Beamforming Design for Multi-Mode STAR-RIS Empowered Multi-Cell Systems

We investigate multi-mode simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) assisted multi-cell systems, consisting of multiple base stations (BSs), their own users (UEs), and one STAR-RIS which can operate in energy splitting (ES), function switching (FS), and time switching (TS) modes. Under these different modes, we formulate three optimization problems to maximize the sum rate performance. To solve these challenging problems, we first transform the original sum-rate maximization problems into more tractable weighted mean-square-error (MSE) minimization problems. Then, by exploiting the properties of different modes, auxiliary variables are introduced for decoupling variables. We propose a double-loop algorithm based on the penalty dual decomposition (PDD) framework to solve their corresponding augmented Lagrangian problems, which optimizes the primal/dual variables in the inner/outer loops. The convergence and complexity of the proposed algorithms are analyzed. Our simulation results demonstrate that the ES mode outperforms the FS mode due to the continuous power allocation, and the TS mode achieves the highest sum-rate performance due to its decoupled phase shifts and degrees of freedom in the time domain at the cost of more convergence iterations, higher implementation complexity, and increased latency. Moreover, all STAR-RIS assisted schemes outperform the conventional RIS assisted scheme.