Maximum sum rate of a restricted FDMA system

In this paper, the sum-rate optimal restricted FDMA system is investigated for asymmetric-power users, when they have individual upper limits on the bandwidths in addition to a constraint on total system bandwidth. A convex optimization problem is formulated to optimally allocate the system bandwidth to the users. First, the users are classified into oversized and non-oversized users, based on the strength of their minimal power spectral densities (PSDs). Then, the maximum sum rate and the unique optimal solution in a closed algorithmic expression are derived by using the Karush-Kuhn-Tucker optimality conditions. An iterative algorithm to construct the optimal solution is also presented that provides insights into the restricted FDMA system. Interestingly, the non-oversized users end up with an equal PSD among one another, which is always less than the PSDs of the oversized users, if they exist. It turns out that the sum-rate optimal restricted FDMA system achieves the sum capacity of the band-limited multiple-access channel if and only if there is no oversized user.