Secrecy Capacity Analysis of 4-WFRFT Based Physical Layer Security in MIMO System

In this paper, the integration of antenna selection(AS) and 4-weighted-type fractional Fourier transform (4-WFRFT) technologies into the multiple-input multiple-output (MIMO) system based channel correlation has been proposed to enhance the security performance of wireless communications, where the energy of transmitting signals is split into four portions by employing the 4-WFRFT technology. This is equivalent to introducing additional artificial noise at the eavesdropper. To characterize system performance, the channel correlation is first considered, then we propose a valid method to model the distribution of composite instantaneous signal-to-noise ratio (SNR) of eavesdropper as the tractable exponential distribution. Furthermore, we drive the close-form expressions for both the joint probability density function (PDF) of channel and the average SNR at the eavesdropper. Based on above results, we deduce the close-form expressions of average security capacity with AS and 4-WFRFT technologies. To obtain further insights, we also derive the theoretical expressions of secrecy outage probability. The analysis results show that AS and 4-WFRFT technologies exist to simultaneously increase the average security capacity and then decrease the secrecy outage probability. The numerical results illustrate that: 1) 4-WFRF technology can validly eliminate the impact of channel correlation due to introducing the artificial noise; 2) the secrecy performance of system can be improved remarkably by employing AS and 4-WFRFT technologies.