A Concave Minimization Approach to Dynamic Spectrum Management for Digital Subscriber Lines

Optimal Spectrum Management (OSM) computes the optimal PSD for all modems in Digital Subscriber Lines (DSL) systems to achieve the maximum possible data rates. Unfortunately, its complexity grows exponentially in the number of users N and becomes computationally intractable for large N. This paper shows that the non-convex optimization problem in OSM can be reformulated as an equivalent global concave minimization problem by representing its objective function as a difference of two convex functions (d.c.). A prismatic branch and bound algorithm is applied to find the global optimum that only requires solving a sequence of linear programming sub-problems with a substantial reduction in complexity, especially for large N.