[Paper Review] Power Scaling Law Analysis and Phase Shift Optimization of RIS-aided Massive MIMO Systems with Statistical CSI

Kangda Zhi, Cunhua Pan+2 more|arXiv (Cornell University)|Oct 26, 2020

Advanced Wireless Communication TechnologiesEngineering30 citations

TL;DR

The paper analyzes uplink RIS-aided massive MIMO with statistical CSI under Rician fading, derives closed-form rate expressions, reveals scaling laws, and optimizes RIS phase shifts via a GA-based approach.

ABSTRACT

This paper considers an uplink reconfigurable intelligent surface (RIS)-aided massive multiple-input multiple-output (MIMO) system with statistical channel state information (CSI). The RIS is deployed to help conventional massive MIMO networks serve the users in the dead zone. We consider the Rician channel model and exploit the long-time statistical CSI to design the phase shifts of the RIS, while the maximum ratio combination (MRC) technique is applied for the active beamforming at the base station (BS) relying on the instantaneous CSI. Firstly, we reveal the power scaling laws and derive the closed-form expressions for the uplink achievable rate which holds for arbitrary numbers of base station (BS) antennas. Based on the theoretical expressions, we discuss the rate performance under some special cases and provide the average asymptotic rate when using random phase shifts. Then, we consider the sum-rate maximization and the minimum user rate maximization problems by optimizing the phase shifts at the RIS. However, these two optimization problems are challenging to solve due to the complicated data rate expression. To solve these problems, we propose a novel genetic algorithm (GA) with low complexity but can achieve considerable performance. Finally, extensive simulations are provided to validate the benefits by integrating RIS into conventional massive MIMO systems. Besides, our simulations demonstrate the feasibility of deploying large-size but low-resolution RIS in massive MIMO systems.

Motivation & Objective

• Motivate the integration of RIS to enhance coverage and throughput in massive MIMO while reducing channel estimation overhead.
• Derive closed-form uplink achievable rate expressions that hold for arbitrary numbers of BS antennas under Rician fading.
• Characterize power scaling laws and rate behavior with RIS elements and BS antennas.
• Develop a genetic-algorithm based method to maximize sum-rate and ensure fairness through minimum-user-rate optimization.
• Evaluate RIS-enabled massive MIMO gains and feasibility of large, low-resolution RIS deployments.

Proposed method

• Model the uplink RIS-aided massive MIMO system with Rician fading and long-term statistical CSI.
• Derive closed-form expressions for the uplink achievable rate using Jensen’s inequality.
• Analyze power scaling laws and asymptotic rate behavior under special cases (e.g., with RIS phase-alignment).
• Propose a GA-based optimization of RIS phase shifts to maximize sum rate and to maximize the minimum user rate, including discrete phase shifts.
• Provide extensive simulations to validate RIS gains and feasibility of large-size, low-resolution RIS.

Experimental results

Research questions

• RQ1 How does RIS-aided massive MIMO perform under statistical CSI and Rician fading in terms of uplink rate?
• RQ2 What are the power scaling laws when scaling BS antennas and RIS elements in RIS-aided massive MIMO?
• RQ3 How should RIS phase shifts be designed (continuous vs discrete) to maximize sum rate or ensure fairness under statistical CSI?
• RQ4 What is the impact of RIS design on interference and achievable gains in multi-user uplink scenarios?

Key findings

• Closed-form approximate uplink rate expressions are derived that depend on RIS phase shifts, antenna counts, powers, and Rician factors.
• Under certain scalings, the rate can grow with the number of RIS elements N and/or BS antennas M, and random RIS phases yield bounded asymptotic rates.
• Phase-aligned RIS designs can achieve favorable scaling, with specific corollaries showing power can be reduced as M or N grows while maintaining non-zero rates.
• A GA-based RIS phase-shift design effectively solves sum-rate and minimum-rate optimization problems with both continuous and discrete phase shifts.
• Simulations confirm RIS gains in RIS-aided massive MIMO and demonstrate feasibility of large-size, low-resolution RIS deployments.