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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. [ABSTRACT FROM AUTHOR]

There are two types of crosstalk in digital subscriber line (DSL) systems, namely near-end crosstalk (NEXT) and far-end crosstalk (FEXT). NEXT is usually much stronger than FEXT. Therefore, high-speed DSL systems transmit in preplanned disjoint downstream (DS) and upstream (US) frequency bands to avoid NEXT. Although easy for implementation, such a fixed bandplan can lead to inefficient bandwidth usage, depending on the DS and US bit rate requirements and the loop topology, particularly in so-called vectored DSL systems, which include signal coordination for FEXT cancellation. In dynamic bandplanning (DBP), each frequency band is allocated to either DS, US, or to both directions depending on the aforementioned parameters. In this paper, we consider optimal DBP for vectored DSL with linear as well as with nonlinear transmitter/receiver structures. We propose an optimal DBP algorithm for systems with disjoint DS and US bands. For systems with overlapping bands, the problem of finding the optimal transmitter/receiver filters is nonconvex and we propose two iterative algorithms based on recent optimum spectrum balancing schemes from the literature. We also study the effect of echo and US NEXT cancellation on the system performance. Finally, simulation results are provided to demonstrate that our algorithms can indeed significantly increase the achievable bit rates. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate joint level 2 and 3 dynamic spectrum management (joint DSM 2/3) for downstream (DS) DSL. We consider a DS scenario in which users are divided into a few separate groups, where vector encoding based signal coordination can be applied in each group and spectrum coordination is possible for all users. This can be seen as a mixed interference/broadcast channel (IF/BC) scenario. In order to obtain the optimal transmitter structure, we develop a generalized duality between the vector broadcast and multiple-access channel (MAC) for scenarios in which partial signal coordination is available among users. This theory together with optimal spectrum balancing (OSB) is exploited to calculate the jointly optimal filters and transmit powers for non-linear vector dirty paper coding structures (in the form of Tomlinson-Harashima precoder (THP)) in the groups. The proposed scheme is compared to several other joint DSM 2/3 algorithms for DS DSL. Simulation results show that the proposed scheme (referred to as the IF/BC-OSB algorithm) achieves considerably higher bit rates than the other schemes. IF/BC-OSB encompasses the earlier developed BC-OSB algorithm as a special case. A simplified version of IF/BC-OSB avoiding exhaustive search with near-optimal performance is also proposed. [ABSTRACT FROM PUBLISHER]

To gradually expand their networks, operators deploy new xDSL technologies from remote terminals (RT's) closer to the customer. However, since xDSL lines deployed from an RT can share a binder with lines deployed from the central office (CO), a near-far problem is introduced and crosstalk may cause a severe performance degradation for the CO-deployed lines. RT lines have to be careful about how to allocate transmit power to the transmission frequencies, such that the impact on the CO lines is acceptable. Noise Impact (NI) methods have been proposed based on a target noise shape generated by the disturbers (RT lines). In this paper new methods based on the actual impact on the bit rate of the victims (CO lines) are proposed. These Bit Impact (BI) methods closely approximate the optimal power allocation. [ABSTRACT FROM AUTHOR]

Recently, the duality between multiple-input multiple-output (MIMO) multiple-access channels (MAC) and MIMO broadcast channels (BCs) has been established under a total power constraint. The same set of rates for MAC can be achieved in BC exploiting the MAC-BC duality formulas while preserving the total power constraint. In this paper, we describe the BC optimal power allocation applying this duality in a downstream x-digital subscriber lines (xDSLs) context under a total power constraint for all modems over all tones. Then, a new algorithm called BC-optimal spectrum balancing (BC-OSB) is devised for a more realistic power allocation under per-modem total power constraints. The capacity region of the primal BC problem under per-modem total power constraints is found by the dual optimization problem for the BC under per-modem total power constraints which can be rewritten as a dual optimization problem in the MAC by means of a precoder matrix based on the Lagrange multipliers. We show that the duality gap between the two problems is zero. The multiuser power allocation problem has been solved for interference channels and MAC using the OSB algorithm. In this paper we solve the problem of multiuser power allocation for the BC case using the OSB algorithm as well and we derive a computational efficient algorithm that will be referred to as BC-OSB. Simulation results are provided for two VDSL2 scenarios: the first one with differential-mode (DM) transmission only and the second one with both DM and phantom-mode (PM) transmissions. [ABSTRACT FROM AUTHOR]

