Abstract
The reconfigurability of fluid antenna systems (FASs) and reconfigurable intelligent surfaces (RISs) provides significant flexibility in optimizing channel conditions by jointly adjusting the positions of fluid antennas and the phase shifts of RISs. However, it is challenging to acquire the instantaneous channel state information (CSI) for both fluid antennas and RISs, while frequent adjustment of antenna positions and phase shifts will significantly increase the system complexity. To tackle this issue, this paper investigates the two-timescale design for FAS-RIS multi-user systems with linear precoding, where only the linear precoder design requires instantaneous CSI of the end-to-end channel, while the FAS and RIS optimization relies on statistical CSI. Leveraging on random matrix theory (RMT), we first investigate the fundamental limits of FAS-RIS systems with RZF/ZF precoding by deriving the ergodic sum rate (ESR). This result is utilized to determine the minimum number of activated antennas to achieve a given ESR. Based on the evaluation result, we propose an algorithm to jointly optimize the antenna selection, regularization factor of RZF, and phase shifts at the RIS. Numerical results validate the accuracy of performance evaluation and demonstrate that the performance gain brought by joint FAS and RIS design is more pronounced with a larger number of users.
Introduction
As we look toward 6G, two technologies stand out: Fluid Antenna Systems (FAS), which use "position-flexible" antennas to find the best local signal spots, and Reconfigurable Intelligent Surfaces (RIS), which use smart surfaces to steer signals in the environment. The "holy grail" is to optimize both simultaneously. However, doing so is a nightmare for two reasons:
- CSI Overhead: To pick the best antenna "port" (position) out of hundreds of possibilities, you traditionally need to measure the channel at every single port. This is incredibly slow and power-hungry.
- Complexity: Jointly picking discrete antenna positions and continuous RIS phase shifts is a "non-convex" mathematical problem, meaning it's very hard to find the absolute best solution efficiently.
This paper tackles these by proposing a two-timescale design: the system optimizes the antenna positions and RIS settings slowly (based on long-term statistics), while only the signal precoding (how the data is actually sent) adapts quickly to instantaneous changes.
Methodology
The authors employ several sophisticated mathematical tools to make this work:
- Random Matrix Theory (RMT): Instead of running millions of simulations to see how the system performs, they use RMT to derive "deterministic equivalents"—math formulas that accurately predict the Ergodic Sum Rate (ESR) based only on statistical parameters like channel correlation and path loss. The complexity of these derivations is captured in the definitions of various auxiliary functions.
- Two-Timescale Framework:
- Slow Scale: Port selection and RIS phase shifts are updated based on statistical CSI.
- Fast Scale: Linear precoders (Regularized Zero-Forcing or RZF) are updated based on the instantaneous CSI of the selected ports.
- Optimization Algorithms: To solve the joint optimization problem, they use the Frank-Wolfe (FW) method to handle the discrete nature of picking antenna ports and Alternating Optimization (AO) to fine-tune the RIS phase shifts and the RZF regularization factor. The port selection process is specifically handled by a dedicated algorithm.
Performance is evaluated using Monte-Carlo realizations of correlated Rayleigh fading channels, employing standard 3GPP-like path-loss models and spatial correlation models for both the fluid antenna array and the RIS elements.
Key Insights and Theoretical Contributions
- The Synergy Effect: The paper shows that FAS and RIS are better together. An RIS can "shape" the environment to be more favorable, which in turn makes the fluid antenna's job of finding a high-signal "port" much easier.
- Port Efficiency: A key finding is that an FAS-RIS system requires significantly fewer selected ports to achieve the same data rate as a standalone FAS system, directly translating to lower hardware complexity.
- The "Independence" of Regularization: For homogeneous channels, the authors proved that the optimal RZF regularization factor is simply $K\sigma^2/M$ (users $\times$ noise / antennas), regardless of the specific port selection or RIS configuration.
- Scaling with Users: The performance gains from jointly designing FAS and RIS become much more pronounced as the number of users in the system increases, making this a strong candidate for dense 6G networks.
Performance Evaluation
- Accuracy: The RMT-derived formulas for the sum rate were shown to be highly accurate, matching time-consuming Monte-Carlo simulations almost perfectly, even for relatively small system sizes.
- Gain over Uniformity: The proposed optimization algorithm significantly outperforms "uniform selection" (just picking ports at equal intervals).
- Precoding Superiority: RZF and Zero-Forcing (ZF) precoding were shown to vastly outperform simpler methods like Maximal Ratio Transmission (MRT) in high-interference scenarios.
Conclusion and Future Work
While the paper solves the problem of needing CSI for all ports, it still assumes the system can perfectly measure the instantaneous CSI for the selected ports. Real-world systems deal with "imperfect CSI," which the authors suggest as a vital next step. Additionally, future work could look at "mutual coupling" (electromagnetic interference between close antenna ports) and hardware impairments like low-resolution RIS phase shifts.