Robust Transmission Design for RIS-assisted Secure Multiuser Communication Systems in the Presence of Hardware Impairments

This paper investigates reconfigurable intelligent surface (RIS)-assisted secure multiuser communication systems subject to hardware impairments (HIs). We jointly optimize the beamforming vectors at the base station (BS) and the phase shifts of the reflecting elements at the RIS so as to maximize the weighted minimum secrecy rate (WMSR), subject to both transmission power constraints at the BS and unit-modulus constraints at the RIS. To address the formulated optimization problem, we first decouple it into two tractable subproblems and then use the block coordinate descent (BCD) method to alternately optimize the subproblems. Two different methods are proposed to solve the two obtained subproblems. The first method transforms each subproblem into a second order cone programming (SOCP) problem, which can be directly solved using CVX. The second method leverages the Minorization- Maximization (MM) algorithm. Specifically, we first derive a concave approximation function, which is a lower bound of the original objective function, and then the two subproblems are transformed into two simple surrogate problems with closedform solutions. Simulation results verify the performance gains of the proposed robust transmission method over existing nonrobust designs. In addition, the MM algorithm is shown to have much lower complexity than the SOCP-based algorithm.