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

Driven by the exceedingly high data rates achieved in single-user implementations, interest in a multi-user (MU) full-duplex (FDX) transmission for digital subscriber line (DSL) networks is surging. However, near-end crosstalk (NEXT) is no longer avoided in such networks, and hence, appropriate dynamic spectrum management (DSM) techniques are needed. Therefore, this paper proposes three novel DSM algorithms for the MU FDX DSL network. First, an optimal spectrum balancing (OSB) algorithm is derived that calculates the globally optimal resource allocation but does so at an exceedingly high computational cost. The key to this algorithm is a novel multiple access channel broadcast channel (MAC-BC) duality for the specific case of perfect NEXT cancellation at the distribution point unit. The two low-complexity distributed spectrum balancing (DSB) algorithms are then proposed, for which simulations show that their performance is very close to what is achieved by the OSB algorithm. Therefore, these DSB algorithms can be used to estimate the achievable performance of an MU FDX DSL network. Such performance estimations show that the FDX transmission can indeed lead to significant gains in MU DSL networks as well.INDEX TERMS DSL, dynamic spectrum management, G.mgfast, multi-user full-duplex, vectoring.

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