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  • Research Article
  • Open Access

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

EURASIP Journal on Advances in Signal Processing20062006:024012

  • Received: 3 December 2004
  • Accepted: 22 July 2005
  • Published:


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.


  • Nash Equilibrium
  • Nash
  • Linear Complementarity Problem
  • Linear Convergence
  • Contraction Property

Authors’ Affiliations

Department of Electrical and Computer Engineering, University of Minnesota, 200 Union Street SE, Minneapolis, MN 55455, USA
Department of Mathematical Sciences and Department of Decision Sciences and Engineering Systems, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA


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