The Worst-Case Interference in DSL Systems Employing Dynamic Spectrum Management
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The Worst-Case Interference in DSL Systems Employing Dynamic Spectrum Management Mark H. Brady and John M. Cioffi Department of Electrical Engineering, Stanford University, Stanford, CA 94305-9515, USA Received 1 December 2004; Revised 28 July 2005; Accepted 31 July 2005 Dynamic spectrum management (DSM) has been proposed to achieve next-generation rates on digital subscriber lines (DSL). Because the copper twisted-pair plant is an interference-constrained environment, the multiuser performance and spectral compatibility of DSM schemes are of primary concern in such systems. While the analysis of multiuser interference has been standardized for current static spectrum-management (SSM) techniques, at present no corresponding standard DSM analysis has been established. This paper examines a multiuser spectrum-allocation problem and formulates a lower bound to the achievable rate of a DSL modem that is tight in the presence of the worst-case interference. A game-theoretic analysis shows that the rate-maximizing strategy under the worst-case interference (WCI) in the DSM setting corresponds to a Nash equilibrium in pure strategies of a certain strictly competitive game. A Nash equilibrium is shown to exist under very mild conditions, and the rate-adaptive waterfilling algorithm is demonstrated to give the optimal strategy in response to the WCI under a frequency-division (FDM) condition. Numerical results are presented for two important scenarios: an upstream VDSL deployment exhibiting the near-far effect, and an ADSL RT deployment with long CO lines. The results show that the performance improvement of DSM over SSM techniques in these channels can be preserved by appropriate distributed power control, even in worst-case interference environments. Copyright © 2006 M. H. Brady and J. M. Cioffi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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INTRODUCTION
In recent years, increased demands on data rates and competition from other services have led to the development of new high-speed transmission standards for digital subscriber line (DSL) modems. Dynamic spectrum management (DSM) is emerging as a key component in next-generation DSL standards. In DSM, spectrum is allocated adaptively in response to channel and interference conditions, allowing mitigation of interference and best use of the channel. As multiuser interference is the primary limiting factor to DSL performance, the potential for rate improvement by exploiting its structure is substantial. DSM contrasts with current DSL practice, known as static spectrum management (SSM). In SSM, masks are imposed on transmit power spectrum densities (PSDs) to bound the amount of crosstalk induced in other lines sharing the same binder group [1]. As SSM masks are fixed for all loop configurations, they can often be far from optimal or even prudent spectrum usage in typical deployments. Standardized tests for “
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