Asymptotic Max-Min SINR Analysis of Reconfigurable Intelligent Surface Assisted MISO Systems (1903.08127v3)

Abstract: This work focuses on the downlink of a single-cell multi-user system in which a base station (BS) equipped with $M$ antennas communicates with $K$ single-antenna users through a reconfigurable intelligent surface (RIS) installed in the line-of-sight (LoS) of the BS. RIS is envisioned to offer unprecedented spectral efficiency gains by utilizing $N$ passive reflecting elements that induce phase shifts on the impinging electromagnetic waves to smartly reconfigure the signal propagation environment. We study the minimum signal-to-interference-plus-noise ratio (SINR) achieved by the optimal linear precoder (OLP), that maximizes the minimum SINR subject to a given power constraint for any given RIS phase matrix, for the cases where the LoS channel matrix between the BS and the RIS is of rank-one and of full-rank. In the former scenario, the minimum SINR achieved by the RIS-assisted link is bounded by a quantity that goes to zero with $K$. For the high-rank scenario, we develop accurate deterministic approximations for the parameters of the asymptotically OLP, which are then utilized to optimize the RIS phase matrix. Simulation results show that RISs can outperform half-duplex relays with a small number of passive reflecting elements while large RISs are needed to outperform full-duplex relays.

• The paper establishes a signal model for RIS-assisted MISO systems and derives closed-form minimum SINR expressions in rank-one channels, revealing limits in serving multiple users.
• The paper employs random matrix theory to develop deterministic approximations for precoder parameters in full-rank channels, reducing reliance on instantaneous channel state information.
• The paper formulates an optimization framework using a projected gradient ascent algorithm to design the RIS phase matrix, showing that larger RIS arrays can outperform traditional relay systems.

Analyzing Max-Min SINR in RIS-Assisted MISO Systems

The paper explores the performance analysis of Reconfigurable Intelligent Surfaces (RIS) in Multi-user Multiple Input Single Output (MISO) systems under the max-min Signal-to-Interference-plus-Noise Ratio (SINR) criterion. Specifically, this paper evaluates the minimum SINR achieved by an optimal linear precoder (OLP) under two scenarios: a rank-one line-of-sight (LoS) channel and a full-rank channel matrix between the base station (BS) and the RIS. Through this analysis, the authors aim to highlight the efficacy of RIS in enhancing wireless communication capabilities while maintaining low energy consumption.

Key Contributions

1. Signal Model and System Constraints: The paper establishes a signal model to describe the RIS-assisted downlink MISO system. It introduces a BS with multiple antennas and an RIS composed of passive elements to aid communication with single-antenna users.
2. Rank-One Channel Scenario: For a rank-one channel setting, the paper presents a closed-form solution for the minimum SINR under OLP. The results indicate that with an increase in the number of users (K), the system's ability to maintain optimal SINR diminishes, reaching a bound that approaches zero. This suggests that an RIS with a rank-one BS-to-RIS channel may efficiently serve only one user at a time.
3. Full-Rank Channel Analysis: The paper proceeds to analyze scenarios with full-rank LoS channels using tools from random matrix theory (RMT). Deterministic approximations for the precoder parameters are developed, which rely on large-scale channel statistics rather than instantaneous channel state information (CSI). This approach offers significant computational advantages by reducing dependency on instantaneous CSI.
4. Optimization Framework: Utilizing the deterministic approximations, the paper formulates an optimization problem to design the RIS phase matrix that maximizes the minimum user SINR. A projected gradient ascent algorithm is proposed to solve this non-convex problem.
5. Performance Benchmarks: Numerical simulations compare RIS performance against half-duplex (HD) and full-duplex (FD) amplify-and-forward (AF) relays. The results suggest that while a small RIS may outperform HD relays, significantly larger RIS configurations are necessary to match FD relay performance levels.

Implications and Future Work

The research posits RIS as a promising technology for enhancing the spectral efficiency of wireless networks with energy-efficient designs. The insights gained suggest that RIS could serve as a viable alternative to traditional relays, particularly in scenarios with favorable conditions, such as smaller cell sizes or environments where deploying vast numbers of passive elements is feasible.

However, practical deployment of RIS requires further investigation, especially concerning channel estimation and synchronization challenges. Future work may focus on advancing estimation protocols which maintain the passive nature of RIS, and the handling of dynamic channel conditions without excessive latency. Moreover, extending the analysis to scenarios with multiple RISs could provide broader insights into maximizing network performance.

In conclusion, this paper adds substantial value to the field by presenting an in-depth analysis of RIS-assisted architectures and paving the way for future explorations into efficient wireless communication systems.