On the Design of 3D Steerable Beamformers With Uniform Concentric Circular Microphone Arrays

Circular microphone arrays (CMAs) and concentric CMAs (CCMAs) have been used in a wide range of applications such as smartspeakers and teleconferencing systems because of their flexible steering ability. Although many efforts have been devoted to beamforming with CCMAs, most existing methods consider only the 2-dimensional (2D) case and assume that the sound sources of interest are in the same plane as the sensor array (generally the horizontal plane), which often does not hold true in practical applications. This paper deals with the problem of beamforming with uniform CCMAs (UCCMAs) in the 3-dimensional (3D) space to control the steering of the spatial response and meanwhile form frequency-invariant beampatterns for processing broadband acoustic and speech signals. The major contributions of this work are summarized as follows: 1) it presents an analysis based on the spherical harmonics decomposition about the Nth-order optimal and steerable directivity patterns; 2) a beamforming method is developed in which the beamformer's coefficients are identified by solving a linear system of equations formed by approximating the Nth-order optimal target beampattern with the beamformer's beampattern while the resulting beampattern can be steered flexibly in the 3D space; 3) the sufficient and necessary condition on the array geometry and sensors' placement are given to ensure that the beamformer exists and is unique; and 4) the analytical forms of the directivity factor (DF) and white noise gain (WNG) of the resulting beamformer is given and discussion is presented on what conditions irregularities (deep nulls) in WNG and DF may occur. Simulations are provided to illustrate the property of the developed beamforming methods.