[Paper Review] Downlink Interference Management in Dense Interference-Aware Drone Small Cells Networks Using Mean-Field Game Theory

Zihe Zhang, Lixin Li+5 more|arXiv (Cornell University)|Jun 7, 2018

UAV Applications and Optimization7 references3 citations

TL;DR

This paper proposes a mean-field game (MFG)-based distributed altitude control scheme for dense drone small cells (DSCs) to mitigate downlink interference and improve signal-to-interference-plus-noise ratio (SINR). By modeling each DSC's altitude adjustment as a strategic decision in a large-population game, the framework derives coupled Hamilton-Jacobi-Bellman and Fokker-Planck-Kolmogorov equations, solved via a finite difference method with an upwind scheme, achieving superior SINR performance over uniform and static control policies.

ABSTRACT

The use of drone small cells (DSCs) has recently drawn significant attentions as one key enabler for providing air-to-ground communication services in various situations. This paper investigates the co-channel deployment of dense DSCs, which are mounted on captive unmanned aerial vehicles (UAVs). As the altitude of a DSC has a huge impact on the performance of downlink, the downlink interference control problem is mapped to an altitude control problem in this paper. All DSCs adjust their altitude to improve the available signal-to-interference-plus-noise ratio (SINR). The control problem is modeled as a mean-field game (MFG), where the cost function is designed to combine the available SINR with the cost of altitude controling. The interference introduced from a big amount of DSCs is derived through a mean-field approximation approach. Within the proposed MFG framework, the related Hamilton-Jacobi-Bellman and Fokker-Planck-Kolmogorov equations are deduced to describe and explain the control policy. The optimal altitude control policy is obtained by solving the partial differential equations with a proposed finite difference algorithm based on the upwind scheme. The simulations illustrate the optimal power controls and corresponding mean field distribution of DSCs. The numerical results also validate that the proposed control policy achieves better SINR performance of DSCs compared to the uniform control scheme.

Motivation & Objective

• To address the challenge of co-channel downlink interference in ultra-dense, co-located drone small cells (DSCs) operating in urban environments.
• To model the distributed altitude control problem of DSCs as a mean-field game (MFG), where each DSC optimizes its altitude to maximize SINR while minimizing energy cost.
• To derive and solve the forward-backward equations (HJB and FPK) that characterize the optimal control policy under mean-field approximation.
• To validate the proposed algorithm's performance through simulations, comparing it against static and uniform velocity control benchmarks.
• To enable practical deployment by ensuring the algorithm can be executed offline and distributively, reducing central coordination overhead.

Proposed method

• Models the DSC network as a mean-field game (MFG), where each DSC acts as a player optimizing its altitude to improve downlink SINR.
• Uses a mean-field approximation (MFA) to represent the aggregate interference from a large number of DSCs as a continuous distribution.
• Derives the coupled Hamilton-Jacobi-Bellman (HJB) and Fokker-Planck-Kolmogorov (FPK) equations to characterize the optimal control policy and mean field evolution.
• Applies a finite difference method based on the upwind scheme to numerically solve the HJB and FPK partial differential equations.
• Designs a cost function that balances SINR improvement and altitude control energy cost, with parameters α and η for trade-off tuning.
• Implements a distributed control policy where each DSC adjusts its velocity based on its current altitude and the estimated mean field, enabling offline and decentralized execution.

Experimental results

Research questions

• RQ1 How can downlink interference be effectively managed in a dense network of co-channel drone small cells (DSCs) with high spatial and temporal variability?
• RQ2 What is the optimal dynamic altitude control policy for DSCs that balances SINR gain and energy cost in a large-scale, distributed deployment?
• RQ3 How does the mean-field approximation accurately represent the interference from a massive number of DSCs in a dense urban environment?
• RQ4 What is the performance gain of the proposed MFG-based control policy compared to static and uniform velocity control schemes in terms of average SINR?
• RQ5 Can the proposed algorithm be implemented in a distributed and offline manner without requiring real-time central coordination?

Key findings

• The proposed MFG-based altitude control policy achieves significantly higher average SINR compared to both the static strategy and the uniform velocity control benchmark.
• The mean field distribution evolves over time, with DSCs progressively descending from higher altitudes to lower ones to reduce path loss and improve link quality.
• The optimal velocity control policy shows a decreasing trend over time, indicating that DSCs reduce their descent speed as more units converge at lower altitudes due to increased interference.
• The probability distribution of DSCs at 1020m shows a slight increase toward the end, while the distribution at 1080m stabilizes initially before declining, reflecting dynamic convergence to lower altitudes.
• The finite difference algorithm based on the upwind scheme successfully converges to a stable solution of the coupled HJB and FPK equations, enabling practical implementation.
• The algorithm can be executed distributively and offline, reducing the need for centralized coordination and making it suitable for real-world deployment in dense DSC networks.