Speech denoising (SD) is an important task of many, if not all, modern signal processing chains used in devices and for everyday-life applications. While there are many published and powerful deep neural network (DNN)-based methods for SD, few are optimized for resource-constrained platforms such as mobile devices. Additionally, most DNN-based methods for SD are not focusing on full-band (FB) signals, i.e. having 48 kHz sampling rate, and/or low latency cases. In this paper we present a causal, low latency, and lightweight DNN-based method for full-band SD, leveraging both short and long temporal patterns. The method is based on a modified UNet architecture employing look-back frames, temporal spanning of convolutional kernels, and recurrent neural networks for exploiting short and long temporal patterns in the signal and estimated denoising mask. The DNN operates on a causal frame-by-frame basis taking as an input the STFT magnitude, utilizes inverted bottlenecks inspired by MobileNet, employs causal instance normalization for channel-wise normalization, and achieves a real-time factor below 0.02 when deployed on a modern mobile phone. The proposed method is evaluated using established speech denoising metrics and publicly available datasets, demonstrating its effectiveness in achieving an (SI-)SDR value that outperforms existing FB and low latency SD methods.

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.

Multi-user full duplex (FDX) transmission is instrumental to provide sufficient coverage and reach for the multi-gigabit data rates targeted by MGfast. However, to seamlessly introduce such a technology into access networks, it is important to consider coexistence with legacy half duplex G.fast. We propose a novel frame structure with two alternating FDX operating points, as well as a corresponding synchronization scheme, which enable coexistence without impacting the rate nor the reach of either technology. This multi-user FDX method is referred to as Friendly Full Duplex, and is a low complexity solution that exploits existing G.fast mechanisms and that can be optimized over transmission direction and time. Simulation results illustrate the significant gains in data rate performance and coexistence properties.

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.

The growing demand for wireless connectivity has turned bandwidth into a scarce resource that has to be carefully managed and fairly distributed to users. However, the variability of the wireless channel can severely degrade the service received by each user. The Double Relay Communication Protocol (DRCP) [1] is a transmission scheme that addresses these problems by exploiting spatial diversity to enhance the fairness of the system without requiring any additional infrastructure (i.e relay nodes or a backhaul connection). Although DRCP has originally been proposed to work without channel state information at the transmitter (CSIT), in this paper we study how the performance of DRCP can be further improved through power control when CSIT is available. Our approach provides the highest fairness and the largest minimum spectral efficiency for most conditions compared to other studied baseline approaches.

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.

Precoding is a technique that counteracts the crosstalk in downlink digital subscriber line (DSL) transmission. While linear precoding is adequate in the VDSL2 technology because of the moderate crosstalk environment, this might no longer be the case in the G.fast technology, which uses higher frequencies and therefore is affected by higher crosstalk levels. In this contribution we compare linear and nonlinear precoding for G.fast transmission protected by trellis-coded modulation, and present two bitloading algorithms that are suited for both precoding schemes. We show that for a set of measured broad-band channels, each representing a binder of eight twisted-pair cables, these bitloading algorithms have substantially different complexities but yield a similar information bitrate, which is about 10% higher for nonlinear precoding as compared to linear precoding.

In this paper, we optimize the use of existing DSL low-power sleeping modes (L2 and L3) in order to improve the energy efficiency of DSL access networks. Given that switching on a DSL line can cause instability by increasing the amount of time-varying crosstalk in the cable bundle, and that it takes energy and time to switch a DSL line on and off, we develop a method to optimally choose the appropriate sleeping state based on the line and traffic characteristics. We further develop and prove the structural properties of the optimal policy for switching to the appropriate sleeping state, allowing transitions between submodes with different power and transmit rate characteristics. We also present techniques that guarantee stable sleep mode operation. Using a realistic DSL simulator, we demonstrate the three-way tradeoff among energy consumption, delay performance, and stability. The increased flexibility of control introduced by our approach improves the energy-delay Pareto optimal tradeoff, and results in a more energy efficient and stable DSL operation compared to existing power saving policies.

