Linear Precoder Design for Physical Layer Security via Reconfigurable Intelligent Surfaces

The feasibility of provisioning physical layer security via reconfigurable intelligent surfaces (RISs) is investigated. The key idea is to constructively combine the signals received through the direct and reflected channels at a legitimate user, while degrading the signal quality at a passive eavesdropper by destructive combining of these two signals enabled via a joint effect of intelligent phase control at a large number of passive reflective elements of the RIS and a corresponding precoder design of the base-station. To this end, we advocate adoption of linear precoders, which are designed based on cascaded channels, with sole optimization of phase-shifts at the RIS to maximize the achievable secrecy rate in the presence of a passive eavesdropper. The underlying optimization problem is solved by developing an alternating algorithm to iteratively update the phase-shifts of the RIS. Specifically, the optimal phase-shift design problem can be modeled as a semidefinite program by using relaxation techniques. Thereby, the optimal phase-shift values can be closely approximated by using Gaussian randomization techniques. Our numerical results show that the proposed technique serves as a practical-viable low-complexity alternative to joint optimization of non-linear precoder and RIS phase-shifts.