We study the multi-user and multi-carrier power allocation (spectrum balancing) problem in digital subscriber line (DSL) networks under inter-carrier and inter-user interference as well as self-interference. The key assumption of this work is that we do not have knowledge of the interference coefficients, but only have access to the total per-line interference noise power. Furthermore, lines may support different technologies or be part of linear crosstalk cancellation (Vectoring) groups, which implies coupling among lines through per-transceiver sum-power and spectral mask constraints. We propose a novel generalized Nash equilibrium formulation for spectrum balancing in a virtual network with modified selfinterference coefficients and an associated variational inequality problem. The latter allows for intuitive analytical criteria for algorithms' convergence to a unique solution in the virtual network as well as in the real network, related to the sum of interference coefficients. Exemplarily a fully autonomous projected gradient algorithm is proposed which requires no information exchange among Vectoring groups and obeys transmit power limitations throughout its run-time. The applicability of the proposed framework is demonstrated by testing this algorithm on two previously studied power allocation problems in Vectoring G.fast networks.

The next digital subscriber line (DSL) generation, called G.fast, extends the frequency band up to 212MHz and achieves Gigabit data-rates. Vectoring technology cancels the performance-limiting crosstalk among DSL lines on a signal level, but requires co-located line termination. Differently, dynamic spectrum management level 2 (DSM-L2) coordinates the transmit power spectra among interferers and thus, does not require all line termination units to be co-located. In this work we analyze the data-rates of G.fast under full vectoring, partial vectoring restricted to groups of users, and non-vectoring scenarios. We also propose interference alignment (IA) as an alternative method to DSM-L2 for dealing with the interference in G.fast and show that IA is superior to DSM-L2 in non-vectoring scenarios. Furthermore, we also propose time division multiple access (TDMA) for coordination of multiple vectoring groups in partial vectoring scenarios.

We present a new approach to identify the parameters of a given digital predistortion (DPD) structure for power amplifier (PA) linearization. Traditional methods optimize a single objective, typically the time-domain mean squared error. We propose to use a multi-objective optimization algorithm to jointly optimize the in-band and out-of-band performance as quantified by the respective metrics defined in the particular communication standard. Our constrained approach allows for checking standard-compliance at the time of DPD identification. Furthermore, the DPD model is not required to be linear in the parameters. We exemplify our approach with a WLAN simulation using a PA model at low back-off. By jointly optimizing the error vector magnitude (EVM) and spectral mask margin, we achieve significantly better results than the widely-used indirect learning architecture for the same memory polynomial DPD structure.

G.fast is the next-generation digital subscriber line (DSL) technology targeting bit-rates of up to 1 Gbps. Very high speed digital subscriber line 2 (VDSL2) is the the latest DSL technology delivering bit-rates of up to 100 Mbps. Replacement of VDSL2 by G.fast modems will be gradual, which implies coexistence of these two systems. G.fast and VDSL2 use different symbol durations, carrier frequency spacings, and sampling rates, which results in inter-carrier and inter-symbol interference (ICSI). We derive an analytical model of ICSI capturing these differences in modulation. Furthermore, through simulations we show that for particular network topologies coexistence of the two systems results in significant bit-rate losses compared to an interference-free scenario.

Vectoring very high speed digital subscriber line 2 (VDSL2) lines will coexist with legacy VDSL2 lines during copper access network migration. Without the ability of legacy lines to cooperate for crosstalk channel estimation, Vectoring lines may still suffer from crosstalk noise. We study the spectral protection of Vectoring lines by dynamic upstream power back-off (UPBO) and provide a multiobjective methodology for fairness optimization between legacy and Vectoring lines. Extensive simulation and exemplary testbed results with up to 20 lines illustrate the tradeoff in mean-rate offered to network operators, as well as the effect of various fairness definitions.

Cooperation of transceivers on signal level at the remote terminal-often referred to as vectoring-is an effective approach to mitigate crosstalk in wireline transmission systems. While the gain in bitrate compared to crosstalk-limited transmission is substantial, the initialization of a vectoring system requires time and care to ensure system stability. In this contribution, a fast initialization scheme for vectored wireline systems based on spectral protection is analyzed. Two scenarios are considered, where in the first one no prior channel information is available, and in the second one erroneous prior knowledge of channel coefficients is utilized. Measurements on a commercial VDSL2 vectoring platform and throughput simulations demonstrate the potential of the fast initialization scheme.