We extend studies on power optimization in VDSL2 to G.fast, the technology under definition. In vectored G.fast the power of the signals before precoding needs to be optimized to meet power spectral density and maximum aggregate transmit power constraints per line. We formulate this interplay between vectoring and power optimization, with non-vectored transmission as a particular case. Three power allocation algorithms are devised that allow a tradeoff between optimality and computational complexity. Measured channel data from a European operator up to 106 MHz is considered. Numerical evaluation reveals that low complex heuristics for power optimization yield near optimal solutions both with perfect and imperfect channel state information. Similar conclusions hold for the 212 MHz profile.

Iterative power difference balancing (IPDB) has recently been proposed as a first real-time dynamic spectrum management (RT-DSM) algorithm. It consists of a primal coordinate ascent approach where each coordinate step is performed using an exhaustive discrete grid line search. In this paper we present an iterative convex approximation based approach to perform the coordinate ascent search so as to reduce its computational complexity. By exploiting the problem structure, a closed-form solution is derived for the convex approximations. The resulting RT-DSM algorithm is referred to as fast IPDB (F-IPDB). Compared to IPDB, F-IPDB exhibits similar data rate performance with significantly reduced computational complexity, while also providing smoother final transmit spectra.

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.

Dynamic spectrum management is recognized as a key technique to tackle interference in multi-user multi-carrier communication systems and networks. However existing dynamic spectrum management algorithms may not be suitable when the available computation time and compute power are limited, i.e., when a very fast responsiveness is required. In this paper, we present a new paradigm, theory and algorithm for real-time dynamic spectrum management (RT-DSM). Specifically, a RT-DSM algorithm is real-time in the sense that it can be stopped at any point in time while guaranteeing a feasible and improved solution. This is enabled by the introduction of a novel difference-of-variables (DoV) transformation and problem reformulation, for which a primal coordinate ascent approach is proposed with exact line search via a logarithmically-scaled grid search. The proposed algorithm is referred to as iterative power difference balancing (IPDB). Simulations for different realistic wireline and wireless interference-limited systems demonstrate its good performance, low complexity and wide applicability under different configurations.

We focus on the effects of intercarrier interference (ICI) in digital subscriber line (DSL) systems due to asynchronous discrete multitone (DMT) transmission and its impact on dynamic spectrum management (DSM). ICI arises when the DMT blocks of interfering users in the network are not aligned in time and it may significantly impact the system performance. Our contribution is the derivation of a simple and accurate model for the effect of the ICI. We propose both an ICI model based on the particular delay between two users and an ICI model averaged over the delays between two users. Simulation results show that an accurate characterization of the ICI positively impacts the performance of DSM solutions.

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.

Time domain synchronous OFDM (TDS-OFDM) can achieve a higher spectrum efficiency than standard cyclic prefix OFDM (CP-OFDM). Currently, it can support constellations up to 64QAM, but cannot support higher-order constellations like 256QAM due to the residual mutual interferences between the pseudorandom noise (PN) guard interval and the OFDM data block. To solve this problem, we break the traditional approach of iterative interference cancellation and propose the idea of using multiple inter-block-interference (IBI)-free regions of very small size to realize simultaneous multi-channel reconstruction under the framework of structured compressive sensing, whereby the sparsity nature of wireless channels as well as the characteristic that path delays vary much slower than path gains are jointly exploited. In this way, the mutually conditional time-domain channel estimation and frequency-domain data demodulation in TDS-OFDM can be decoupled without the use of IBI removal. We then propose the adaptive simultaneous orthogonal matching pursuit (A-SOMP) algorithm with low complexity to realize accurate multi-channel reconstruction, whose performance is close to the Cramér-Rao lower bound (CRLB). Simulation results confirm that the proposed scheme can support 256QAM without changing the current signal structure, so the spectrum efficiency can be increased by about 30%.

