Tuning to Resonances With Iterative Time Reversal

This paper considers a distributed wave-based sensing system that probes a scene consisting of multiple interacting idealized targets. Each sensor is a collocated transmit-receive pair that is capable of transmitting arbitrary wideband waveforms. We address the problem of finding the space-time transmit waveform that provides the best target detection performance in the sense of maximizing the energy scattered back into the receivers. Our approach is based on earlier theoretical work that showed, for an idealized infinite half-space geometry, that the solution could be constructed by an iterative time-reversal (TR) process. In this paper, we give a more realistic example involving a two-sensor time-domain system. We show that for this system, the iterative TR process can be used to tune automatically to all the target resonances that are within the bandwidth of the interrogating radar system. We show that although obtaining eigenvalues (and hence resonances) of the scattering operator is in general unstable, using the iterative TR process to obtain the resonances is a stable process. Moreover, we show that these resonance frequencies are connected to the poles of the singularity expansion method.