

This paper contains 5 sections, 21 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Signal Model, Problem Formulation, and Performance Measures
  3. Steerable Differential Beamformers via Directional Derivative Constraints
  4. Simulations
  5. Conclusions

Figures (5)

  • Figure 1: Beampattern of the beamformer designed with null constraints at the specified null directions. The parameters are $M = 8$, a UCA with radius $r = 2.0$ cm, $f = 1$ kHz, $\theta_{\mathrm{s}} = 50^\circ$, and two nulls at $122^\circ$ and $194^\circ$.
  • Figure 2: Beampatterns at $f = 1$ kHz of first-order differential beamformers designed using the proposed method for steering directions: (a) $\theta_{\mathrm{s}} = 20^\circ$, (b) $\theta_{\mathrm{s}} = 50^\circ$, (c) $\theta_{\mathrm{s}} = 120^\circ$, and (d) $\theta_{\mathrm{s}} = 240^\circ$.
  • Figure 3: DF and WNG comparison of first-order differential beamformers designed using the DMA-Null, DMA-SymNull, DMA-SeriesExp, and proposed DMA-DerivCon methods: (a) DF and (b) WNG. Conditions are $M = 8$, UCA with $r=2.0$ cm and $\theta_{\mathrm{s}} = 50^\circ$.
  • Figure 4: Beampatterns at $f = 1$ kHz of second-order differential beamformers designed using the proposed method for steering directions: (a) $\theta_{\mathrm{s}} = 20^\circ$, (b) $\theta_{\mathrm{s}} = 50^\circ$, (c) $\theta_{\mathrm{s}} = 120^\circ$, and (d) $\theta_{\mathrm{s}} = 240^\circ$.
  • Figure 5: DF and WNG comparison of second-order differential beamformers designed using the DMA-Null, DMA-SymNull, DMA-SeriesExp, and proposed DMA-DerivCon methods: (a) DF and (b) WNG. Conditions are $M = 8$, UCA with $r=2.0$ cm and $\theta_{\mathrm{s}} = 50^\circ$.