[Paper Review] A Potential Game for Power and Frequency Allocation in Large-Scale Wireless Networks

Brage Ellingsæter, Magnus Skjegstad+1 more|arXiv (Cornell University)|Dec 4, 2012

Cooperative Communication and Network Coding14 references3 citations

TL;DR

This paper proposes a potential game framework for joint power and frequency allocation in large-scale wireless networks using the physical SINR model. By characterizing minimal neighbor information requirements, it proves the game admits a generalized ordinal potential function, ensuring convergence to stable equilibria with limited message passing, validated through simulations under realistic neighbor discovery conditions.

ABSTRACT

In this paper we analyze power and frequency allocation in wireless networks through potential games. Potential games are used frequently in the literature for this purpose due to their desirable properties, such as convergence and stability. However, potential games usually assume massive message passing to obtain the necessary neighbor information at each user to achieve these properties. In this paper we show an example of a game where we are able to characterize the necessary neighbor information in order to show that the game has a potential function and the properties of potential games. We consider a network consisting of local access points where the goal of each AP is to allocate power and frequency to achieve some SINR requirement. We use the physical SINR model to validate a successful allocation, and show that given a suitable payoff function the game emits a generalized ordinal potential function under the assumption of sufficient neighbor information. Through simulations we evaluate the performance of the proposed game on a large scale in relation to the amount of information at each AP.

Motivation & Objective

• To address the challenge of distributed resource allocation in large-scale wireless networks with minimal global information exchange.
• To characterize the minimal neighbor information required for a potential game to ensure convergence and stability in power and frequency allocation.
• To design a payoff function that reflects both individual and system-level performance under the physical SINR model.
• To validate the proposed game's convergence and performance through simulations under progressive neighbor discovery.
• To demonstrate that a generalized ordinal potential function exists when each AP knows sufficient neighboring strategies, enabling distributed implementation.

Proposed method

• Formalizing the network as a non-cooperative game where each access point (AP) optimizes power and frequency to meet a SINR target.
• Defining a utility function based on interference and required power, adjusted by a normalization factor to reflect system performance.
• Proving the existence of a generalized ordinal potential function by showing that individual payoff improvements align with system-wide potential function increases.
• Establishing that only knowledge of neighboring APs' strategies on each channel is required for the potential function to hold, reducing message overhead.
• Using the physical SINR model to validate successful transmission and interference calculation, ensuring realistic performance evaluation.
• Simulating the game under progressive neighbor discovery to assess convergence and performance under incomplete information.

Experimental results

Research questions

• RQ1 What is the minimal amount of neighbor information required for a potential game to ensure convergence in power and frequency allocation?
• RQ2 Can a generalized ordinal potential function be constructed in a large-scale wireless network using the physical SINR model?
• RQ3 How does limited neighbor information affect the convergence and performance of the proposed game-based resource allocation scheme?
• RQ4 Does the proposed utility function ensure that individual improvements in payoff correspond to system-wide performance gains?
• RQ5 Can the game converge to a stable equilibrium with only local information exchange, avoiding global coordination?

Key findings

• The proposed game admits a generalized ordinal potential function when each AP has knowledge of at least one neighboring AP's strategy on each channel, ensuring convergence to a pure Nash equilibrium.
• The potential function is constructed such that any unilateral improvement in an AP's payoff corresponds to an increase in the system-wide potential, guaranteeing system-level performance improvement.
• Simulations show that convergence is achieved when neighbor discovery provides sufficient information, even in large-scale networks with dynamic topology.
• The game maintains stability and convergence under the physical SINR model, which accounts for cumulative interference from all transmitters, unlike simpler protocol models.
• The required neighbor information is significantly less than global knowledge, enabling scalable and distributed deployment in real-world scenarios.
• The utility function design ensures that minimizing interference through channel and power selection leads to both individual and system-wide performance gains.