An improved dual decomposition approach to DSL dynamic spectrum management

Modern DSL networks suffer from crosstalk among different lines in the same cable bundle. By carefully choosing the modems´ transmit power spectra, the impact of crosstalk can be minimized leading to spectacular data rate performance gains. This is also referred to as dynamic spectrum management (DSM). DSM algorithms based on an iterative convex approximation approach are recognized as being very effective in tackling the corresponding non-convex optimization problems. One crucial ingredient of this type of algorithms, is a subgradient-based dual decomposition approach to solve the corresponding convex approximations. Although a dual decomposition approach decouples the problem into manageable subproblems, the subgradient-based updates are known to exhibit a slow convergence,with a difficult but crucial stepsize selection. This paper presents an improved dual decomposition approach that improves on the convergence of existing subgradient-based approaches by one order of magnitude. It uses a smoothing technique for the Lagrangian combined with an optimal gradient-based scheme for updating the Lagrange multipliers. Furthermore, the optimal stepsize parameters are selected automatically. The proposed approach makes an important step towards obtaining numerically fast and effective DSM algorithms.