Focusing Gain Model of Time-Reversed Signals in Dense Multipath Channels

The time reversal (TR) technique consists of transmitting in the channel a signal filtered by the time-reversed channel impulse response. To assess the performance of a TR system using impulse radio ultrawideband signals, one interesting parameter is the focusing gain defined as the ratio of the maxima in the time waveforms of the received signal with and without the time-reversal operation. We propose a heuristic approach to get an approximate analytical expression for the distribution function of this gain, as a function of the channel delay spread normalized to the pulse width and assuming a dense multipath environment. Predicted results are compared to experimental values obtained in reverberating chambers.