Improved Dual Decomposition Based Optimization for DSL Dynamic Spectrum Management

Dynamic spectrum management (DSM) has been recognized as a key technology to significantly improve the performance of digital subscriber line (DSL) broadband access networks. The basic concept of DSM is to coordinate transmission over multiple DSL lines so as to mitigate the impact of crosstalk interference amongst them. Many algorithms have been proposed to tackle the nonconvex optimization problems appearing in DSM, many of them relying on a standard subgradient based dual decomposition approach. In practice however, this approach is often found to lead to extremely slow convergence or even no convergence at all, one of the reasons being the very difficult tuning of the stepsize parameters. In this paper we propose a novel improved dual decomposition approach inspired by recent advances in mathematical programming. It uses a smoothing technique for the Lagrangian combined with an optimal gradient based scheme for updating the Lagrange multipliers. The stepsize parameters are furthermore selected optimally removing the need for a tuning strategy. With this approach we show how the convergence of current state-of-the-art DSM algorithms based on iterative convex approximations (SCALE and CA-DSB) can be improved by one order of magnitude. Furthermore we apply the improved dual decomposition approach to other DSM algorithms (OSB, ISB, ASB, (MS)-DSB, and MIW) and propose further improvements to obtain fast and robust DSM algorithms. Finally, we demonstrate the effectiveness of the improved dual decomposition approach for a number of realistic multiuser DSL scenarios.