A game-theoretic approach for distributed power control in interference relay channels

Yi Shi, Jiaheng Wang, Khaled Letaief, Ranjan K. Mallik

Research output: Contribution to journalArticle

53 Citations (Scopus)


This paper considers the multiuser power control problem in Gaussian frequency-flat interference relay channels using a game-theoretic framework. While a lot of attention has been paid to Gaussian interference games, where sufficient conditions for the uniqueness of the Nash equilibrium (NE) have been established, these types of games have not been studied in the context of interference relay channels. We consider here Gaussian interference relay games (GIRGs), where instead of allocating the power budget across a set of sub-channels, each player aims to decide the optimal power control strategy across a set of hops. We show that the GIRG always possesses a unique NE for a two-player version of the game, irrespective of any channel realization or initial system parameters such as power budgets and noise power. Furthermore, we derive explicitly a sufficient condition under which the NE achieves Pareto-optimality. To facilitate decentralized implementation, we propose a distributed and asynchronous algorithm. We also prove that the proposed algorithm always converges to the unique NE from an arbitrary starting point. We then conclude that the distributed game-theoretic approach exhibits great potential in the context of interference relay channels and qualifies as a practically appealing candidate for power control.

Original languageEnglish
Article number5089996
Pages (from-to)3151-3161
Number of pages11
JournalIEEE Transactions on Wireless Communications
Issue number6
Publication statusPublished - Jun 2009
Externally publishedYes



  • Distributed algorithm
  • Game theory
  • Interference relay channels
  • Pareto-optimality
  • Power control

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Computer Science Applications
  • Applied Mathematics

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