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Robust Rate Maximization Game Under Bounded Channel Uncertainty

Anandkumar, Amod J. G. and Anandkumar, Animashree and Lambotharan, Sangarapillai and Chambers, Jonathon A. (2011) Robust Rate Maximization Game Under Bounded Channel Uncertainty. IEEE Transactions on Vehicular Technology, 60 (9). pp. 4471-4486. ISSN 0018-9545.

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We consider the problem of decentralized power allocation for competitive rate maximization in a frequency-selective Gaussian interference channel under bounded channel uncertainty. We formulate a distribution-free robust framework for the rate maximization game. We present the robust optimization equilibrium for this game and derive sufficient conditions for its existence and uniqueness. We show that an iterative waterfilling algorithm converges to this equilibrium under certain sufficient conditions. We analyze the social properties of the equilibrium under varying channel uncertainty bounds for the two-user case. We also observe an interesting phenomenon that the equilibrium moves toward a frequency-division multiple-access solution for any set of channel coefficients under increasing channel uncertainty bounds. We further prove that increasing channel uncertainty can lead to a more efficient equilibrium and, hence, a better sum rate in certain two-user communication systems. Finally, we confirm, through simulations, that this improvement in equilibrium efficiency is also observed in systems with a higher number of users.

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Additional Information:© 2011 IEEE. Manuscript received March 1, 2011; revised July 10, 2011; accepted September 2, 2011. Date of publication October 10, 2011; date of current version December 9, 2011. This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) under Grant EP/F065477/1. The work of A. Anandkumar was supported in part by ARO Grant W911NF-06-1-0076 and in part by setup funds at UCI and AFOSR award FA9550-10-1-0310. This paper was presented in part at the 2010 IEEE International Conference on Acoustics, Speech, and Signal Processing and the 43rd Asilomar Conference on Signals, Systems and Computers. The review of this paper was coordinated by Dr. S. Zhong. The authors would like to thank Dr. I. Menache of Microsoft Research for his input on the robust game theory, Dr. G. Scutari of the University of Illinois at Urbana-Champaign for his initial guidance and advice on waterfilling algorithms, P. von Wrycza of the Royal Institute of Technology (KTH) and Dr. M. R. Bhavani Shankar of the University of Luxembourg for pointing out a typographical error in an early version of the proofs, Prof. B. Ottersten of KTH for the valuable discussions, and the anonymous reviewers for their valuable feedback.
Funding AgencyGrant Number
Engineering and Physical Sciences Research Council (EPSRC)EP/F065477/1
Army Research Office (ARO)W911NF-06-1-0076
University of California, IrvineUNSPECIFIED
Air Force Office of Scientific Research (AFOSR)FA9550-10-1-0310
Subject Keywords:Channel-state information (CSI) uncertainty, game theory, Nash equilibrium, rate maximization, robust games, waterfilling
Issue or Number:9
Record Number:CaltechAUTHORS:20170925-094601829
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Official Citation:A. J. G. Anandkumar, A. Anandkumar, S. Lambotharan and J. A. Chambers, "Robust Rate Maximization Game Under Bounded Channel Uncertainty," in IEEE Transactions on Vehicular Technology, vol. 60, no. 9, pp. 4471-4486, Nov. 2011. doi: 10.1109/TVT.2011.2171011 URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81801
Deposited By: Tony Diaz
Deposited On:25 Sep 2017 16:54
Last Modified:03 Oct 2019 18:47

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