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RIS-assisted Cell-Free MIMO with Dynamic Arrivals and Departures of Users: A Novel Network Stability Approach

This paper proposes a low-complexity optimization framework for RIS phase shifts in cell-free MIMO systems with dynamic user arrivals and departures, providing theoretical proof and numerical validation that the approach ensures network stability and covers over 78.5% of the stability region.

Original authors: Charbel Bou Chaaya, Mohamad Assaad, Tijani Chahed

Published 2026-05-26

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Charbel Bou Chaaya, Mohamad Assaad, Tijani Chahed

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a massive, high-tech concert hall where hundreds of musicians (the Access Points) are trying to play a symphony for a crowd of listeners (the Users). In a traditional setup, the musicians might struggle because the sound bounces off walls, gets blocked by pillars, or gets drowned out by noise.

Now, imagine installing a giant, magical wall of mirrors (the RIS or Reconfigurable Intelligent Surface) inside the hall. This wall isn't just a mirror; it's a smart wall. It can instantly change the angle of every single tiny mirror on its surface to bounce the sound waves perfectly toward the listeners, ensuring everyone hears the music clearly, even if they are sitting in a "dead zone."

This paper is about how to control that magical wall when the audience is constantly changing.

The Problem: A Chaotic Crowd

Most previous studies looked at this setup assuming the audience was fixed—like a seated theater where everyone stays in their seat for the whole show. But in real life (like a busy shopping mall or a stadium), people arrive, listen to a song or download a file, and then leave. New people are constantly walking in.

If the "smart wall" doesn't adjust its mirrors quickly enough to handle this flowing crowd, the system gets overwhelmed. The "files" (or songs) pile up, the network gets clogged, and eventually, the system crashes. The goal of this paper is to keep the network stable, meaning everyone gets their turn to listen and leaves without waiting forever.

The Solution: A Smart Traffic Controller

The authors propose a new way to tell the smart wall how to angle its mirrors. Instead of just trying to make the signal as loud as possible for one person at a time (which is like shouting at one person while ignoring the rest), their method looks at the whole crowd.

They created a mathematical "recipe" (an optimization framework) that asks: "Given how many people are currently waiting at each spot, how should we tilt the mirrors to clear the queue the fastest?"

The "Magic" Trick: A Simple Shortcut

Calculating the perfect mirror angles for a crowd of thousands is incredibly hard, like trying to solve a million-piece puzzle at once. The authors found a clever shortcut.

They proved that you don't need the perfect solution to keep the network stable. You just need a "good enough" solution. They developed a low-complexity algorithm (a fast, simple method) that finds a solution guaranteed to be at least 78.5% as good as the perfect one.

Think of it like a GPS. The "perfect" route might save you 2 minutes, but the "good enough" route gets you there just as fast for all practical purposes, and it calculates the route instantly without draining your battery.

The Proof: It Actually Works

The authors didn't just guess; they used rigorous math (involving "fluid limits" and "Lyapunov functions"—which are like proving a dam won't overflow by checking the water pressure) to show that their method works.

They proved that as long as the crowd isn't arriving faster than the network could possibly handle (even with the best possible mirror angles), their method will keep the system stable. If the crowd arrives at a manageable speed, their system ensures everyone gets served in a finite time.

The Results: Real-World Simulation

To test this, they ran computer simulations:

The "Stable" vs. "Chaotic" Test: When they used their smart method, the number of people waiting in line stayed low and manageable. When they used a "random" method (just guessing mirror angles), the line grew infinitely long, and the system failed.
The "Capacity" Test: They showed that their method can handle a much larger crowd than older methods (like taking turns one by one) before the system breaks down.

In a Nutshell

This paper introduces a new way to manage a future wireless network where users come and go constantly. By using a smart, adaptable "mirror wall" and a simple, fast algorithm to control it, the authors guarantee that the network won't crash under pressure. They proved mathematically that their simple method keeps the system running smoothly for more than 78% of all possible crowd scenarios, ensuring that no one is left waiting forever.