In xDSL systems, crosstalk can be separated into two categories, namely in-domain crosstalk and out-of-domain crosstalk. In-domain crosstalk is also refered to as self crosstalk. Out-of-domain crosstalk is crosstalk originating from outside the multi-pair system and is also denoted as external noise (alien crosstalk, radio frequency interference,…). While self crosstalk in itself can easily be canceled by a linear detector like the ZF detector, the presence of external noise requires a more advanced processing. Coordination between transmitters and receivers enables the self crosstalk and the external noise to be mitigated using MIMO signal processing, usually by means of a whitening filter and SVD. In this paper, we investigate the problem of finding the optimal power allocation in MIMO xDSL systems in the presence of self crosstalk and external noise. Optimal Tx/Rx structures and power allocation algorithms will be devised under practical limitations from xDSL systems, namely per-modem total power constraints and/or spectral mask constraints, leading to a generalized SVD-based transmission. Simulation results are given for bonded VDSL2 systems with external noise coming from ADSL2+ or VDSL2 disturbing lines, along with a comparison between algorithms with one-sided signal coordination either only at the transmit side or the receive side. [ABSTRACT FROM AUTHOR]

Per-tone equalization (PTEQ) has been proposed as an alternative to time-domain equalization in asymmetric digital subscriber line (ADSL) modems. It optimizes the bit rate performance of the system as each tone can be equalized independently. In a per-tone equalization-based ADSL system a fixed-length frequency-domain equalizer is typically used for every tone. The ADSL channel has, however, a lower channel gain at high frequencies; therefore, using a longer equalizer for these frequencies does not result in a significant performance gain. With a fixed equalizer length, the length of the equalizer is determined by the required length at the lower frequencies; hence, a significant number of equalizer taps are wasted in the high-frequency range without any performance gain. Using a variable-length equalizer designed such that an overall performance criterion is optimized can significantly decrease the total number of equalizer taps without coripromising performance. In this correspondence, a resource allocation technique is presented for a variable-length equalizer design using a dual problem formulation. This optimally solves the problem of equalizer length distribution over tones for given resource constraints, with a relatively low complexity. [ABSTRACT FROM AUTHOR]

Dynamic spectrum management (DSM) refers to a wide range of techniques for counteracting crosstalk in digital subscriber line (DSL) networks. DSM is categorized into three levels based on the degree of coordination among users. In this article, we investigate optimal joint level 2 and 3 DSM for upstream DSL. We will discuss the difficulties of finding the universally optimal solution and we propose an optimal algorithm, referred to as IF/MAC-OSB, under some practical and implementation assumptions for this problem. Using computer simulations, we show that IF/MAC-OSB is capable of increasing the user bit rates considerably compared to several other DSM techniques. The proposed algorithm involves using the minimum mean squared error (MMSE)-generalized decision feedback equalizer (GDFE) together with Lagrange dual optimization. We address several aspects of the problem including the optimal decoding order in the GDFE receiver, GDFE error propagation, and the computational complexity of the algorithm. We also study effects of channel model randomness and upstream power back-off utilization on the performance of the algorithm. [ABSTRACT FROM AUTHOR]

Modern digital subscriber line (DSL) networks suffer from crosstalk among different lines in the same cable bundle. This crosstalk can lead to a major performance degradation. By balancing the transmit power spectra, the impact of crosstalk can be minimized leading to spectacular performance gains. This is referred to as spectrum management. In this paper, a unifying perspective is presented on distributed spectrum management algorithms based on the Karush-Kuhn-Tucker (KKT) conditions. Furthermore, novel distributed algorithms are presented within the same KKT framework. The proposed distributed algorithms consist of local water-filling-like algorithms running in the individual modems, controlled by the spectrum management center. Extensive simulation results show that the proposed algorithms perform very well for several multi-user ADSL and VDSL scenarios. [ABSTRACT FROM AUTHOR]

