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The reconfigurability of fluid antenna systems (FASs) and reconfigurableintelligent surfaces (RISs) provides significant flexibility in optimizingchannel conditions by jointly adjusting the positions of fluid antennas and thephase shifts of RISs. However, it is challenging to acquire the instantaneouschannel state information (CSI) for both fluid antennas and RISs, whilefrequent adjustment of antenna positions and phase shifts will significantlyincrease the system complexity. To tackle this issue, this paper investigatesthe two-timescale design for FAS-RIS multi-user systems with linear precoding,where only the linear precoder design requires instantaneous CSI of theend-to-end channel, while the FAS and RIS optimization relies on statisticalCSI. The main challenge comes from the complex structure of channel and inverseoperations in linear precoding, such as regularized zero-forcing (RZF) andzero-forcing (ZF). Leveraging on random matrix theory (RMT), we firstinvestigate the fundamental limits of FAS-RIS systems with RZF/ZF precoding byderiving the ergodic sum rate (ESR). This result is utilized to determine theminimum number of activated antennas to achieve a given ESR. Based on theevaluation result, we propose an algorithm to jointly optimize the antennaselection, regularization factor of RZF, and phase shifts at the RIS. Numericalresults validate the accuracy of performance evaluation and demonstrate thatthe performance gain brought by joint FAS and RIS design is more pronouncedwith a larger number of users.

Fluid Antenna Meets RIS: Random Matrix Analysis and Two-Timescale Design for Multi-User Communications