Global Concave Minimization for Optimal Spectrum Balancing in Multi-User DSL Networks

摘要

Dynamic spectrum management (DSM) is an effective technique for mitigating detrimental effect of crosstalk in digital subscriber lines (DSL). Among various DSM techniques, centralized optimal spectrum balancing (OSB) achieves the maximum possible data rates by computing the optimal power spectral densities (PSDs) for all modems in DSL systems. Unfortunately, its computational complexity grows exponentially in the number of users $N$ and becomes intractable for large $N$. To reduce the complexity of OSB, this paper exploits the fact that the non-convex optimization problem in OSB can be reformulated as an equivalent global concave minimization problem by representing its objective function explicitly as the difference of two convex functions (dc). This dc structure makes the non-convex optimization problem in OSB suitable for being solved by various dc algorithms developed over the decades. In particular, a modified prismatic branch-and-bound algorithm, which only requires solving a sequence of linear programming subproblems, is applied to find the global optimum with substantial reduction in complexity especially for large $N$.