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Time-reversal processing (TRP) has been intensively studied for underwater object detection, however, most of the current research focuses on demonstration of the concept and development of the methods. This paper concerns the application of TRP to improving detection performance of multidimensional signals from the statistical signal processing perspective. Two commonly used time-reversal (TR) methods, the iterative time-reversal (ITR) and the decomposition of the time-reversal operator (DORT), are considered, and the detection probability given the false-alarm probability is used as the performance measure. The optimal detectors in the Neyman-Pearson sense are first derived given that the signal transfer function is known; then the corresponding generalized likelihood ratio tests (GLRTs) are developed when the transfer function is unknown. Analyses and example simulations demonstrate the following: 1) due to choosing the right wavefront at the transmitter to compensate for distortions introduced by propagation through medium, TR detectors provide performance improvements over the conventional plane wave beam-steering approach, whether the signal transfer function is known or not; 2) while they perform equally well with a known transfer function, with an unknown transfer function, the DORT detector can be superior to the ITR detector; 3) by trying to match the waveguide transfer function at both the transmitter and the receiver, performance of the TR detectors degrades more compared to the conventional approach when the transfer function is unknown.