Ergodic Achievable Secrecy Rate of Multiple-Antenna Relay Systems With Cooperative Jamming

This paper investigates the ergodic achievable secrecy rate (EASR) 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 expressions of the EASR for three secure transmission schemes: artificial noise aided precoding (ANP), destination based jamming (DBJ) and eigen-beamforming (EB). We also derive the lower bounds of the EASR for ANP and DBJ with a large antenna array at the relay, and investigate their corresponding asymptotic performance in the high SNR and low SNR regimes to show valuable intrinsic insights as well. 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 DBJ and EB, while in the low SNR regime, EB outperforms the other two schemes with equal power allocation. As SNR grows large, the EASR of EB approaches a constant independent of the first hop channel. Moreover, in the high SNR regime, it is optimal to allocate around half of total power to artificial noise for ANP and most of the power to artificial noise for DBJ.