Detection by time reversal: Single antenna

This paper studies the binary hypothesis test of detecting the presence or absence of a target in a highly cluttered environment by using time reversal. In time reversal, the backscatter of a signal transmitted into a scattering environment is recorded, delayed, energy normalized, and retransmitted through the medium. We consider two versions of the test-target channel frequency response assumed known or unknown-and, for each version, contrast two approaches: conventional detection (where no time reversal occurs) and time reversal detection. This leads to four alternative formulations for which we derive the optimal detector and the generalized likelihood ratio test, when the target channel frequency response is known or unknown, respectively. We derive analytical expressions for the error probabilities and the threshold for all detectors, with the exception of the time reversal generalized likelihood ratio test. Experiments with real-world electromagnetic data for two channels (free space with a target immersed in 20 scatterers and a duct channel) confirm the analytical results and show that time reversal detection provides significant gains over conventional detection. This gain is explained by the empirical distribution or type of the target channel frequency response-richer scattering channels induce types with heavier tails and larger time reversal detection gains.