Gaussian Target Detection in Multipath Clutter With Single-Antenna Time Reversal

We derive the time reversal likelihood ratio optimal detector for a target in stationary random multipath clutter, extending prior work where both are assumed to be deterministic. We suppress the stationary clutter through adaptive power allocation. We show that the Time Reversal Likelihood Ratio Test performs much better than the conventional Weighted Energy Detector. We provide analytical results on the performance of the time reversal detector by approximating it with the Time Reversal Linear Quadratic detector, which models the received signal as a Complex Gaussian. Our simulations show that the Linear Quadratic detector is a good approximation to the Time Reversal Likelihood Ratio Test and that both show a significant improvement of 4 to 7 dB effective signal-to-noise ratio gain over the Weighted Energy Detector. This gain is dependent on the target and clutter power spectral densities.