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.

本文基于特征波束分解和合成理论，提出了带有声粒子速度传感器（APVS）的圆形阵列解析超指向性解决方案。主要发现概括如下。（1）圆形APVS阵列的最佳波束图，全局方向性因子和总误差敏感性函数（如带压力传感器的圆形阵列）也可以表示为特征光束之和，其方向性因子及其误差敏感性功能。（2）在低频下，方向性因子增加，但鲁棒性随阶数的增加而降低，并且降秩技术可用于通过截断一些高阶本征光束来合成鲁棒的超指向性波束图形。（3）推导了极限理论最大指向性因子和最佳波束图，这为圆形APVS阵列提供了性能的上限，表明这种类型的阵列也具有改善指向性的潜力。降秩技术应用于圆形APVS阵列，以在仿真中获得鲁棒的高阶超方向性，这在改善鲁棒性方面显示出良好的性能。