A flexible high directivity beamformer with spherical microphone arrays

Area of Science:

• Acoustics
• Signal Processing
• Array Signal Processing

Background:

• Maximum directivity (MD) beamformers using spherical microphone arrays excel at processing broadband acoustic and speech signals.
• However, MD beamformers are sensitive to sensor self-noise and mismatches, often addressed by increasing microphone count, which introduces design challenges.
• Increasing microphone numbers improves white noise gain (WNG) but can negatively impact cost, array aperture, and overall performance.

Purpose of the Study:

• To address the sensitivity of MD beamformers to sensor noise and mismatches.
• To present a flexible high directivity (HD) beamforming algorithm that improves WNG and offers a tunable directivity factor (DF).
• To establish analytical links between DF, WNG, and a tuning parameter for optimal beamformer configuration.

Main Methods:

• Approximating ideal directivity patterns and beamformer beampatterns using spherical harmonic series.
• Deriving the relationship between directivity patterns and beampatterns to formulate the HD beamformer.
• Establishing analytical relationships between the directivity factor (DF), white noise gain (WNG), and a tuning parameter.

Main Results:

• A flexible HD beamforming algorithm is presented, improving WNG while achieving a DF between Nth-order and (N-1)th-order MD beamformers.
• Analytical links between DF, WNG, and a tuning parameter are derived.
• The optimal tuning parameter can be determined based on specified DF or WNG values.

Conclusions:

• The proposed flexible HD beamformer offers a robust solution to the sensitivity issues of MD beamformers.
• The algorithm provides a tunable trade-off between directivity and noise suppression.
• The derived analytical links facilitate straightforward optimization of the beamformer's performance parameters.