Design of Circular Array Beamformer Based on Orthogonal Criterion

In order to solve the high computational complexity and low temporal resolution issues in the beamforming process of circular differential microphone arrays, a broadband beamformer design method based on the zero-point interval characteristic information is proposed, leveraging the unique geometrical properties of the circular array. This method establishes an orthogonal criterion between the beamformer and the anticipated zero-point direction of the beam pattern. Initially, the design of the beamformer is transformed into an optimization problem, considering the incident angle of the target signal and the angle of the anticipated zero points of the beam pattern, and a solution is designed. Subsequently, by optimizing the number of zeros and the white noise gain, a series of beamformers with adjustable white noise gain and directivity factor are designed, and their equivalence to beamformers designed by traditional methods is proven. Finally, using the characteristic information of zeros and noise within a given interval, a beamformer with adjustable signal-to-noise ratio gain was designed. To validate the beamforming effect, a circular microphone array and the zero-point characteristic information are designed, and simulations of the broadband beam pattern and signal-to-noise ratio gain are conducted. The simulation results confirm the feasibility and effectiveness of this method. It is evident that when the anticipated zero-point information of the beam pattern is given, the beamformers designed by this method can produce a frequency-invariant beam pattern and achieve controllable signal-to-noise ratio gain.