Robust superdirective end-fire arrays

Oversteering is a technique to achieving robust superdirective performance by end-fire arrays whose transducers are spaced less than half wavelength. To reduce the beamwidth, the main-lobe is pushed past end-fire by the introduction of additional delays. The reduction of the main-lobe sensitivity produces, in turn, an increase of the side-lobe level and a fall of the white noise gain. This paper proposes a method to compute the real-valued weight coefficients that yield the maximum directivity for a given oversteering amount and assure a white noise gain above a given threshold. If this optimization is carried out in parallel with the exhaustive search for the best oversteering amount, the optimum oversteering performance can be reached. Finally, it is shown that for a linear array composed of 8 transducers, the oversteering technique yields a directivity which is very close to that provided by the optimum complex-valued weight coefficients, requiring a simpler processing system and assuring the same robustness (i.e., the two solutions show the same white noise gain).