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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]

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]

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]

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]

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]

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]