Asymptotically perfect wideband focusing of multiring circular arrays

The concept of coherent focusing of sensor arrays, introduced by Wang and Kaveh, led to the development of high-performance and computationally efficient algorithms for wideband direction finding and beamforming. Nonetheless, the quality of focusing depends on the understanding and the proper exploitation of specific array manifold properties. Circular arrays exhibit uniform (isotropic) performance over the entire azimuthal range and allow the use of fast algorithms, originally developed for uniform linear arrays, by decomposing the manifold into circular harmonics. Coherent wideband focusing of circular arrays suffers from ambiguities, noise warping, and numerical ill conditioning. In this work, it is shown that a fast orthonormal beamspace transformation combining the responses of two concentric rings can perfectly focus wideband sources at all azimuth angles in the circular harmonic domain in the limit of infinite number of sensors. The information loss after focusing is minimized through an analytical approach. The proposed focusing scheme is computationally very efficient and can be directly extended to multiring circular arrays that are arranged into a set of nested two-ring subarrays to cover very large bandwidths.