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Open Access

Spectrum Allocation for Decentralized Transmission Strategies: Properties of Nash Equilibria

  • Peter von Wrycza1Email author,
  • M. R. Bhavani Shankar1,
  • Mats Bengtsson1 and
  • Björn Ottersten1, 2
EURASIP Journal on Advances in Signal Processing20092009:354890

Received: 1 October 2008

Accepted: 4 March 2009

Published: 26 March 2009


The interaction of two transmit-receive pairs coexisting in the same area and communicating using the same portion of the spectrum is analyzed from a game theoretic perspective. Each pair utilizes a decentralized iterative water-filling scheme to greedily maximize the individual rate. We study the dynamics of such a game and find properties of the resulting Nash equilibria. The region of achievable operating points is characterized for both low- and high-interference systems, and the dependence on the various system parameters is explicitly shown. We derive the region of possible signal space partitioning for the iterative water-filling scheme and show how the individual utility functions can be modified to alter its range. Utilizing global system knowledge, we design a modified game encouraging better operating points in terms of sum rate compared to those obtained using the iterative water-filling algorithm and show how such a game can be imitated in a decentralized noncooperative setting. Although we restrict the analysis to a two player game, analogous concepts can be used to design decentralized algorithms for scenarios with more players. The performance of the modified decentralized game is evaluated and compared to the iterative water-filling algorithm by numerical simulations.


Nash EquilibriumOperating PointPlayer GameTransmission StrategySignal Space

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Authors’ Affiliations

Department of Electrical Engineering, ACCESS Linnaeus Centre, Signal Processing Laboratory, Royal Institute of Technology (KTH), Stockholm, Sweden
Interdisciplinary Centre for Security, Reliability, and Trust, University of Luxembourg, Luxembourg, Luxembourg


© Peter vonWrycza et al. 2009

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.