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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, almost all 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, 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, 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 multi-user DSL scenarios. EDICS: SPC-TDLS

Abstract-In the G.fast digital subscriber line (DSL) frequency range (up to 106 or 212 MHz), where crosstalk channels may even become larger than direct channels, linear zero-forcing (ZF) precoding is no longer near-optimal for downstream (DS) vectored transmission. To improve performance, we develop a novel low-complexity algorithm for both linear and nonlinear precoding based dynamic spectrum management (DSM) that maximizes the weighted sum-rate under realistic per-line total power and per-tone spectral mask constraints. It applies to DS scenarios with a single copper line at each customer site [i.e. broadcast channel (BC) scenarios], as well as to DS scenarios with multiple copper lines at some or all customer sites (i.e. the so-called multiple-input-multiple-output (MIMO)-BC scenarios). The algorithm alternates between precoder and equalizer optimization, where the former relies on a Lagrange multiplier based transformation of the DS dual decomposition approach formulation into its dual upstream (US) formulation, together with a low-complexity iterative fixed-point formula to solve the resulting US problem. Simulations with measured G.fast channel data of a very high crosstalk cable binder are provided revealing a significantly improved performance of this algorithm over ZF techniques for various scenarios, and in addition, a faster convergence rate compared to the state-of-the-art WMMSE algorithm.Index Terms-DSL, G.fast, dynamic spectrum management (DSM), optimal spectrum balancing (OSB), precoding, broadcast channel (BC), MIMO-BC