Tuning the performance of the superdirective frequency-invariant beamforming applied to end-fire arrays

In this paper, starting from a frequency-invariant filter-and-sum beamformer, we propose and assess a technique to tune the trade-off between the directivity and the robustness of the related beam pattern, without the need to modify the designed FIR filters. Our technique can be seen as a post-synthesis optimization that allows to choose a given system performance, after the investigation of a wide space of realistic possibilities. It can be applied only to end-fire array and will be referred to as oversteering. The idea is to steer the beam pattern past end-fire (i.e., to steer the beam pattern outside the visible region) in order to tune the beamformer performance without actually change the main response axis of the array, which remains pointed to end-fire. The oversteering is obtained just by applying opportune delays to the signals received by the array transducers, and for each steering direction past end-fire a different balance between directivity and robustness occurs. By analyzing the results of the proposed technique it is possible to evaluate the effectiveness in producing frequency-invariant beam patterns with an end-fire looking direction and a number of interesting trade-offs between directivity and robustness.