Center for Embedded Network Sensing

In this paper, we investigate the optimal spectrum management problem in multiuser frequency selective interference channels. First, a simple pairwise condition for FDMA to be optimal is discovered: for any two among all the users, as long as the normalized cross couplings between them two are both larger than or equal to 1/2, orthogonalization between these two users is optimal for every existing user. Therefore, this single condition applies to achieving all Pareto optimal points of the rate region. Furthermore, not only is this condition sufficient, but in symmetric channels, it is also necessary for FDMA to be always optimal. When the normalized cross couplings are less than 1/2, the optimal spectrum management strategy can be a mixture of frequency sharing and FDMA, depending on users’ power constraints. We first explicitly solve the sum-rate maximization problem in two user symmetric flat channels by solving a closed form equation, providing the optimal spectrum management with a clear intuition as the optimal combination of flat FDMA and flat frequency sharing. Next, we show that this result leads to a primal domain convex optimization formulation for generalizations to frequency selective channels. Finally, we show that all the general optimization problems with n>=2 users and an arbitrary weighted sum-rate objective function in non-symmetric frequency selective channels can be solved by primal domain convex optimization with the same methodology.