Frequency invariant beamforming in very short arrays

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 by an FIR filter for each sensor) with a frequency invariant beam pattern, till now the case in which the spatial aperture is shorter than the involved wavelengths has not been addressed. In such a case, the use of a superdirective beam pattern is essential to attain an efficient system. In this paper, a novel method to design a broadband beamforming that produces a frequency invariant beam pattern 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; (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 to array imperfections of the attained broadband beamformer increases the applicability of the system, for instance, in underwater communications for small vehicles.