Abstract: In modern DSL systems, multi-user crosstalk is a major source of performance degradation. Optimal spectrum balancing (OSB) is a centralized algorithm that mitigates the effect of crosstalk by allocating optimal transmit spectra to all interfering DSL modems. By the use of Lagrange multipliers the algorithm decouples the spectrum management problem into per-tone optimization problems. The remaining issues are then finding the Lagrange multipliers that enforce the constraints and solving the per-tone optimization problems. Finding the optimal Lagrange multipliers can become complex when more than two users are considered. Starting from the single-user case, this paper presents a number of properties, which are then extended to the multi-user case and lead to an efficient search algorithm for the Lagrange multipliers. Simulations show that the number of Lagrange multiplier evaluations is as small as 20–50, independent of the number of users. Secondly, the complexity of the per-tone optimization problems grows exponentially with the number of lines in the binder. For multiple-user scenarios this becomes computationally intractable. This paper presents an efficient branch-and-bound approach for the per-tone optimization problem. Simulations show enormous complexity reductions, especially for a large number of users. [Copyright &y& Elsevier]

Crosstalk is a major issue in modern digital subscriber line (DSL) systems such as ADSL and VDSL. Static spectrum management, which is the traditional way of ensuring spectral compatibility, employs spectral masks that can be overly conservative and lead to poor performance. This paper presents a centralized algorithm for optimal spectrum balancing in DSL. The algorithm uses the dual decomposition method to optimize spectra in an efficient and computationally tractable way. The algorithm shows significant performance gains over existing dynamis spectrum management (DSM) techniques, e.g., in one of the cases studied, the proposed centralized algorithm leads to a factor-of-four increase in data rate over the distributed DSM algorithm iterative waterfilling. [ABSTRACT FROM AUTHOR]

Very high bit-rate digital subscriber line (VDSL) is the latest generation in the ongoing evolution of DSL standards. VDSL aims at bringing truly broadband access, greater than 52Mbps in the downstream, to the mass consumer market. This is achieved by transmitting in frequencies up to 12MHz. Operating at such high frequencies gives rise to crosstalk between the DSL systems in a binder, limiting achievable data-rates. Crosstalk is typically 10–15dB larger than other noise sources and is the primary limitation on performance in VDSL. In downstream transmission several crosstalk precompensation schemes have been proposed to address this issue. Whilst these schemes lead to large performance gains, they also have extremely high complexities, beyond the scope of current implementation.In this paper we develop the concept of partial crosstalk precompensation. The majority of the crosstalk experienced in a DSL system comes from only a few other lines within the binder. Furthermore its effects are limited to a small subset of tones. Partial precompensation exploits this by limiting precompensation to the tones and lines where it gives maximum benefit. As a result, these schemes achieve the majority of the gains of full crosstalk precompensation at a fraction of the run-time complexity. In this paper we develop several partial precompensation schemes. We show that with only 20% of the run-time complexity of full precompensation it is possible to achieve 80% of the performance gains. [Copyright &y& Elsevier]

An improved optimization algorithm for the time domain equalizer (TEQ) is developed for discrete multitone (DMT) based asymmetric digital subscriber line (ADSL). In contrast with existing algorithms, our algorithm explicitly disregards the unused tones in the cost function as well as in the non-triviality constraint. Simulation results are presented for the upstream channel. It is shown that the achievable bitrate is higher than for a popular existing algorithm. [Copyright &y& Elsevier]

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 $ \alpha $ -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 $ \alpha $ -fair DSM algorithms that are tractable for large scenarios against little performance loss. Simulations of a G.fast cable binder show that the $ \alpha $ -fair DSM algorithms achieve an efficient trade-off between fairness and performance in contrast to current UEO methods. [ABSTRACT FROM AUTHOR]

