  Acoustic beamforming aims to focus acoustic signals to a specific direction
and suppress undesirable interferences from other directions. Despite its
flexibility and steerability, beamforming with circular microphone arrays
suffers from significant performance degradation at frequencies corresponding
to zeros of the Bessel functions. To conquer this constraint, baffled or
concentric circular microphone arrays have been studied; however, the former
needs a bulky baffle that interferes with the original sound field whereas the
latter requires more microphones that increase the complexity and cost, both of
which are undesirable in practical applications. To tackle this challenge, this
paper proposes a circular microphone array equipped with virtual microphones,
which resolves the performance degradation commonly associated with circular
microphone arrays without resorting to physical modifications. The sound
pressures at the virtual microphones are predicted from those measured by the
physical microphones based on an acoustics-informed neural network, and then
the sound pressures measured by the physical microphones and those predicted at
the virtual microphones are integrated to design the beamformer. Experimental
results demonstrate that the proposed approach not only eliminates the
performance degradation but also suppresses spatial aliasing at high
frequencies, thereby underscoring its promising potential.
