Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Analysis of Iterative Waterfilling Algorithm for Multiuser Power Control in Digital Subscriber Lines | Hindawi Publishing Corporation EURASIP Journal on Applied Signal Processing Volume 2006 Article ID24012 Pages 1-10 DOI ASP 2006 24012 Analysis of Iterative Waterfilling Algorithm for Multiuser Power Control in Digital Subscriber Lines Zhi-Quan Luo1 and Jong-Shi Pang2 1 Department of Electrical and Computer Engineering University of Minnesota 200 Union Street SE Minneapolis MN 55455 USA 2 Department of Mathematical Sciences and Department of Decision Sciences and Engineering Systems Rensselaer Polytechnic Institute Troy NY 12180-3590 USA Received 3 December 2004 Revised 19 July 2005 Accepted 22 July 2005 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. Copyright 2006 Hindawi Publishing Corporation. All rights reserved. 1. INTRODUCTION In modern DSL systems all users share the same frequency .
