Robust Energy-Efficient RIS-Aided Multi-Antenna DF Relay Cooperative MIMO

We consider a robust energy-efficient reconfigurable intelligent surface (RIS)-aided multi-antenna decode-and-forward (DF) relay cooperative multiple-input multiple-output (MIMO). Although RIS and relay share some similarities in common, they have fundamental differences and can indeed complement each other. Due to the passive characteristic of RIS, it is much challenging to obtain the perfect channel state information (CSI) and the channel estimation error (CEE) is inevitable in practice. Taking into account the imperfect CSI, we formulate the robust energy efficiency (EE) optimization problems under the bounded CEE and statistical CEE models, where the precoding matrices at the source and relay, and the passive beamforming at the RIS in two slots are jointly designed. At first, the original problems under two CEE models are transformed into deterministic forms with the help of S-procedure and Bernstein-type Inequality, respectively. Subsequently, the reformulated problems are solved by the alternating optimization (AO)-based Dinkelbach algorithm in an iterative manner. Particularly, for the passive beamforming subproblem, the semi-definite relaxation (SDR) method and penalty concave-convex procedure (PCCP) method are utilized to deal with the rank-one constraint. Numerical simulations demonstrate that the EE performance of the considered scheme obviously outperforms the benchmarks. Simulation results also show the superiorities of the robust EE optimization compared with the non-robust optimization.