Spectrum Allocation for Decentralized Transmission Strategies: Properties of Nash Equilibria
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Research Article Spectrum Allocation for Decentralized Transmission Strategies: Properties of Nash Equilibria Peter von Wrycza,1 M. R. Bhavani Shankar,1 Mats Bengtsson,1 and Bj¨orn Ottersten (EURASIP Member)1, 2 1 Department
of Electrical Engineering, ACCESS Linnaeus Centre, Signal Processing Laboratory, Royal Institute of Technology (KTH), SE-100 44 Stockholm, Sweden 2 Interdisciplinary Centre for Security, Reliability, and Trust, University of Luxembourg, Luxembourg 1511, Luxembourg Correspondence should be addressed to Peter von Wrycza, [email protected] Received 1 October 2008; Accepted 4 March 2009 Recommended by Holger Boche 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 waterfilling 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. Copyright © 2009 Peter von Wrycza et al. 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.
1. Introduction Over the last few years, many theoretical connections have been established between problems arising in wireless communications and those in the field of game theory [1]. One such instance is when several coexisting links consisting of transmit-receive pairs compete with an objective of maximizing their individual data rates while treating the interference as Gaussian noise [2]. Due to the wireless communication channel, the received signal at each receiver is interfered by all transmitters, and the performance of the transmission strategies is, therefore, mutually dependent. Further, since no cooperation is assumed among the links, we have an instance of the interference channel [3, 4] whose complete characterization is still an open problem. Viewed in a noncooperative game theoretic setting [5], the links can be regarded as playe
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