Mixed-Timescale Channel Estimation and Beamforming for STAR-RIS Assisted Communication

Mixed-Timescale Channel Estimation and Beamforming for STAR-RIS Assisted CommunicationEstimating the instantaneous high-dimensional channel state information (CSI) associated with STAR-RIS is generally impractical due to the large number of STAR-RIS elements. Estimating real-time low-dimensional equivalent channels, represented as $/bar{/bm h}{k}^H/triangleq{/bm h}^H{r,k}{/bm /Theta}{/bm F}k{/bm G}+{/bm h}^H{d,k}$, offers a more practical approach. Moreover, frequently switching the states of STAR-RIS elements would result in prohibitively high hardware costs.To address these challenges, we introduce a novel mixed-timescale scheme. This scheme operates across three distinct timescales:* Long-Timescale: The element mode selection matrix ${/bm F}$ is updated based on the large-scale fading information exchanged between the base station (BS) and the users. This infrequent update leverages the slow-varying nature of large-scale fading. * Medium-Timescale: The passive beamforming matrix ${/bm /Theta}$ is optimized by utilizing the STAR-RIS-related CSI. This optimization occurs at a moderate timescale, striking a balance between accuracy and overhead.* Short-Timescale: At each time slot, the real-time low-dimensional equivalent channels $/bar{/bm h}_{k}$ are estimated, and the BS beamforming matrix ${/bm W}$ is optimized accordingly. This ensures that the beamforming adapts to the fast-fading channel conditions.By decoupling the optimization across these three timescales, our proposed scheme effectively reduces the complexity of channel estimation and beamforming in STAR-RIS-assisted communication systems, paving the way for efficient and reliable future wireless communication technologies.