This paper deals with the problem of power allocation in a multi-user, multicarrier communication system. This problem arises, for example, in wireless OFDM or digital subscriber line networks. Users transmitting concurrently on the same sub-carriers cause interference to each other, and this interference is a serious limitation for system performance. We consider the problem of maximizing the weighted sum of users' data rates. The optimization variables are vectors containing the powers for all users on each tone. The problem is intrinsically difficult due to the non-concavity of the utility function. We propose to change the (cartesian) power vector by its polar coordinates vector equivalent. The main contribution of this paper is to show that at least for one dimension of the polar coordinates vector, the radius, the problem is concave and thus easy to solve. We develop an algorithm based in such a polar coordinates formulation to exploit such concavity. It is demonstrated that the algorithm we propose saves considerably on computational cost compared to previous algorithms.

Vectoring is recognized as a very efficient technique to tackle crosstalk interference in multi-user DSL systems. In this paper we focus on sparse linear zero-forcing based vectoring schemes with a shared resource pool, which are known to obtain a good trade-off between online computational complexity and near-optimal performance. We propose a new system setup with a controller that dynamically (in time) optimizes and allocates computational complexity resources taking into account variable data rate demands with real-time constraints. The controller is designed to minimize the online computational complexity over time and allows for flexible fixed and variable data rate allocations. Simulation results with variable real-time constrained video streams for a realistic downstream VDSL scenario demonstrate that this novel controller-based approach allows to significantly reduce the average as well as peak online computational complexity.

Switching off a DSL line to a low-power sleeping state is becoming an important method to enhance energy efficiency of DSL broadband access networks. Although a low-power (L2) state and an off (L3) state are already defined in DSL standards, they have not been fully exploited due to concern about the resulting time-varying crosstalk. In this paper, we develop a method to optimally choose the appropriate sleeping state based on the modem's switching cost characteristics and the power consumption incurred during each sleeping state. We further develop the optimal policy for switching to the appropriate sleeping state, allowing transitions between operating modes with different power and transmit rate. Numerical results on our realistic DSL simulator show that more flexibility in control, introduced by our approach, improves the energy-delay Pareto optimal tradeoff, and results in a more energy efficient and stable DSL system compared to the existing power saving policies.

Spectrum optimization is a promising means to tackle the crosstalk problem in DSL systems, and corresponds to a challenging nonconvex optimization problem. Iterative convex approximation (ICA) methods have been proposed in the literature to deal with this optimization problem. These methods consist in solving a series of improving convex approximations and are typically implemented in a per-user iterative approach. In this paper we develop a novel class of iterative methods that focus explicitly on per-user iterative implementations, and which consist of improved per-user approximations that are tighter and simpler to solve (in closed-form) than state-of-the-art ICA methods. As a result, the proposed methods improve the convergence speed as fewer approximations are required to converge, and display a significantly lower computational cost. Furthermore, three of the proposed methods can tackle the issue of getting stuck in bad locally optimal solutions, and hence improve solution quality with respect to existing ICA methods.

DSL broadband access suffers from crosstalk among different lines within the same cable bundle. Dynamic spectrum management (DSM) refers to a set of techniques to mitigate the impact of crosstalk leading to spectacular performance gains. DSM research has mainly aimed at physical layer performance metrics, such as data rates and transmit powers. However, for many applications higher-layer performance metrics, such as throughput and delay, may be much more important to improve user satisfaction. In this paper, we provide a cross-layer DSM framework to study throughput and delay performance by looking at scheduling and DSM together. We show how optimal scheduling can be combined with both optimal and suboptimal DSM and provide throughput-optimal scheduling algorithms which require only polynomial complexity. We analytically study the impact on delay performance of achieving throughput-optimality with suboptimal DSM compared to optimal DSM. We then present extensions that significantly improve delay performance by exploiting the specific structure of the problem, such as the temporal-spectral correlation property. Furthermore, we propose a second cross-layer DSM framework that achieves throughput-optimal scheduling with suboptimal DSM, but in addition also significantly reduces overall power consumption. Finally, we analyze and quantify the tradeoff between throughput, delay and power consumption for concrete DSL scenarios.

