Average Sum-Rate Maximization for Coupled Phase-Shift STAR-RIS Enhanced Multi-User MISO-OFDM System

Simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) is emerging as a promising technology by achieving full-space coverage and further improving system performance. However, most existing works adopted an independent phase-shift model, which is high-cost and may be difficult to achieve in realistic wideband systems. Consequently, a coupled phase-shift STAR-RIS enhanced downlink multi-user multiple-input single-output orthogonal frequency division multiplexing system is investigated for both unicast and broadcast communications in this paper. We aim to maximize the average sum-rate (ASR) for all subcarriers by jointly optimizing the precoding matrices and the reflecting and transmitting coefficients (RTCs). Specifically, a block coordinate descent algorithm is proposed to iteratively design each block of a multiblock problem reformulated by the original one. The precoding matrices are optimized by the Lagrangian multiplier method for low computational complexity. For the RTCs, an element-based alternating optimization algorithm is proposed to optimize the coupled phase-shift and amplitude coefficients. Simulation results validate the effectiveness of the proposed algorithm by comparing the ASR with that of other benchmarks. Moreover, its performance closely approaches the upper bound under various practical user proportion scenarios on both sides of the STAR-RIS.