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The authors consider the problem of rate and power allocation in a multiple-access channel. The objective is to obtain rate and power allocation policies that maximize a general concave utility function of average transmission rates on the information theoretic capacity region of the multiple-access channel. The policies does not require queue-length information. They consider several different scenarios. First, the authors address the utility maximization problem in a non-fading channel to obtain the optimal operating rates, and present an iterative gradient projection algorithm that uses approximate projection. By exploiting the polymatroid structure of the capacity region, they show that the approximate projection can be implemented in time polynomial in the number of users.
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