Optimal rate allocation for multiple access wideband systems with rate profile constraint and adaptive power control

The optimal transmission strategy for multiple access time-invariant channels, in the sense of maximum sum-rate, under the constraint of a maximum transmitted power for each user, is multiuser water-filling. However, maximizing the sum-rate might assign very low (even null) rates for the users with the deepest fades. In practice, in 3G (and beyond) systems, different users access the network asking for different rates. We denote as normalized rate profile the ratio between the rates of all users and the rate of a reference user. To avoid the possible unfair rate distribution of the maximum sum-rate algorithm, we propose a method which computes the power and codes of each user in order to maximize the rates of all the users, under the constraint of a maximum global (rather then individual) available power, guaranteeing the desired rate profile. We show under which conditions this optimization problem admits a unique set of rates. Then, building on such a strategy, we propose a simple iterative strategy to compute the capacity region under the constraint that the global power in the network is bounded, but each user can adapt its power.