Designing superdirective microphone arrays with a frequency-invariant beam pattern

Frequency-invariant beam patterns are often required in systems using an array of sensors to process broadband signals. Although several methods have been proposed to design a broadband beamformer [typically realized with a finite-impulse-response (FIR) filter for each sensor] with a frequency-invariant beam pattern (FIBP), until now the case in which the spatial aperture is shorter than the involved wavelengths has very rarely been addressed. In such a case, the use of a superdirective beam pattern is essential for attaining an efficient system. In this paper, a novel method to design a broadband beamformer that produces an FIBP for a data-independent superdirective array is proposed and compared with other potential approaches. The method generates a far-field beam pattern that reproduces the desired profile over a very wide frequency band, also if the array is shorter than the wavelength. Two steps are necessary: 1) the generation of many apodizing windows at different frequency values by a stochastic method and 2) the synthesis of the FIR filters with the Parks-McClellan technique. At the end of the design chain, the very simple implementation and the robustness of the attained broadband beamformer to array imperfections increases the applicability of the system, for instance, in audio signal processing using microphone arrays