Technical Summary: RIS-assisted Cell-Free MIMO with Dynamic Arrivals and Departures of Users

Problem Statement
Reconfigurable Intelligent Surfaces (RIS) have emerged as a promising technology for next-generation wireless communications by passively altering propagation environments to enhance signal quality. While existing literature extensively investigates the physical layer benefits of RIS in terms of throughput and coverage, these studies predominantly assume a static set of users. In realistic scenarios, users dynamically arrive, exchange data bursts, and depart once served. This dynamic traffic introduces a critical challenge: ensuring network stability. Network stability is defined as the ability of the system to serve all arriving users (files) within a finite time. The core problem addressed in this paper is determining the optimal RIS phase shift configuration that guarantees network stability for dynamic user populations in a Cell-Free Multiple-Input Multiple-Output (MIMO) setting, where distributed Access Points (APs) cooperate to serve users.

Methodology
The authors propose a cross-layer approach that integrates physical layer channel modeling with flow-level network dynamics.

System Model: The study considers the uplink of a RIS-assisted Cell-Free MIMO system with $N$ single-antenna APs and $K$ single-antenna users. The RIS comprises $M$ reflecting elements. The channel model assumes block fading with spatially correlated ergodic processes. The direct links between users and APs are considered weak compared to the RIS-reflected paths.
Traffic Model: Users arrive at specific locations according to a Poisson process with rate $\lambda_k$ . Each user carries a "flow" (a file) with an exponentially distributed size. The system operates on two time scales: fast physical layer slots and slower flow-level time steps.
Optimization Framework: To ensure stability, the authors formulate an optimization problem (P1) to maximize a utility function based on the current traffic volume ( $X_k$ $X_{k}$ ) and the Effective Signal-to-Interference-and-Noise Ratio (ESINR) of the users. The objective is to maximize $\sum X_k \log(\text{ESINR}_k)$ $\sum X_{k} lo g (ESINR_{k})$ .
- The problem is transformed into maximizing a quadratic form $\phi^H R \phi$ subject to unit modulus constraints on the phase shifts, which is an NP-hard problem.
- A low-complexity sub-optimal solution is derived using Semi-Definite Relaxation (SDR) followed by Gaussian randomization. This approach approximates the optimal solution with a guaranteed accuracy factor.
Stability Analysis: The authors employ fluid limit analysis and Lyapunov drift techniques to prove stability. They demonstrate that if the optimization problem is solved (even with the sub-optimal approximation), the resulting rate allocation ensures that the fluid limit of the user queue lengths reaches zero in finite time, provided the arrival rates lie within a specific fraction of the maximum stability region.

Key Contributions

Novel Scenario: This work is the first to consider RIS-assisted wireless environments with dynamic user arrivals and departures, moving beyond static user assumptions prevalent in prior RIS research.
Optimization Framework: The paper proposes a specific phase shift optimization framework that depends on current flow intensity and user ESINR, rather than just maximizing instantaneous throughput.
Theoretical Guarantees: The authors rigorously prove that their low-complexity solution stabilizes a guaranteed fraction of the maximum stability region. Specifically, they prove that the solution achieves at least $\pi/4$ (approximately 78.5%) of the optimal stability region.
Analytical Derivation: The paper derives a closed-form expression for the achievable uplink rate using the "use-and-then-forget" bounding technique, leading to a tractable ESINR expression that facilitates the stability analysis.

Results
Numerical simulations validate the theoretical claims:

Stability Region: In a scenario with two locations, the stability region achieved by the proposed RIS configuration significantly outperforms a Time Division Multiple Access (TDMA) baseline where RIS phases are optimized only for the active user's Signal-to-Noise Ratio (SNR).
Queue Stability: In a scenario with 400 locations, the proposed phase shift design keeps the number of active flows bounded over time. In contrast, using random phase shifts causes the number of flows to grow rapidly, indicating network instability.
Sensitivity to Arrival Rates: The stability metric (average queue length) remains low for a wider range of arrival rates when using the optimized phases compared to random phases, which diverge at lower arrival rates.

Significance and Claims
The paper claims that while maximizing physical layer throughput is a common goal, it is insufficient for dynamic networks where stability is paramount. By shifting the focus to network stability, the proposed framework ensures that the network can handle dynamic traffic loads without queue explosion. The authors emphasize that their solution provides a guaranteed fraction (higher than 78.5%) of the maximum possible stability region, offering a robust and computationally feasible method for managing RIS in dynamic Cell-Free MIMO networks. The work bridges the gap between physical layer signal processing and network layer control, addressing a critical oversight in current RIS literature regarding dynamic traffic management.