Superdirectivity solutions of circular arrays with acoustic particle velocity sensors

This paper presents analytical superdirectivity solutions for circular arrays with acoustic particle velocity sensors (APVSs) based on the eigenbeam decomposition and synthesis theory. The main findings are summarized as follows. (1) The optimal beampattern, the global directivity factor, and the total error sensitivity function of circular APVS arrays, like those of circular arrays with pressure sensors, can also be expressed as the sums of eigenbeams, their directivity factors, and their error sensitivity functions, respectively. (2) The directivity factor increases but robustness decreases with an increase in the order number at low frequencies, and the reduced-rank technique can be used to synthesize robust superdirective beampatterns by truncating some high-order eigenbeams. (3) The limit theoretical maximum directivity factor and optimal beampattern are derived, which provide the upper bound of performance for circular APVS arrays and show that this type of arrays also has good potential for improving directivity. The reduced–rank technique is applied for circular APVS arrays to obtain robust high-order superdirectivity in simulations, which shows good performance for improving the robustness.