In this paper, we treat the combined signal and spectrum coordination problem in digital subscriber line (DSL) networks with linear design for transmitters and receivers. The transmission is modeled as a multitone MIMO system where each user has a number of transceivers and there is coordination between sets of users on the transmitter and on the receiver sides. We consider the possibility of an asynchronous transmission, i.e. when the transmission of DMT blocks for different users is not aligned in time. This gives rise to inter-carrier interference. Our objective is the maximization of the weighted sum of users' data rates subject to power constraints. Although this problem is well known in the literature, previous works have always based their designs on strong assumptions about the network infrastructure. In this paper, we propose a general framework and algorithm that apply for any infrastructure, including any number of users, any number of transceivers, any number of tones, any kind of coordination on both the transmitter and on the receiver sides, and synchronous or asynchronous transmission. We also do not assume any special structure of the channel matrix. Our algorithm is seen to perform very well and is polynomial time solvable. [ABSTRACT FROM AUTHOR]

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 slowconvergence 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 improvedby one order of magnitude. Furthermore we apply the improved dual decomposition approach to otherDSM 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. [ABSTRACT FROM AUTHOR]

The main performance bottleneck of modern digital subscriber line (DSL) networks is the crosstalk among different lines (i.e., users). By deploying dynamic spectrum management (DSM) techniques and reducing excess crosstalk among users, a network operator can dramatically increase the data rates and service reach of broadband access. However, current DSM algorithms suffer from either substantial suboptimality in typical deployment scenarios or prohibitively high complexity due to centralized computation. This paper develops, analyzes, and simulates a new suite of DSM algorithms for DSL interference-channel models called autonomous spectrum balancing (ASB). The ASB algorithms utilize the concept of a ‘reference line,’ which mimics a typical victim line in the interference channel. In ASB, each modem tries to minimize the harm it causes to the reference line under the constraint of achieving its own target data-rate. Since the reference line is based on the statistics of the entire network, rather than any specific knowledge of the binder a modem operates in, ASB can be implemented autonomously without the need for a centralized spectrum management center. ASB has a low complexity and simulations using a realistic simulator show that it achieves large performance gains over existing autonomous algorithms, coming close to the optimal rate region in some typical scenarios. Sufficient conditions for convergence of ASB are also proved. [ABSTRACT FROM AUTHOR]

This letter presents a linear crosstalk precoder for very-high-speed digital subscriber lines (VDSL) that has a low run-time complexity. A lower bound on the data rate of the precoder is developed, and guarantees that the precoder achieves near-optimal performance in 99% of VDSL channels. [ABSTRACT FROM AUTHOR]

Crosstalk is the major source of performance degradation in VDSL. Several crosstalk cancelers have been proposed to address this. Unfortunately, they suffer from error propagation, high complexity, and long latency. This paper presents a simple, linear zero-forcing (ZF) crosstalk canceler. This design has a low complexity and no latency and does not suffer from error propagation. Furthermore, due to the well-conditioned structure of the VDSL channel matrix, the ZF design causes negligible noise enhancement. A lower bound on the performance of the linear ZF canceler is derived. This allows performance to be predicted without explicit knowledge of the crosstalk channels, which simplifies service provisioning considerably. This bound shows that the linear ZF canceler operates close to the single-user bound. Therefore, the linear ZF canceler is a low-complexity, low-latency design with predictable near-optimal performance. The combination of spectral optimization and crosstalk cancellation is also considered. Spectra optimization in a multiaccess channel generally involves a complex optimization problem. Since the linear ZF canceler decouples transmission on each line, the spectrum on each modem can be optimized independently, leading to a significant reduction in complexity. [ABSTRACT FROM AUTHOR]

The classical discrete multitone receiver as used in, e.g., digital subscriber line (DSL) modems, combines a channel shortening time-domain equalizer (TEQ) with one-tap frequency-domain equalizers (FEQs). In a previous paper, the authors proposed a nonlinear bit rate maximizing (BM) TEQ design criterion and they have shown that the resulting BM-TEQ and the closely related BM per-group equalizers (PGEQs) approach the performance of the so-called per-tone equalizer (PTEQ). The PTEQ is an attractive alternative that provides a separate complex-valued equalizer for each active tone. In this paper, the authors show that the BM-TEQ and BM-PGEQ, despite their nonlinear cost criterion, can be designed adaptively, based on a recursive Levenberg-Marquardt algorithm. This adaptive BM-TEQIBM-PGEQ makes use of the same second-order statistics as the earlier presented recursive least-squares (RLS)-based adaptive PTEQ. A complete range of adaptive BM equalizers then opens up: the RLS-based adaptive PTEQ design is computationally efficient but involves a large number of equalizer taps; the adaptive BM-TEQ has a minimal number of equalizer taps at the expense of a larger design complexity; the adaptive BM-PGEQ has a similar design complexity as the BM-TEQ and an intermediate number of equalizer taps between the BM-TEQ and the PTEQ. These adaptive equalizers allow us to track variations of transmission channel and noise, which are typical of a DSL environment. [ABSTRACT FROM AUTHOR]

