Optimization of pre-equalized time reversal security transmission systems assisted with artificial noise

Time reversal (TR) transmission technology can focus the power of a signal in both time and space domains and reduce signal energy leakage to unintended receivers, making it suitable for physical layer security systems. By adding a pre-equalizer to the transmitter and optimizing it, the performance of multi-antenna TR transmission system can be improved obviously with an acceptable optimization complexity. In this paper, the pre-equalizer and artificial noise (AN) are jointly optimized to improve the security performance of pre-equalized TR (ETR) systems when eavesdropping channel state information (ECSI) is unknown or known. When ECSI is unknown, null-space AN is adopted, and the pre-equalizer is optimized to minimize the signal power under the constraint of the minimum signal-to-interference-plus-noise ratio (SINR) of the legitimate receiver, so the AN power and the interference with the eavesdropper are maximized. The optimization problem is transformed into the problem of finding the maximum generalized eigenvalue of a matrix pencil. When ECSI is known, under the minimum SINR constraint of the legitimate receiver, the pre-equalizer and AN’s covariance matrix are jointly optimized to minimize the SINR of the eavesdropper. The optimization problem is non-convex and is transformed into a convex problem, which can be solved using the CVX toolbox. The optimization complexity is independent of the number of transmit antennas. Simulation results demonstrate that compared with TR systems, by optimizing the pre-equalizer, the security performance of ETR multi-antenna systems can be significantly improved, and the optimization complexity is acceptable.