In next-generation digital subscriber line networks such as G.fast, employing discrete multi-tone transmission in high frequencies up to 212 MHz, the crosstalk among lines reaches very high levels. To precompensate the crosstalk in downstream transmission, QRD-based precoding has been proposed as a near-optimal dynamic spectrum management (DSM) technique. However, the performance of QRD-based precoding is greatly affected by the user encoding ordering (UEO). Since current multi-tone UEO methods are rather heuristic in the way they approach fairness, we develop, in this paper, a set of novel DSM algorithms for joint power allocation and UEO that enforce a generalized α -fairness policy. Since finding the globally optimal UEO entails a combinatorial optimization problem with excessive computational complexity, an iterative algorithm is proposed which uses per-tone exhaustive searches (PTESs) and provides near-optimal approximate solutions. To further reduce the computational complexity, two suboptimal methods are suggested to replace the expensive PTESs, leading to two additional α -fair DSM algorithms that are tractable for large scenarios against little performance loss. Simulations of a G.fast cable binder show that the α -fair DSM algorithms achieve an efficient trade-off between fairness and performance in contrast to current UEO methods.

We consider nonlinear zero-forcing (ZF) precoding design to improve the downstream G.fast peak-rates when only a few users in the cable binder are active. In order to compute the optimal nonlinear ZF precoder under per-line power constraints (PLPCs), we present a novel low-complexity dual decomposition algorithm, in which the key is the use of Lagrange multiplier based virtual precoders to transform the PLPCs into an easier virtual sum-power constraint (SPC), such that the SPC-optimality of the QR decomposition-based precoder may be exploited. We show a reduced computational complexity of this algorithm over the state-of-the-art SVD-block-diagonalization-based dual decomposition algorithm. We present simulations of a 10-line cable binder that demonstrate substantial peak-rate gains over standard QR decomposition-based ZF precoding in DSL, due to the increasingly stronger crosstalk channels in the G.fast frequency range (up to 212 MHz). Furthermore, we show that the proposed algorithm naturally extends to the scenario with multiple lines terminating at the customer premise equipments.

In the G.fast frequency range with strong levels of crosstalk, nonlinear precoding (NLP) is proposed as a near-optimal technique for crosstalk precompensation in downstream transmission. While existing methods for multi-tone NLP user encoding ordering (UEO) are rather heuristic in how they approach fairness and suffer from substantial suboptimality, we develop a novel algorithm for joint dynamic spectrum management (DSM) and UEO that enforces a generalized alpha-fairness policy. Since finding the optimal UEO is a combinatorial optimization problem with excessive computational complexity, the proposed algorithm uses a low-complexity iterative method which provides near-optimal approximate solutions. Simulations demonstrate that the novel algorithm achieves a trade-off between fairness and performance that outperforms current UEO methods.

Full-duplex (FDX) transmission is a promising technique emerging in DSL networks that theoretically may double the spectral efficiency by simultaneously transmitting in the downstream (DS) and upstream (US) on the same frequency band. Unfortunately, this may lead to severe near-end crosstalk (NEXT) interference in addition to the usual far-end crosstalk (FEXT) among the lines within a cable binder. To limit the NEXT impact by balancing the user transmit powers, tailored vectoring-based dynamic spectrum management (DSM) techniques are vital. In this paper, we develop a DSM algorithm for the specific case of perfect NEXT cancellation at the access node. This assumption in combination with US-DS duality theory allows to reformulate the DS-US structure of the non-convex weighted sum-rate maximization problem into an easier US-US structure, which can be solved with low-complexity iterative fixed-point power updates. Simulations of G.fast multi-user FDX transmission demonstrate significant improvements over time division duplex transmission.

In the G.fast digital subscriber line 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 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-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 with the state-of-the-art WMMSE algorithm.

In the G.fast frequency range (up to 212 MHz), the diagonal dominance structure of the channel matrix is no longer valid at the higher frequencies. As a result, the linear Zero Forcing (ZF) precoder in combination with dynamic spectrum management (DSM) is no longer near-optimal for downstream vectored G.fast transmission. To boost performance, we develop a novel low-complexity algorithm for both linear and non-linear precoding based DSM that maximizes the weighted line sum-rate under realistic per-line total power and per-tone spectral mask constraints. The algorithm relies on a Lagrange multiplier based transformation of the downstream dual decomposition approach formulation into its dual upstream formulation, together with a low-complexity iterative fixed-point formula to solve the resulting upstream problems. Simulations with measured G.fast channel data up to both 106 and 212 MHz are provided revealing a significantly increased performance of this algorithm over linear ZF precoding.