Consider a scenario in which K users and a jammer share a common spectrum of N orthogonal tones. Both the users and the jammer have limited power budgets. The goal of each user is to allocate its power across the N tones in such a way that maximizes the total sum rate that he/she can achieve, while treating the interference of other users and the jammer's signal as additive Gaussian noise. The jammer, on the other hand, wishes to allocate its power in such a way that minimizes the utility of the whole system; that being the total sum of the rates communicated over the network. For this noncooperative game, we propose a generalized version of the existing iterative water-filling algorithm whereby the users and the jammer update their power allocations in a greedy manner. We study the existence of a Nash equilibrium of this noncooperative game as well as conditions under which the generalized iterative water-filling algorithm converges to a Nash equilibrium of the game. The conditions that we derive in this paper depend only on the system parameters, and hence can be checked a priori. Simulations show that when the convergence conditions are violated, the presence of a jammer can cause the, otherwise convergent, iterative water-filling algorithm to oscillate.
Bibliographical noteFunding Information:
Manuscript received May 14, 2008; revised December 18, 2008. First published February 02, 2009; current version published June 17, 2009. The associate editor coordinating the review of this manuscript and approving it for publication wasDr.Wing-KinMa.TheworkofR.H.Gohary,Y.Huang.andZ.-Q.Luoissup-ported in part by the National Science Foundation, Grant DMS-0610037, and in part by the USDOD ARMY, Grant W911NF-05-1-0567. The work of J.-S. Pang is supported by the National Science Foundation, Grant CMMI 0802022.
Copyright 2009 Elsevier B.V., All rights reserved.
- Contraction mapping
- Iterative water-filling
- Nash equilibrium
- Noncooperative games
- Open-spectrum communication