Multiple-Source Time-Reversal Transmissions in Random Media

Abstract

Abstract-The ability of time-reversed signals in reproducing a given time-dependence of the electromagnetic field within random media is investigated. A general setup consisting of multiple sources cooperating in providing the best transmission is considered, where the constructive interference of their individual contributions is meant to improve the quality of the field generation with respect to a single-source setup. The medium response is described by means of tools from random-process theory, for the case of stationary media complex enough to ensure a large number of multi-path contributions. It is shown that even a very weak spatial coherence in the medium is sufficient to significantly hinder the improvement expected from the use of multiple-source scenarios. Experimental results obtained in a reverberation chamber support the validity of the proposed theory. Direct applications of these results can be found in recent proposals about the potential benefits of time-reversed signals used in wireless communications, imaging techniques, as well as in pulsed-field generation devices based on energy compression through dispersive media.

Steering Focusing Waves in a Reverberation Chamber With Generalized Time Reversal

“…The reason for the optimal performance for this case can be understood by recalling that wavefront-related quantities (e.g., received signals) present a mixture of coherent components, i.e., the wavefront meant to be generated, and incoherent ones, i.e., the random background fluctuations observed in the field distributions. It was shown in [25] that the ratio between the average energy densities conveyed by these two components is fixed by the statistical properties of the medium itself; e.g., for a diffusive medium it is equal to one. This result has a very practical implication: if the coherent energy is fixed, then depending on how it is shaped, the instantaneous power can take very different values.…”

Influence of Medium Statistics on Robustness of Time-Reversal Transmissions

“…Modelling H(ν) as a random process, fluctuations in y(t) appear as the result of deviations from line-of-sight transmissions. The effectiveness of TRT can be measured by first separating the received signal y(t) as done in [10]…”

“…A natural metric is therefore the energy contrast Λ [10], which measures the ratio between the energy E c = α 2 of the portion of received signal proportional to the target p(t) and that of the background fluctuations, E f , i.e.,…”

“…For a diffusive medium, it was shown [10] that its ensemble average Λ ≤ 1, with the extreme case attained only in the case of a Rayleigh or diffusive medium. Introducing the TRT function W (ν) = |H(ν)| 2 , [10] demonstrated that the second-order statistics of W (ν) provide a direct estimate of the energy contrast as Λ = ς −2 W , where ς is the standard deviation of W (ν) normalized to its mean. This relationship is useful as it gives a straightforward understanding of the performance of TRT as a function of the medium statistics and complexity.…”

“…Once the energy contrast is known, it can be translated into a peak contrast, measuring the ratio of the peak of coherent focusing and the rms amplitude of the background fluctuations [10].…”