Global synthesis of superdirective frequency-invariant beam patterns

Abstract

Frequency-invariant beam patterns are often required by systems using an array of sensors to process broadband signals. If the spatial aperture is shorter than the involved wavelengths, the use of a superdirective beam pattern is essential to attain an efficient system. In this context, robustness to array imperfections is a crucial feature. In the literature, only a few approaches have been proposed to design a robust, superdirective, frequency-invariant beamformer, based on a filter and sum architecture: in all of them, the frequency invariance is achieved imposing an a priori desired beam pattern. However the choice of a suitable desired beam pattern is not trivial and depends on the specific design case: an improper selection of the desired beam pattern can produce unsatisfactory performances. We propose a new method of global synthesis, computationally inexpensive, allowing to design a robust broadband beam pattern with an optimal trade-off between the frequency invariance and the directivity, without the need of imposing a priori a desired beam pattern. The results show that the synthesized beam patterns have a directivity, a frequency-invariance, and a robustness that are very similar to or better than those of the beam patterns obtained by the literature methods.