A single-channel virtual receiving array using a time-reversal chaotic cavity

Abstract

Chaotic reverberation in a cavity, when coupled with time reversal acoustics, can be harnessed to build a perfect time-reversal mirror for transmitting and receiving highly focused sounds with a small number of transducers. In this article, a virtual receiving array, comprised of a single receiving transducer and a chaotic cavity, is developed based on time reversal processing of the reverberation inside the cavity. A prototype array, having 10 × 10 virtual receiving elements, is built and evaluated against a comparable physical array in terms of its localization and waveform reproduction capabilities. It turns out that the most crucial factor in the success of a virtual array is the ergodicity of its chaotic cavity, the exact mathematical expression for which is also derived. The virtual receiving array presented here may find some niche applications in reverberant environments, where a physical array turns out to be too costly or cumbersome to operate.