On a Particular Family of Differential Beamformers with Cardioid-Like and No-Null Patterns

Differential microphone arrays (DMAs), which are responsive to the differential acoustic pressure fields, have been used in a wide range of applications related to audio and speech. The core part of a DMA is the so-called differential beamformer, which is generally designed by placing a number of nulls in its beampattern to attenuate noise from some directions. But the presence of these nulls may cause some great issues, e.g., leading to suboptimal performance if the interference/noise is incident from directions other than the nulls' directions, and making the beamformer less robust to sensors' self noise and array imperfections. To overcome these problems, this letter is devoted to the design of differential beamformers with no nulls in its beampattern. A design method and its multistage implementation are presented and analyzed. An improved solution is then developed, which is able to form frequency-invariant beampatterns with no nulls in the frequency range of speech signals. Simulations are provided to illustrate the properties of the developed methods.