Game theoretic dynamic channel allocation for frequency-selective interference channels

Ilai Bistritz*, Amir Leshem

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

27 Scopus citations

Abstract

We consider the problem of distributed channel allocation in large networks under the frequency-selective interference channel. Performance is measured by the weighted sum of achievable rates. Our proposed algorithm is a modified Fictitious Play algorithm that can be implemented distributedly, and its stable points are the pure Nash equilibria of a given game. Our goal is to design a utility function for a non-cooperative game, such that all of its pure Nash equilibria have close to optimal global performance. This will make the algorithm close to optimal while requiring no communication between users. We propose a novel technique to analyze the Nash equilibria of a random interference game, determined by the random channel gains. Our analysis is asymptotic in the number of users. First, we present a natural non-cooperative game where the utility of each user is his achievable rate. It is shown that, asymptotically in the number of users and for strong enough interference, this game exhibits many bad equilibria. Then, we propose a novel non-cooperative M frequency-selective interference channel game as a slight modification of the former, where the utility of each user is artificially limited. We prove that even its worst equilibrium has asymptotically optimal weighted sum rate for any interference regime and even for correlated channels. This is based on an order statistics analysis of the fading channels that is valid for a broad class of fading distributions (including Rayleigh, Rician, m-Nakagami, and more). We carry out simulations that show fast convergence of our algorithm to the proven asymptotically optimal pure Nash equilibria.

Original languageAmerican English
Article number8453878
Pages (from-to)330-353
Number of pages24
JournalIEEE Transactions on Information Theory
Volume65
Issue number1
DOIs
StatePublished - Jan 2019
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 1963-2012 IEEE.

Keywords

  • Frequency-selective fading channels
  • ad hoc networks
  • random games
  • resource allocation
  • utility design

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