Radial Acoustic Beamforming via Near-Field Array Processing in the Spherical Harmonics Domain

When two speakers are in the same direction but at different distances, far-field beamforming fails to isolate the desired speech signal. We develop two radial acoustic beamformers using near-field processing for spherical microphone arrays (SMAs). First, we present the near-field array signal model in both the spatial and spherical harmonics (SH) domains, where the steering vector decomposes into separate radial and angular components—a key aspect we exploit. For the first beamformer, the desired speech time-frequency (TF) coefficients are modelled as zero-mean circular complex Gaussian random variables with time-varying variances; for the second, a Laplacian distribution is used to enhance the modelling of the desired speech at the beamformer output. Both beamformers enforce a distortionless constraint on the desired source and employ maximum likelihood estimation (MLE) to iteratively update the beamformer weights and TF-domain variances. Simulation results show our methods outperform the conventional technique in near-field scenarios.