Broadband time-reversing array retrofocusing in noisy environments

Acoustic time reversal is a promising technique for spatial and temporal focusing of sound in unknown environments. Acoustic time reversal can be implemented with an array of transducers that listens to a remote sound source and then transmits a time-reversed version of what was heard. In a noisy environment, the performance of such a time-reversing array (TRA) will be degraded because the array will receive and transmit noise, and the intended signal may be masked by ambient noise at the retrofocus location. This article presents formal results for the signal-to-noise ratio at the intended focus (SNRf) for TRAs that receive and send finite-duration broadband signals in noisy environments. When the noise is homogeneous and uncorrelated, and a broadcast power limitation sets the TRA's electronic amplification, the formal results can be simplified to an algebraic formula that includes the characteristics of the signal, the remote source, the TRA, and the noisy environment. Here, SNRf is found to be proportional to the product of the signal bandwidth and the duration of the signal pulse after propagation through the environment. Using parabolic-equation propagation simulations, the formal results for SNRf are illustrated for a shallow water environment at source-array ranges of 1 to 40 km and bandwidths from several tens of Hz to more than 500 Hz for a signal center frequency of 500 Hz. Shallow-water TRA noise rejection is predicted to be superior to that possible in free space because TRAs successfully exploit multipath-propagation.