Optimal Spectrum Management of DSL With Nonstrictly Convex Rate Region

Recently, the problem of optimal spectral balancing (OSB) for digital subscriber lines (DSL) with constrained transmit power has been solved using Lagrange's dual optimization technique and a weighted sum rate maximization (WSRM) approach. In many cases, the total power constraint is not binding. Although, this means a huge computational complexity reduction, the algorithm fails to reach certain points on the rate region (RR). In this paper, an in-depth analytical view of the WSRM approach is provided, and it is shown that when the RR is not strictly convex, the WSRM approach fails to reach certain points on the RR. Moreover, using N-dimensional geometry, a novel iterative facet dividing algorithm (IFDA) capable of reaching any point on the RR is proposed. Analytical and simulation results show that our technique is much more reliable and considerably faster than current algorithms. Moreover, it can be used for a wide range of problems which use WSRM approach, including OSB in the general case.