Stochastic Time Reversal for Radar Detection
Time Reversal is an adaptive waveform transmission technique particularly suited to dispersive or non-homogenous media that focuses energy on a desired point in space. Early work concentrated on optical and acoustic/ultrasonic applications, followed more recently by applications in the electromagnetic domain. Time Reversal has been used for single- and multi-antenna detection, imaging, communications, non-destructive testing, and beam steering, among other applications.
This thesis develops Time Reversal detection algorithms for randomly varying targets embedded in randomly varying clutter. We model the target and clutter as independent complex Gaussian random variables and consider both single-antenna and multi-antenna detection scenarios. We derive the optimal Time-Reversal Likelihood Ratio Test (TR-LRT) for the single-antenna case, as well as a sub-optimal Time Reversal-Linear Quadratic (TR-LQ) detector that allows for a priori threshold and performance computation. These detectors are compared against a benchmark Weighted Energy Detector (WED). For the multi-antenna scenario, we present the Time Reversal MIMO (TR-MIMO) detector and compare its performance to a conventional Spatial MIMO (S-MIMO) radar. We show that, for both scenarios, the relative performance of Time Reversal detection methods depends on the coherence of the channel between the forward and TR transmission stages. We discuss the potential for detection gains with Time Reversal in single-antenna and multi-antenna systems. We discuss lower and upper bounds on gain and show that Time Reversal provides a useful and computationally simple approximation to the optimal transmit signal.
To compute the optimal hypothesis test for a Blind TR detection system, we derive a new statistical distribution, the Complex Double Gaussian distribution, which characterizes the complex product Z = XY of independent complex Gaussian random variables X and Y . We also apply this new probability distribution to analyze the performance of M-ary Phase Shift Keying (MPSK) communication systems, showing its applicability well beyond the realm of Time Reversal problems.