A stochastic approach to the synthesis of a robust frequency-invariant filter-and-sum beamformer

Frequency-invariant beam patterns (FIBPs) are often required by systems using an array of sensors to process broadband signals. Although several methods have been proposed to design a broadband beamformer (typically characterized by a finite impulse response (FIR) filter for each sensor) with an FIBP, until now, the case in which the spatial aperture is shorter than the involved wavelengths has very rarely been considered. In such a case, the use of a superdirective beam pattern is essential to attaining an efficient system. In this context, robustness to array imperfections and random errors is a very crucial feature. In this paper, a method to design a robust 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) and is based on a stochastic approach to the direct synthesis of the FIR filters. The very simple implementation and the resulting robustness of the attained filter-and-sum beamformer to array imperfections increase the applicability of the system. This fact is particularly important in the context of a audio signal processing carried out by microphone arrays, which is the main application considered in this paper.