🔢 mathematics

Maximizing Connectivity of Uplink RIS-Assisted UAV Networks

This paper proposes an efficient iterative approach that jointly optimizes UAV positioning, RIS partitioning, and link selection to maximize the Fiedler value of uplink RIS-assisted UAV networks while satisfying SINR constraints.

Original authors: Mohammed Saif, Shahrokh Valaee

Published 2026-06-11

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Mohammed Saif, Shahrokh Valaee

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 busy city where a group of delivery drones (UAVs) are trying to receive packages from people on the ground (User Equipment). The problem is that tall buildings and bad weather sometimes block the direct path between the people and the drones, causing dropped connections.

To fix this, the researchers in this paper propose using a "smart mirror" on the side of a building called a Reconfigurable Intelligent Surface (RIS). This mirror can catch signals from the ground and bounce them up to the drones. However, just having one mirror isn't enough; you need to figure out exactly where to fly the drones, how to aim the mirror, and how to split the mirror's surface to serve multiple drones at once.

Here is a breakdown of their solution using simple analogies:

1. The Goal: Keeping the Team Connected

The researchers want to maximize network connectivity. Think of the drones and people as a team of hikers trying to stay in radio contact.

The Metric: They use a mathematical concept called the Fiedler value. Imagine this as a "team cohesion score." If the score is high, the team is tightly knit and everyone can talk to everyone. If the score is zero, the team is split into isolated groups, and communication breaks down.
The Challenge: Drones can run out of battery or crash (fail). The goal is to arrange the system so that even if one drone fails, the rest of the team stays connected.

2. The Three-Part Puzzle

The researchers realized that to get the highest "team cohesion score," they need to solve three things at the same time. They broke this massive, difficult puzzle into three smaller steps that they solve over and over until they get the best result:

A. Choosing the Best Paths (Link Selection)

Imagine the smart mirror is a busy intersection. You need to decide which person on the ground should send a signal to which drone.

The Strategy: Instead of guessing, they use a "perturbation method." Think of it like testing a few different traffic routes to see which one reduces congestion the most. They look at the current map of connections and pick the new path that would boost the "team cohesion score" the most.

B. Splitting the Mirror (RIS Partitioning)

This is the most creative part. Usually, a mirror reflects a signal to just one place. But this paper suggests virtual partitioning.

The Analogy: Imagine the mirror is a large pizza. Instead of giving the whole pizza to one hungry person, you slice it up.
- Slice A is angled to bounce a signal to Drone 1.
- Slice B is angled to bounce a signal to Drone 2.
The Optimization: The researchers figured out the perfect mathematical way to cut the pizza (allocate the mirror's elements) so that every drone gets enough signal strength to stay connected, without the slices getting too small to be useful. They derived a specific formula to calculate exactly how big each slice should be.

C. Flying the Drones to the Right Spot (UAV Positioning)

Even with a perfect mirror, if the drones are flying in the wrong place, the signal will be weak.

The Strategy: They treat the sky like a giant 3D grid of potential parking spots. They use a sophisticated math tool (called Semi-Definite Programming) to find the best "parking spots" for the drones.
The Result: This ensures the drones are positioned where they can catch the strongest signals from the mirror slices, maximizing the overall network strength.

3. What the Simulations Showed

The researchers tested their idea in a computer simulation that mimicked a real city environment.

More Mirror = Better Connection: They found that having a mirror with more "tiles" (elements) significantly improved the connection score.
Smart Flying vs. Random Flying: Their method of carefully placing the drones and splitting the mirror worked much better than just randomly flying drones or using the mirror to serve only one drone at a time.
Handling Mistakes: They also tested what happens if the system doesn't know the exact location of the drones perfectly (imperfect data). They found that their system is quite robust; it keeps working well even if the data isn't 100% perfect, only starting to struggle if the errors become very large.

Summary

In short, this paper presents a recipe for making drone networks more reliable. Instead of just flying drones randomly or using a mirror for one person at a time, they propose a system that:

Slices the smart mirror to serve multiple drones simultaneously.
Calculates the perfect flight path for the drones.
Iterates through these steps to ensure the entire network stays connected, even if some drones fail.

The result is a stronger, more resilient network where the "team" stays together no matter the obstacles.