Energy efficient and stable operation of the DSL broadband access infrastructure has become an essential part of the emerging trend towards green communications. One promising means to obtain energy savings is the use of low power "sleep modes", putting DSL modems to sleep when they are not used. Executing the optimal sleeping policies is, however, not straightforward since turning the modem ON and OFF consumes both energy and time, and it also impacts the stability of the DSL network. We present an analytic framework providing optimal sleeping policies that achieve a Pareto-optimal tradeoff between energy consumption and delay performance. Furthermore, we present mechanisms achieving stable sleep mode operation that improve overall stability of DSL systems. Using a realistic DSL simulator, we demonstrate the three-way tradeoff between energy consumption, delay performance and stability.

Dynamic spectrum management (DSM) aims to optimally al locate per-user transmit spectra so that the effect of multiuser interference (crosstalk) is minimized and the capabilities of the network are maximized. Work on DSM has progressed considerably over the past decade. Most of this work, however, deals with the idealized situation of perfect synchronization amongst the multiple users. This work deals with a more realistic albeit more difficult situation, i.e we consider the DSM problem with asynchronous crosstalk. We propose a novel solution for this problem, one that is mainly based on the approximate summability of the crosstalk damage ratio (CDR). Performance of the algorithm is assessed through numerical experiments and is shown to be better than the performance of state-of-the-art methods.

The design of crosstalk mitigation techniques for DSL broadband access systems has mainly focused on physical layer transmit rate maximization. However, for certain applications, upper-layer performance metrics like network throughput, stability and delay performance may be more relevant. In this paper, we present a number of dynamic resource allocation based algorithms for partial crosstalk cancellation (PCC) that focus on these upper-layer metrics. A first algorithm focuses on preserving transmission queueing stability while maximizing the transmit rate. This is then extended towards budget adaptive algorithms, which dynamically adapt the PCC so as to improve the resource efficiency and to obtain a desirable trade-off between delay performance and resource consumption. Simulation results demonstrate the improved stability of the proposed algorithms and the obtained trade-off between delay performance and resource consumption.

Dynamic spectrum management (DSM) has been recognized as a key technology for tackling multi-user crosstalk interference for DSL broadband access. Up to now, DSM design has mainly been focusing on maximization of data rates. However, recently, reducing the total power has become a main target, as IT power consumption has been identified as a significant contributor to global warming. In this paper we extend traditional DSM design towards a much wider energy-efficient scope and show how to tackle the corresponding optimization problems. The impact of this 'green DSL' approach is evaluated for practice with some surprisingly good numerical results. Furthermore bounds are provided on the trade-off between data rate performance and power saving.

In modern DSL networks, crosstalk among different lines (i.e., users) is the major source of performance degradation. Dynamic spectrum management (DSM) refers to a set of techniques to mitigate the effect of crosstalk leading to spectacular performance gains. However the main research efforts in DSM aim at only physical layer performance whereas the true end user experience depends on what they see at the application rather than the physical layer. Upper layer performance metrics like throughput and delay may be much more important to improve the user satisfaction. To that end, we provide a framework to study upper layer performance by looking at scheduling and DSM together. We show how optimal scheduling can be combined with optimal DSM and provide throughput-optimal scheduling algorithms which require only polynomial complexity. We furthermore present extentions that significantly improve delay performance by using the specific structure of the underlying problem.

Modern DSL networks suffer from crosstalk between different lines in the same cable bundle. By carefully choosing the transmit power spectra, the impact of crosstalk can be minimized leading to spectacular performance gains. This is also referred to as dynamic spectrum management (DSM). This paper presents three novel low-complexity DSM algorithms with a different level of required message-passing. This level ranges from fully autonomous and distributed to semi-centralized execution. Simulations show good performances compared to existing state-of-the-art DSM algorithms.

