Oversteering of end-fire arrays with frequency-invariant beam patterns

In this paper we propose and assess a technique to tune the trade-off between the directivity and the robustness of a frequency-invariant beam pattern, without the need to modify the designed FIR filters. Starting from a filter-and-sum beamformer over a superdirective array, synthesized by a stochastic and analytic method, which possesses the maximum directivity that the array may achieve and taking into account the probability density functions of the transducers' characteristics, we introduce a post-synthesis optimization that allows to choose a given system performance, after the investigation of a wide space of realistic possibilities. The a posteriori performance tuning will be referred to as oversteering and is effective only for end-fire array. By comparing the results of the proposed technique with those of the optimum synthesis, it is possible to evaluate the proposed method effectiveness in producing frequency-invariant beam patterns with an end-fire looking direction and a number of interesting trade-offs between directivity and robustness.