Robust amplify-and-forward relay beamforming for security with mean square error constraint

In this study, security schemes at the physical layer are proposed for an amplify-and-forward relay system in the presence of a passive eavesdropper. We focus on maximising the transmit power of the artificial noise (AN) to degrade the minimum mean square error (MMSE) level at the eavesdropper, while achieving MMSE constraint for the desired receiver. Assuming that the desired receiver and the passive eavesdropper possess perfect channel state information (CSI), AN is designed to lie in the null space of legitimate channels. However, the available CSI is impossible to be perfect in practice. Therefore the authors present a robust beamforming scheme which maximises the worst-case transmit power of the AN under the condition of imperfect CSI and recovers a large fraction of the performance in the perfect CSI case. A classical alternating optimisation algorithm is proposed to obtain the relay beamforming weights, and simulation results show the benefit of proposed schemes.