Asymptotic FDMA capacity region for broadcast channels with ISI

We consider the problem of optimal power allocation for a broadcast channel with ISI under the FDMA restriction. Due to the FDMA restriction, the resulting problem is combinatorial in nature and hard to solve. However, by relaxing the FDMA restriction, we obtain a convex reformulation that allows for efficient computation of the optimal solution and therefore, a characterization of the capacity region. It is also shown that under certain conditions on the channel responses, the optimal frequency partition has an ordered structure that can be exploited to further reduce the computational complexity