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Reconfigurable intelligent surface (RIS) has the potential to significantlyenhance the network secure transmission performance by reconfiguring thewireless propagation environment. However, due to the passive nature ofeavesdroppers and the cascaded channel brought by the RIS, the eavesdroppers'channel state information is imperfectly obtained at the base station. Underthe channel uncertainty, the optimal phase-shift, power allocation, andtransmission rate design for secure transmission is currently unknown due tothe difficulty of handling the probabilistic constraint with coupled variables.To fill this gap, this paper formulates a problem of energy-efficient securetransmission design while incorporating the probabilistic constraint. Bytransforming the probabilistic constraint and decoupling the variables, thesecure energy efficiency maximization problem can be solved via alternativelyexecuting concave-convex procedure and semidefinite relaxation technique. Toscale the solution to massive antennas and reflecting elements scenario, anaccelerated first-order algorithm with low complexity is furtherproposed.Simulation results show that the proposed accelerated first-orderalgorithm achieves identical performance to the conventional method but savesat least two orders of magnitude in computation time. Moreover, the resultantRIS aided secure transmission significantly improves the energy efficiencycompared to baseline schemes of random phase-shift, fixed phase-shift, and RISignoring CSI uncertainty.

Secure Massive RIS aided Multicast with Uncertain CSI: Energy-Efficiency Maximization via Accelerated First-Order Algorithms