The use of a cyclic prefix (CP) in orthogonal frequency-division multiplexing (OFDM) allows to avoid inter-carrier interference (ICI), but also diminishes the efficiency of the modulation scheme. We study the problem of jointly optimizing the CP length and the discrete bit and power-loading under ICI in OFDM, exemplified by its application to power line communication (PLC). We derive a low-complexity linear programming (LP) based performance upper-bound which is applicable to analyze the suboptimality of bit-loading heuristics under varying CP lengths. Furthermore, a branch-and-bound heuristic is proposed for low-complexity CP-length selection. While we do not expect the LP bound to be tight in all possible interference scenarios, our simulation results support the hypothesis that it is sufficiently tight in the range of near-optimal CP lengths in order to provide guidelines for optimal as well as heuristic CP-length selection.

The large number of broadband users and its forecast growth has recently triggered research on energy-efficiency in digital subscriber lines (DSLs). A promising technique are low-power modes (LPMs) as standardized in asymmetric DSL 2 (ADSL2) which let the DSL connection operate in downstream direction with reduced transmit rate and power. We study the problem of optimizing the LPM rate-level for energy-efficiency. A traffic-independent rate setting is proposed based on an analytical competitive framework. Also, a Markov chain based LPM model is derived which facilitates the fast numerical optimization of the LPM rate-level under realistic traffic models and system constraints. Simulation results under various traffic settings and DSL scenarios demonstrate energy savings by LPMs of around 30–40% of the ADSL2 transceiver’s power consumption. Furthermore, they provide insights on how to set the LPM rate-levels in practice for energy-efficient DSL operation.

We consider a constrained multi-carrier power allocation problem in interference-limited multi-user systems with a finite set of transmission rates. The Lagrange relaxation is a common technique for decomposing such problems into independently solvable per-subcarrier problems. Deviating from this approach our main contribution is the proposal of a novel spectrum management framework based on a Nonlinear Dantzig-Wolfe problem decomposition. It allows for suboptimal initialization and suboptimal power allocation methods with low complexity. While we show that the combinatorial per-subcarrier problems have polynomial complexity in the number of users, we find that such suboptimal methods are indispensable in large systems. Thus we give an overview of various basic dual heuristics and provide simulation results on a set of thousand digital subscriber line (DSL) networks which show the superior performance of our framework compared to previous power control algorithms.

A multi-user signal coordination scheme known as Vectoring will play a crucial role in next generation digital subscriber lines (DSL). Previous studies have demonstrated that vectoring increases the bitrate of DSL systems due to its ability to mitigate the interference. In this work we show how Vectoring improves the energy-efficiency of DSL over state-of-the-art spectrum balancing methods. In addition we investigate the impact of channel-state information errors and low-complexity implementations on the performance of Vectoring. We find that Vectoring yields large energy savings in terms of line-driver power consumption even under high channel estimation errors.

Spectrum balancing is an established optimization approach in multi-carrier digital subscriber line (DSL) systems. It has previously been applied to very different performance objectives such as sum-rate, min-rate, or fairness maximization and sum-power minimization. In this work we study the maximization of the service coverage, which will be defined as the number of DSL lines which can be granted an operator-specified high-bandwidth service. The proposed algorithm is based on a previously described mathematical decomposition framework. We extend this framework for our new problem and enhance its scalability by various low-complexity heuristics. Simulations demonstrate the applicability of our algorithm for DSL networks of realistic sizes. More precisely, our results obtained in thousand 25 user near-far DSL scenarios show an average gain in service coverage of more than 13% compared to state-of-the-art sum-rate maximizing spectrum balancing algorithms.

We investigate a novel cross-layer optimization problem for jointly performing dynamic spectrum management (DSM) and periodic rate-scheduling in time. The large number of carriers used in digital subscriber lines (DSL) makes DSM a large-scale optimization problem for which dual optimization is a commonly used method. The duality-gap which potentially accompanies the dual optimization for non-convex problems is typically assumed to be small enough to be neglected. Also, previous theoretical results show a vanishing duality-gap as the number of subcarriers approaches infinity. We will bound the potential performance improvements that can be achieved by the additional rate-scheduling procedure. This bound is found to depend on the duality-gap in the physical layer DSM problem. Furthermore, we will derive bounds on the duality-gap of the two most important optimization problems in DSL, namely the maximization of the weighted sum-rate and the minimization of the weighted sum-power. These bounds are derived for a finite number of subcarriers and are also applicable to the respective problems in orthogonal frequency division multiplex (OFDM) systems.