Jan Vangorp

A low complexity optimal spectrum balancing algorithm for digital subscriber lines

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.

An Efficient Search Algorithm for the Lagrange Multipliers of Optimal Spectrum Balancing in Multi-User XDSL Systems

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

Multiple Access Channel Optimal Spectrum Balancing for Upstream DSL Transmission

Upstream DSL transmission suffers from in-domain crosstalk as well as out-of-domain or alien crosstalk. Here, the use of multi-user receiver signal coordination e.g. generalized decision feedback equalization, can lead to spectacular performance gains. This paper presents a transmission scheme, referred to as MAC-OSB, which focuses on the weighted rate sum capacity by joint receiver signal coordination and transmit spectrum coordination. The proposed scheme incorporates per-user total power constraints, spectral mask constraints and discrete bit or power loading constraints. Furthermore a low-complexity scheme, referred to as MAC-ISB, is presented which performs similar to MAC-OSB. Simulations show large performance gains over existing methods especially for scenarios with significant alien crosstalk

Partial crosstalk cancellation in a multi-user xDSL environment

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.

Convex Relaxation Based Low-Complexity Optimal Spectrum Balancing for Multi-User DSL

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.

A Dual Decomposition Approach to Partial Crosstalk Cancelation in a Multiuser DMT-xDSL Environment

In modern DSL systems, far-end crosstalk is a major source of performance degradation. Crosstalk cancelation schemes have been proposed to mitigate the effect of crosstalk. However, the complexity of crosstalk cancelation grows with the square of the number of lines in the binder. Fortunately, most of the crosstalk originates from a limited number of lines and, for DMT-based xDSL systems, on a limited number of tones. As a result, a fraction of the complexity of full crosstalk cancelation suffices to cancel most of the crosstalk. The challenge is then to determine which crosstalk to cancel on which tones, given a 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 favorably to a known resource allocation algorithm, where a multiuser extension is made to incorporate the rate constraints.

CTH01-1: A Low Complexity Branch and Bound Approach to Optimal Spectrum Balancing for Digital Subscriber Lines

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.

Optimal Spectrum Balancing in Multi-User xDSL Systems With On/Off Power Loading

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

Downstream power backoff in CO/RT-deployed xDSL networks

To gradually expand their networks, operators deploy new xDSL technologies from remote terminals (RTs) 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.