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

  • Zhi-Quan LuoEmail author
  • Jong-Shi Pang
Open Access
Research Article
Part of the following topical collections:
  1. Advanced Signal Processing for Digital Subscriber Lines


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 


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Copyright information

© Luo and Pang 2006

Authors and Affiliations

  1. 1.Department of Electrical and Computer EngineeringUniversity of MinnesotaMinneapolisUSA
  2. 2.Department of Mathematical Sciences and Department of Decision Sciences and Engineering SystemsRensselaer Polytechnic InstituteTroyUSA

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