We study power allocation problems in wireless systems through network utility maximization framework. In this framework, the type of utility function represents the characteristics of each service. Hence, to deal with multi-class services in the system, it is important to accommodate various types of utility functions. In this paper, we develop a simple algorithm that can accommodate four types of utility functions in a unified way, while providing asymptotically optimal power allocation. Those types of utility functions can represent most of services in wireless networks. We first develop an algorithm that solves a general optimization problem and, then, show that our algorithm can be applied to the downlink power allocation problem.
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