Achievable secrecy rate analysis of OFDM-based multi-user untrusted relay networks with imperfect CSI

This study investigates the impact of imperfect channel state information (CSI), caused by channel estimation errors and feedback delays, on the physical-layer security performance of multi-user relay networks. More specifically, a multi-user untrusted half/full-duplex (HD/FD) uni/bi-directional wireless amplify-and-forward (AF) relay network is studied, adopting orthogonal frequency division multiplexing (OFDM). In order to minimize the information leakage, it is considered that a limited number of friendly jammers affect the untrusted relay. In this context, the achievable secrecy rate of the relay network is theoretically analyzed and optimization problems are formulated and solved for the untrusted relay's location and power allocation. Monte Carlo simulations are conducted to validate the theoretical findings, revealing that channel estimation errors cause coding gain losses for low signal-to noise ratio (SNR) while their impact becomes negligible for high SNR. Also, a large number of user-pairs achieves higher secrecy rate while FD relaying further improves the secrecy performance. Finally, bi-directional relaying provides higher achievable secrecy rate over uni-directional relaying.