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This paper presents a novel Reed-Solomon codes based transmission scheme called RS-SC-CP. While RS-SC-CP is essentially a Reed-Solomon (RS) coded single carrier with cyclic prefix (SC-CP) system, a filter bank representation of the RS code is used. This filter bank representation unveils a DFT synthesis bank, just as in a traditional Orthogonal Frequency Division Multiplexing (OFDM) system (allbeit in a finite field). Therefore, RS-SC-CP is topologically equivalent with OFDM. As such, the RS-SC-CP system inherits the advantages of an SC-CP system over a traditional OFDM system like a low Peak to Average Power Ratio (PAPR). But, more importantly, it allows us to use a novel equalization technique that resembles a traditional OFDM equalizer. The equalizer of an RS-SC-CP receiver is split into two stages: the first stage encompasses a partial equalization in the complex field, which ensures that the residual channel response has integer coefficients. It is calculated using a Minimum Mean Square Error (MMSE) criterion. The residual ISI is removed by a Galois field equalizer in the second stage, posterior to the RS decoding removing the noise. Finally, the performance of the RS-SC-CP system is further evaluated by simulations showing the performance gain of the RS-SC-CP system compared to a traditional coded OFDM or Single Carrier with Cyclic Prefix (SC-CP) scheme. Index Terms--Reed-Solomon code, critically subsampled filter bank, single-carrier with cyclic prefix system.

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. Index Terms--MIMO systems, optimization methods.

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. Index Terms--Crosstalk cancellation, digital subscriber lines (DSL).

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. Index Terms--Digital subscriber line (DSL), dual decomposition, dynamic spectrum management (DSM), interference channel, nonconvex optimization.

A time-domain equalizer (TEQ) is inserted in discrete multitone (DMT) receivers to impose channel shortening. Many algorithms have been developed to initialize this TEQ, but none of them really optimizes the bitrate. We present a truly bitrate-maximizing TEQ (BM-TEQ) cost function that is based on an exact formulation of the subchannel signal-to-noise ratio as a function of the TEQ taps. The performance of this BM-TEQ comes close to the performance of the per-tone equalizer. Index Terms--Asymmetric digital subscriber line (ADSL), discrete multitone (DMT), equalization, time-domain equalizer (TEQ).

A new echo cancellation structure for discrete multitone systems is presented where each used tone has its own per-tone echo canceller in addition to a per-tone equalizer, which provides an alternative to current employed time domain and time/frequency domain approaches. The per-tone approach enables us to optimize the signal-to-noise ratio for each tone separately by solving a minimum mean-square error problem for each tone, with implicit so-called joint shortening. Complexity during data transmission is compared for time domain, time/frequency domain, and per-tone echo cancellation. Structures with reduced complexity are derived for an interpolated and a decimated rate setup. Finally, simulation results for an asymmetric digital subscriber line setting demonstrate improved performance over time domain (or time/frequency domain) echo cancellation. Index Terms--Discrete multitone (DMT), echo cancellation.

Per-tone equalization has recently been proposed as an alternative receiver structure for discrete multitone-based systems improving upon the well-known structure based on time-domain equalization. Fast initialization of all the equalizer coefficients has been identified as an open problem. In this letter, a recursive initialization scheme based on recursive least squares with inverse updating is presented for the per-tone equalizers. Simulation results show convergence with an acceptably small number of training symbols. Complexity calculations are made for per-tone equalization and for the case where tones are grouped. It is demonstrated with an example that in the latter case, initialization complexity becomes sufficiently low and comparable to complexity during data transmission. Index Terms--Asymmetric digital subscriber line (ADSL), discrete multitone (DMT), equalization, recursive least squares (RLS).

In this paper, an efficient computational scheme is proposed to calculate the symbol mean and variance from bit a priori information, when a so-called multilinear mapping is employed. The multilinear mapping is exploited to reduce the number of the terms needed for the calculation of the symbol mean and variance. Index Terms--MMSE, iterative detection, turbo receivers.

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]

An alternative receiver structure is presented for discrete multitone-based systems. The usual structure consisting of a (real) time-domain equalizer in combination with a (complex) 1-tap frequency-domain equalizer (FEQ) per tone, is modified into a structure with a (complex) multitap FEQ per tone. By solving a minimum mean-square-error problem, the signal-to-noise ratio is maximized for each individual tone. The result is a larger bit rate while complexity during data transmission is kept at the same level. Moreover, the per tone equalization is shown to have a reduced sensitivity to the synchronization delay. Index Terms--ADSL, discrete multitone, equalization.

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]

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. [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 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. [ABSTRACT FROM PUBLISHER]

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]

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. [ABSTRACT FROM PUBLISHER]

In this paper, an efficient computational scheme is proposed to calculate the symbol mean and variance from bit a priori information, when a so-called multilinear mapping is employed. The multilinear mapping is exploited to reduce the number of the terms needed for the calculation of the symbol mean and variance. [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]

Orthogonal spreading codes play an essential role in code-division multiple-access (CDMA) systems by eliminating multiple-access interference (MAI). In this paper, a novel orthogonal spreading code has been proposed for spectrally-encoded (SE) CDMA, a.k.a., spread-time (ST) CDMA with arbitrary pulse shape. It has been shown that it is possible to retain the orthogonality of the code in the presence of tail truncation by time windowing and in a general multipath fading channel in which users experience different frequency selectivity just by modifying the user codewords. Simulation results show that the proposed codes can achieve single user performance when the code length is twice the number of users. [ABSTRACT FROM AUTHOR]