Secrecy Rate of TAS in AF-Relay Systems With Multi-Antenna Relay and User Over Non-Identical Channel Estimation Error

This work evaluates the secrecy rate of transmit antenna selection (TAS) in the amplify and forward (AF)-relay system with multi-antenna relay and user. This paper considers that the receiver of relays, users, and an eavesdropper have non-identical channel estimation error. To assess the secrecy rate, this work derives new analytical expressions for the cumulative distribution function (CDF) and probability density function (PDF) of the received signal to noise ratio (SNR) using infinite series for maximal-ratio combining (MRC) and selection combining (SC) receivers. Using the CDF for the received SNR, we derive new exact analytical expressions for the secrecy rate with non-identical channel estimation error for four scenarios. Further, using the PDF for the received SNR, we derive the asymptotic analytical expressions for the secrecy rate and quantify the high SNR slope and the high SNR power offset for four scenarios. From the numerical results, we observe that the relay and user selection has the high SNR power offset gain compared to the non-selection. The secrecy rate of the proposed system can be improved according to legitimate receiver's parameters such as the number of receive antennas and channel correlation coefficient and can be degraded according to eavesdropper's parameters. The superiority of the secrecy rate of the MRC receiver and the SC receiver depends on the channel estimation accuracy of the MRC receiver.