Effective secrecy-SINR analysis of time reversal-employed systems over correlated multi-path channel

Based on the capability of harvesting the energy of all paths in the multipath environment, time-reversal (TR) transmission technique offers a great potential of low-complexity energy-efficient communications for future wireless network. The TR-employed systems benefit from a significantly reduced leakage of message-bearing signal to unintended users or eavesdroppers. In this paper, we propose a term so-called average effective secrecy signal-to-interference-plus-noise ratio (SINR) which represents the secrecy performance of TR-employed systems. Furthermore, we also consider: (i) the channel correlation between transmit antennas, and (ii) the channel correlation between a legitimate user and an eavesdropper. Accordingly, we derive the average effective secrecy-SINR in a closed-form expression of TR-employed systems. The obtained expression is based on the exact power-averaged expressions of the desired signal and the inter-symbol interference (ISI) components at both the legitimate user and eavesdropper side. The analytical results confirmed by numerical simulations show that the average effective secrecy-SINR metric is preferred to the average secrecy-SINR term in the perspective of measuring secrecy performance over correlated multi-path channel.