Ergodic Secrecy Capacity of Dual-Hop Multiple-Antenna AF Relaying Systems

This paper investigates the ergodic secrecy capacity (ESC) of multiple-antenna amplify-and-forward relay systems, where one eavesdropper can wiretap the relay. To reveal the capability of the multiple- antenna relay in improving the secrecy performance, we derive new tight closed-form lower bounds of the ESC for two secure transmission schemes: artificial noise aided precoding (ANP) and eigen-beamforming (EB). We also derive the lower bound of the ESC for ANP with a large antenna array at the relay, and investigate their corresponding asymptotic performance in the high and low SNR regimes. Based on the asymptotic analysis, we optimally allocate the power to the information signal and the artificial noise. Both the analysis and simulation results indicate that, in the moderate-to-high SNR regime, ANP achieves considerable performance gain over EB, while in the low SNR regime, EB outperforms ANP with equal power allocation. As SNR grows large, the ESC of EB approaches a constant only related to the number of relay antennas. Moreover, in the high SNR regime, it is optimal to allocate around half of total power to artificial noise for ANP.