Analysis of Iterative Waterfilling Algorithm for Multiuser Power Control in 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.
KeywordsNash Equilibrium Nash Linear Complementarity Problem Linear Convergence Contraction Property
- 2.Cherubini G, Eleftheriou E, Olcer S: On the optimality of power back-off methods. American National Standards Institute, ANSI-T1E1.4/235, August 2000Google Scholar
- 3.Cendrillon R, Moonen M, Verliden J, Bostoen T, Yu W: Optimal multiuser spectrum management for digital subscriber lines. Proceedings of IEEE International Conference on Communications (ICC '04), June 2004, Paris, France 1: 1-5.Google Scholar
- 5.Chung ST, Kim SJ, Lee J, Cioffi JM: A game-theoretic approach to power allocation in frequency-selective Gaussian interference channels. Proceedings of IEEE International Symposium on Information Theory (ISIT '03), June–July 2003, Pacifico Yokohama, Kanagawa, Japan 316-316.Google Scholar
- 6.Chung ST: Transmission schemes for frequency selective Gaussian interference channels, Doctral disseration. Department of Electrical Engineering, Stanford University, Stanford, Calif, USA; 2003.Google Scholar