The performance of time reversal passive detection over underwater multi-path channel

Present a mathematical study of time reversal passive performance over multi-path channel as signal propagation underwater. The study starts with statistical theory due to signal detection, followed by basic dualism hypothesis and the performance of underwater multi-path propagation through passive time reversal is derived. Under a constant false-alarm probability, the relations between detect probability and different signal-to-noise ratio as well as several multi-path amount are deduced in details. The conclusions include two points: performance becomes better as signal-to-noise ratio increasing that can be expected; meanwhile multi-path amount plays the same role as signal-to-noise ratio, the more multi-path amount the better performance. Time-frequency signal detection method based on passive time reversal is simulated simultaneously. The result shows that time reversal is able to self-adaptively modify signal distortion account for multi-path channel, especially for low signal-to-noise ratio such as that bellows zero.