The multi-carrier interference channel where interference is treated as additive white Gaussian noise, is a very active topic of research, particularly important in the area of Dynamic Spectrum Management (DSM) for Digital Subscriber Lines (DSL). Here, multiple users optimize their transmit power spectra so as to maximize the total weighted sum of data rates. The corresponding optimization problem is however nonconvex and thus computationally intractable, i.e. a certificate of global optimality requires exponential time complexity algorithms. This paper shows that under certain channel conditions, this nonconvex problem can be solved in polynomial time with a certificate of global optimality. The channel conditions are discussed consisting of different interference models including synchronous and asynchronous DSL transmission. Simulations demonstrate its applicability to realistic DSL scenarios.

In modern DSL networks, crosstalk between different DSL lines in the same cable bundle is a major source of performance degradation. By balancing the transmit power spectra, also referred to as multi-user power control, the impact of crosstalk can be minimized leading to spectacular performance gains. In this paper a novel low-complexity spectrum balancing algorithm is presented. Its performance is compared to optimal spectrum balancing for multiple-user scenarios and it is seen to yield similar results but with a huge reduction in complexity. Moreover, by the use of a spectrum management center and limited message-passing the algorithm can be executed in a distributed fashion, which is a great asset in current DSL networks.

Crosstalk is a major source of performance degradation in modern xDSL systems. Optimal Spectrum Balancing (OSB) is an algorithm that mitigates the effect of crosstalk by allocating optimal transmit spectra to all interfering DSL modems. Unfortunately, its complexity grows exponentially with the number of lines in the binder. For multiple user scenarios this becomes computationally intractable. This paper presents a branch and bound approach to OSB. The proposed branch and bound operations require almost no computation keeping the total computational complexity low. Simulations show enormous complexity reductions, especially for a large number of users.

In modern DSL systems, multi-user crosstalk is a major source of performance degradation. Optimal spectrum balancing (OSB) is a centralized algorithm that optimally allocates the available transmit power over frequencies, thereby mitigating the effect of crosstalk. OSB uses Lagrange multipliers to enforce constraints that are coupled over frequencies. However, finding the optimal Lagrange multipliers can become complex when more than two users are considered. This paper presents a number of properties of the Lagrange multipliers which lead to an efficient search algorithm. Simulations show that the required number of Lagrange multiplier evaluations is independent of the number of users and much smaller compared to the number of evaluations of currently known search algorithms

Optimal spectrum balancing (OSB) is a centralized algorithm that optimally allocates transmit power over frequencies in a multi-user DSL environment where crosstalk is a major factor limiting performance. By using a dual decomposition, OSB decouples the spectrum management problem over frequencies. This results in per-tone optimization problems that are solved with an exhaustive search. This exhaustive search, however, has an exponential complexity in the number of users. For scenarios with several users this often becomes computationally intractable. In this paper, this complexity is reduced by limiting the possible power loadings on each tone to on/off loading with an adjustable on-level. This leads to a simple OSB algorithm with manageable complexity, simple flat transmit spectra and only minor performance degradation

In modern DSL systems, crosstalk is a major source of performance degradation. Crosstalk cancellation schemes have been proposed to mitigate the effect of crosstalk. However, the complexity of crosstalk cancellation grows with the square of the number of lines in the binder. Fortunately, most of the crosstalk originates from a limited number of lines on a limited number of tones. As a result, a fraction of the complexity of full crosstalk cancellation suffices to cancel most of the crosstalk. The challenge is then to determine which crosstalk to cancel on which tones, given a certain complexity constraint. This paper presents an algorithm based on a dual decomposition to optimally solve this problem. The proposed algorithm naturally incorporates rate constraints and the complexity of the algorithm compares favourably to a known resource allocation algorithm, where a multi-user extension is made to incorporate the rate constraints.