Technical Summary: Maximizing Connectivity of Uplink RIS-Assisted UAV Networks

Problem Statement
This paper addresses the challenge of maximizing network connectivity in uplink Reconfigurable Intelligent Surface (RIS)-assisted Unmanned Aerial Vehicle (UAV) networks. While UAVs offer flexible deployment to establish Line-of-Sight (LoS) links and extend coverage, they are prone to failure due to energy constraints. The authors aim to enhance network resilience and connectivity by jointly optimizing three critical variables:

UAV Positioning: Determining the optimal 3D locations for UAVs.
RIS Partitioning: Dividing a single RIS into multiple virtual sections to serve different UAVs simultaneously.
Link Selection: Choosing which User Equipment (UE)-RIS-UAV links to establish.

The objective is to maximize the network's algebraic connectivity, quantified by the Fiedler value (the second smallest eigenvalue of the graph Laplacian matrix), subject to Signal-to-Interference plus Noise Ratio (SINR) constraints for individual UAVs and RIS element allocation limits. The problem is identified as a computationally expensive combinatorial optimization challenge.

Methodology
To solve the non-convex, combinatorial optimization problem, the authors propose an iterative optimization framework that decomposes the problem into three sub-problems, solved sequentially until convergence:

RIS-Aided Link Selection (Perturbation Method):
Instead of repeatedly computing the algebraic connectivity, the authors propose a low-complexity heuristic based on the Fiedler vector of the original network graph. The method iteratively selects UE-RIS-UAV links that yield the largest weighted increase in connectivity, defined by the product of the UAV's reliability and the squared difference of the Fiedler vector entries for the connected nodes.
RIS Partitioning Optimization:
For fixed UAV positions and link selections, the authors derive a closed-form solution for the RIS partitioning coefficients ( $\alpha$ ). The approach allocates RIS elements to maximize the sum SINR of the new links while satisfying minimum SINR thresholds based on UAV reliability. Specifically, the most reliable UAV is assigned the remaining RIS elements after the other UAVs receive the minimum required allocation to meet their thresholds.
UAV Positioning Optimization:
Given the link selection and RIS partitioning, the UAV positioning problem is reformulated. By discretizing the search space into a grid, the problem is transformed into selecting optimal grid points for the UAVs. This is further relaxed from a binary combinatorial problem to a continuous convex problem, which is then solved as a low-complexity Semi-Definite Programming (SDP) problem using standard CVX solvers.

Key Contributions

Joint Optimization Framework: The paper formulates the network connectivity maximization problem using the Fiedler value, incorporating RIS element allocation and SINR constraints influenced by UAV reliability.
Iterative Algorithm: A novel iterative solution is developed that combines a connectivity-aware perturbation method for link selection, a closed-form solution for RIS partitioning, and an SDP-based approach for UAV positioning.
RIS Virtual Partitioning for Connectivity: Unlike prior works that may use RIS for single links or physical layer security, this work leverages RIS virtual partitioning to establish multiple simultaneous communication links, thereby enhancing spatial efficiency and network connectivity.
Efficient Solvability: The transformation of the UAV positioning subproblem into an SDP allows for efficient solving using off-the-shelf tools, avoiding the intractability of the original combinatorial formulation.

Simulation Results
The proposed scheme was evaluated against three benchmarks: a single-link RIS setup (utilizing the whole RIS for one link), a scheme without RIS (inspired by existing UAV positioning literature), and the proposed scheme with random UAV locations.

Connectivity Gains: The proposed joint optimization consistently outperformed benchmark schemes, particularly in well-connected networks, by enabling the RIS to establish multiple links and optimizing UAV positions to improve link quality.
Impact of RIS Elements: Increasing the number of RIS elements ( $N$ ) was shown to improve network connectivity by boosting the quality of newly established links.
Sparse vs. Dense Networks: In sparse network scenarios (high SINR thresholds), adding more UAVs did not necessarily increase connectivity due to link failures, whereas the proposed RIS-assisted approach maintained robustness.
CSI Imperfections: Simulations regarding imperfect Channel State Information (CSI) indicated that while performance degrades as CSI error variance increases, the network connectivity remains relatively robust to moderate imperfections.

Significance
The paper claims that the proposed iterative solution demonstrates significant potential gains in network connectivity compared to existing literature. By integrating RIS virtual partitioning with UAV positioning, the work offers a practical approach to mitigating UAV failures and extending service coverage without requiring additional hardware deployments. The authors suggest that future work could explore scheduling multiple transmitting UEs to a single RIS, moving beyond the current constraint of assigning one UE per RIS.