Robust beamforming and steering of arbitrary beam patterns using spherical arrays

Spherical microphone and loudspeaker arrays present a compact method for analysis and synthesis of arbitrary three-dimensional sound fields. However, issues such as sensor self noise, placement errors, and mismatch require robustness constraints in beamformer design. This work presents a method for designing robust beam patterns with an arbitrary shape and an efficient method for steering the resulting patterns in three dimensions. The technique is used for two applications: reproducing spherical microphone array recordings over loudspeaker arrays and binaurally over headphones with head tracking.

1. INTRODUCTION

In the 1970s, work by Gerzon and others on Ambisonics established the use of spherical microphone and loudspeaker arrays for capturing and recreating three-dimensional sound fields [1], [2]. However, it hasn't been until recently that a more rigorous understanding of higher order spherical arrays has been established [1], [2], [3], [4]. It is now well known that the capture ability of spherical microphone arrays is limited in the high frequencies by spatial aliasing and in the low frequencies by microphone placement, mismatch, and SNR concerns. Incorporating a white noise gain (WNG) constraint into the beamformer design can ensure that a beam pattern remains controlled at low frequencies [5].