LAUSR

The time reversal (TR) transmission technique can harvest the signal energy from multiple paths and focus the signal power on an intended space–time point. Different from the works which analyze the average signal-to-noise-ratio (SNR), this letter derives the probability density function (PDF) and cumulative distribution function (CDF) of the SNR at the receiver in a TR communication system. Furthermore, based on the derived pdf, the ergodic capacity, outage probability, and bit error rate (BER) when binary phase-shift keying is used are also obtained. The simulation results show that the theoretical pdf and cdf of the SNR are correct, and the ergodic capacity, in theory, is consistent with the simulation result, so are the outage probability and the BER. In the TR system, the inter-symbol interference decreases as the up-sampling factor increases, and the diversity gain increases as the number of paths increases, that is, the received signal quality can be improved by reducing the spectral efficiency.