Secrecy analysis of cooperative NOMA-FDR systems with imperfect CSI and colluding eavesdroppers

This paper analyzes the secrecy attributes of a full-duplex relay (FDR) non-orthogonal multiple access (NOMA) system, where the best relay is chosen from a set of numerous relays by using the partial relay selection (PRS) protocol. This best relay assists the communion from source to two NOMA users under the attendance of many colluding eavesdroppers. We obtain the expressions in closed-form of the exact secure outage probability (SOP) of each user, the approximate SOP, and the exact ergodic secrecy capacity (ESC) of the proposed system, taking into consideration the impacts of outdated channel state information (CSI) at source and imperfect CSI at colluding eavesdroppers. We also give the SOP and ESC of the NOMA-FDR system with PRS protocol for comparison with other benchmark systems such as half-duplex (HD)-NOMA, FD-orthogonal multiple access (OMA) systems with PRS protocol, and NOMA-FDR system with multiple-relay (MR) protocol. The simulation results verify the accuracy of our analysis results. Numerical results demonstrate that the SOP and ESC of the NOMA-FDR system greatly vary according to the number of relays and eavesdroppers, SI cancellation capability, channel estimation error, and the correlation coefficient of outdated channels. Most importantly, the NOMA-FDR system has better secrecy performance than all benchmark relay systems.