Worst case SINR guarantees for secrecy using relay beamforming with imperfect CSI

In this paper, we study beamforming techniques for secrecy with worst case signal-to-interference-plus-noise ratio (SINR) guarantees in cooperative communications with imperfect channel state information (CSI). The worst case SINRs are the minimum SINR at the intended destination and the maximum SINR at the eavesdroppers. We consider a norm bounded CSI error model. With the available imperfect channel estimates, we design beamformers such that the minimum SINR receivable by the intended destination is above a certain threshold, while the maximum value of SINRs receivable at the eavesdroppers are below another lower threshold. We consider amplify-and-forward (AF) and decode-and-forward (DF) relaying schemes. The relays do the worst case transmit beamforming and injection of artificial noise (AN). We jointly optimize the beamformers and the AN for the AF and DF schemes subject to the worst case SINR constraints at the destination and the eavesdroppers. We solve the corresponding optimization problems as semi-definite programming (SDP) problems by rank relaxation and S-procedure. Numerical results show that AN injection at the relays significantly reduces the average total transmit power required to meet the worst case SINR constraints, and improves the solution feasibility of the optimization problems.