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Analysis of Iterative Waterfilling Algorithm for Multiuser Power Control in Digital Subscriber Lines

EURASIP Journal on Advances in Signal Processing volume 2006, Article number: 024012 (2006) Cite this article

Abstract

We present an equivalent linear complementarity problem (LCP) formulation of the noncooperative Nash game resulting from the DSL power control problem. Based on this LCP reformulation, we establish the linear convergence of the popular distributed iterative waterfilling algorithm (IWFA) for arbitrary symmetric interference environment and for certain asymmetric channel conditions with any number of users. In the case of symmetric interference crosstalk coefficients, we show that the users of IWFA in fact, unknowingly but willingly, cooperate to minimize a common quadratic cost function whose gradient measures the received signal power from all users. This is surprising since the DSL users in the IWFA have no intention to cooperate as each maximizes its own rate to reach a Nash equilibrium. In the case of asymmetric coefficients, the convergence of the IWFA is due to a contraction property of the iterates. In addition, the LCP reformulation enables us to solve the DSL power control problem under no restrictions on the interference coefficients using existing LCP algorithms, for example, Lemke's method. Indeed, we use the latter method to benchmark the empirical performance of IWFA in the presence of strong crosstalk interference.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Minnesota, 200 Union Street SE, Minneapolis, MN, 55455, USA

    Zhi-Quan Luo

  2. Department of Mathematical Sciences and Department of Decision Sciences and Engineering Systems, Rensselaer Polytechnic Institute, Troy, NY, 12180-3590, USA

    Jong-Shi Pang

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  1. Zhi-Quan Luo
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  2. Jong-Shi Pang
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Correspondence to Zhi-Quan Luo.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Luo, ZQ., Pang, JS. Analysis of Iterative Waterfilling Algorithm for Multiuser Power Control in Digital Subscriber Lines. EURASIP J. Adv. Signal Process. 2006, 024012 (2006). https://doi.org/10.1155/ASP/2006/24012

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  • DOI: https://doi.org/10.1155/ASP/2006/24012

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