This paper considers the minimization of transmit power in Gaussian parallelinterference channels, subject to a rate constraint for each user. To derivedecentralized solutions that do not require any cooperation among the users, weformulate this power control problem as a (generalized) Nash equilibrium game.We obtain sufficient conditions that guarantee the existence and nonemptinessof the solution set to our problem. Then, to compute the solutions of the game,we propose two distributed algorithms based on the single user waterfillingsolution: The \emph{sequential} and the \emph{simultaneous} iterativewaterfilling algorithms, wherein the users update their own strategiessequentially and simultaneously, respectively. We derive a unified set ofsufficient conditions that guarantee the uniqueness of the solution and globalconvergence of both algorithms. Our results are applicable to all practicaldistributed multipoint-to-multipoint interference systems, either wired orwireless, where a quality of service in terms of information rate must beguaranteed for each link.
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