Secrecy performance of transmit antenna selection with outdated CSI for MIMO relay systems

This paper investigates transmit antenna selection (TAS) to improve the secrecy performances in MIMO secure cooperative relay systems with an adaptive decode-and-forward (DF) relay over Nakagami-m fading channels. Due to the feedback delay of CSI used for TAS, the maximal ratio combining (MRC) receiver at the multi-antenna relay and destination suffers from the outdated channel state information (CSI). To evaluate the impacts of TAS with outdated CSI on the secrecy performance, the closed-form expressions for exact secrecy outage probability (SOP) are derived based on a channel feedback error model. Furthermore, in order to explicitly show the secrecy diversity order and the secrecy array gain, the simple asymptotic expressions for SOP are derived for both cases of perfect and outdated CSI. Analysis and simulation results show that when the CSI is outdated, the SOP performance can be improved by increasing whether the number of antennas at the source, relay, and destination, whereas the secrecy diversity order of the system is related with the number of antennas at the relay, but independent of the number of antennas at the source.