High-order superdirectivity of circular sensor arrays mounted on baffles

In this study, we propose analytical optimal solutions for the high-order superdirectivity of circular sensor arrays mounted on a rigid sphere and an infinite rigid cylinder. Specifically, the optimal beampattern, global optimum directivity factor, and total error sensitivity function can be accurately expressed as the sum of eigenbeams, sum of their directivity factors, and sum of their sensitivity functions, respectively, with the use of the circulant property of the noise cross-spectral matrices of these two types of circular arrays in the isotropic noise field. The limit expressions of the maximum directivity factor and optimal beampattern are derived, which show that the baffled circular arrays possess good potential for directivity improvement. The baffles have been proven to improve robustness and have no effects on the limit expressions. It is further found that the performance of eigenbeams can be regarded as an indicator of robustness. Subsequently, a reduced-rank technique is used to achieve robust highorder superdirective beampatterns. Simulations show that these solutions facilitate the practical implementation of high-order superdirectivity for baffled circular arrays.