To ease equalization in a multicarrier system, a cyclic prefix (CP) is typically inserted between successive symbols. When the channel order exceeds the CP length, equalization can be accomplished via a time-domain equalizer (TEQ), which is a finite impulse response (FIR) filter. The TEQ is placed in cascade with the channel to produce an effective shortened impulse response. Alternatively, a bank of equalizers can remove the interference tone-by-tone. This paper presents a unified treatment of equalizer designs for multicarrier receivers, with an emphasis on discrete multitone systems. It is shown that almost all equalizer designs share a common mathematical framework based on the maximization of a product of generalized Rayleigh quotients. This framework is used to give an overview of existing designs (including an extensive literature survey), to apply a unified notation, and to present various common strategies to obtain a solution. Moreover, the unification emphasizes the differences between the methods, enabling a comparison of their advantages and disadvantages. In addition, 16 different equalizer structures and design procedures are compared in terms of computational complexity and achievable bit rate using synthetic and measured data. [ABSTRACT FROM AUTHOR]

We reconsider the minimum mean square error (MMSE) time-domain equalizer (TEQ), bitrate maximizing TEQ (BMTEQ), and per-tone equalizer design (PTEQ) for discrete multitone (DMT) transmission and cast them in a common least-squares (LS) based framework. The MMSE-TEQ design criterion can be formulated as a constrained linear least-squares (CLLS) criterion that minimizes a time-domain (TD) error energy. From this CLLS-based TD-MMSE-TEQ criterion, we derive two new least-squares (LS) based frequency-domain (FL)) MMSE-TEQ design criteria: a CLLS-based FD-MMSE-TEQ criterion and a so-called separable nonlinear LS (SNLLS) based FD-MMSE-TEQ design. Finally, the original BM-TEQ design is shown to be equivalent to a so-called iteratively-reweighted (IR) version of the SNLLS-based FD-MMSE-TEQ design. This LS-based framework then results in the following contributions. The new, IR-SNLLS-based BM-TEQ design criterion gives rise to an elegant, iterative, fast converging, Gauss-Newton-based design algorithm that exploits the separability property. The intermediate FD-MMSE-TEQ designs establish a link between the TD-MMSE-TEQ on one hand and the BM-TEQ and the PTEQ on the other hand. Moreover, the considered LS-based equalizer designs-although at first sight very different in nature—exhibit remarkable correspondence when turned into equivalent generalized eigenvalue problems. [ABSTRACT FROM AUTHOR]

In discrete multitone (DMT) receivers, as for instance in asymmetric digital subscriber lines (ADSLs), the classical equalizer structure consists of a (real) time domain equalizer (TEQ) combined with complex 1-tap frequency domain equalizers (FEQs). Additionally, receiver windowing can be applied to mitigate the bad spectral containment of the demodulating DFT sidelobes. In this paper, we focus on a combined equalizer and windowing design procedure to maximize the achievable bit rate in DMT-based modems. Whereas the combination of a tEQ with a single window treats all the data carrying tones in a common way, the presented design method can also be used in a "per group" fashion, where smaller groups of tones receive each a different equalizer-window pair. When such groups contain only one single tone, the design procedure can be linked to the performance of an unbiased minimum mean square error (MMSE) per tone equalizer (PTEQ), which then also implicitly implements a per tone window. The general framework introduced in this paper allows us to treat equalizer-only and window-only designs as well, which appear as special cases in a natural way. This set of bit rate maximizing techniques can serve either as practical design methods or as upper bounds for existing (suboptimal) methods. We will also show that for the same achievable bit rate, equalizer taps can be exchanged for windowing coefficients to reduce complexity during data transmission. [ABSTRACT FROM AUTHOR]