A nonconvergent example for the iterative water-filling algorithm

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2011, 1(1): 147-150. doi: 10.3934/naco.2011.1.147

A nonconvergent example for the iterative water-filling algorithm

Simai He ^1, , Min Li ^2, , Shuzhong Zhang ^2, and Zhi-Quan Luo ^3,

1.	Department of Management Sciences, City University of Hong Kong, Kowloon, Hong Kong., China
2.	Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong, China, China
3.	Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455, United States

Received August 2010 Revised November 2010 Published February 2011

Abstract
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Iterative Water-filling Algorithm (IWFA) is a well-known distributed multi-carrier power control method for multi-user communication. It was empirically observed (and conjectured) to be convergent under all channel conditions. In this paper, we present an example showing that IWFA can oscillate, therefore disproving the conjecture.

Keywords: multi-user communication system., Iterative water-filling algorithm.

Mathematics Subject Classification: Primary: 91A10; Secondary: 65K0.

Citation: Simai He, Min Li, Shuzhong Zhang, Zhi-Quan Luo. A nonconvergent example for the iterative water-filling algorithm. Numerical Algebra, Control & Optimization, 2011, 1 (1) : 147-150. doi: 10.3934/naco.2011.1.147

References:

[1]	S. T. Chung, S. J. Kim, J. Lee and J. M. Cioffi, A game-theoretic approach to power allocation in frequency-selective gaussian interference channels,, in, (2003). Google Scholar
[2]	R. Gohary, Y. Huang, Z. Q. Luo and J. S. Pang, A generalized iterative water-filling algorithm for distributed power control in the presence of a jammer,, IEEE Transactions on Signal Processing, 57 (2009), 2660. doi: 10.1109/TSP.2009.2014275. Google Scholar
[3]	S. Hayashi and Z. Q. Luo, Spectrum management for interference-limited multiuser communication systems,, IEEE Transactions on Information Theory, 55 (2009), 1153. doi: 10.1109/TIT.2008.2011433. Google Scholar
[4]	S. Haykin, Cognitive radio: brain-empowered wireless communications,, IEEE Journal Selected Areas in Communications, 23 (2005), 201. doi: 10.1109/JSAC.2004.839380. Google Scholar
[5]	Z. Q. Luo and J. S. Pang, Analysis of iterative waterfilling algorithm for multiuser power control in digital subscriber lines,, EURASIP Journal on Applied Signal Processing, (2006). doi: 10.1155/ASP/2006/24012. Google Scholar
[6]	G. Scutari, D. Palomar and S. Barbarossa, Optimal linear precoding/multiplexing for wideband multipoint-to-multipoint systems based on game theory-part I: Nash equilibria,, IEEE Transactions on Signal Processing, 56 (2008), 1230. doi: 10.1109/TSP.2007.907807. Google Scholar
[7]	G. Scutari, D. P. Palomar and S. Barbarossa, Optimal linear precoding/multiplexing for wideband multipoint-to-multipoint systems based on game theory-part II: algorithms,, IEEE Transactions on Signal Processing, 56 (2008), 1250. doi: 10.1109/TSP.2007.907808. Google Scholar
[8]	S. Shamai and B. M. Zaidel, Enhancing the Cellular Downlink Capacity via Co-Processing at the Transmitting End,, in, (2001), 1745. Google Scholar
[9]	N. Yamashita and Z. Q. Luo, A nonlinear complementarity approach to multi-user power control for digital subscriber lines,, Optimization Methods and Software, 19 (2004), 633. doi: 10.1080/1055678042000218975. Google Scholar
[10]	W. Yu, G. Ginis and J. M. Cioffi, Distributed multi-user power control for digital subscriber lines,, IEEE Journal on Selected Areas in Communications, 20 (2002), 1105. doi: 10.1109/JSAC.2002.1007390. Google Scholar
[11]	W. Yu and R. Lui, Dual methods for nonconvex spectrum optimization of multicarrier systems,, IEEE Transcations of Commucations, 54 (2006), 1310. doi: 10.1109/TCOMM.2006.877962. Google Scholar

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References:

[1]	S. T. Chung, S. J. Kim, J. Lee and J. M. Cioffi, A game-theoretic approach to power allocation in frequency-selective gaussian interference channels,, in, (2003). Google Scholar
[2]	R. Gohary, Y. Huang, Z. Q. Luo and J. S. Pang, A generalized iterative water-filling algorithm for distributed power control in the presence of a jammer,, IEEE Transactions on Signal Processing, 57 (2009), 2660. doi: 10.1109/TSP.2009.2014275. Google Scholar
[3]	S. Hayashi and Z. Q. Luo, Spectrum management for interference-limited multiuser communication systems,, IEEE Transactions on Information Theory, 55 (2009), 1153. doi: 10.1109/TIT.2008.2011433. Google Scholar
[4]	S. Haykin, Cognitive radio: brain-empowered wireless communications,, IEEE Journal Selected Areas in Communications, 23 (2005), 201. doi: 10.1109/JSAC.2004.839380. Google Scholar
[5]	Z. Q. Luo and J. S. Pang, Analysis of iterative waterfilling algorithm for multiuser power control in digital subscriber lines,, EURASIP Journal on Applied Signal Processing, (2006). doi: 10.1155/ASP/2006/24012. Google Scholar
[6]	G. Scutari, D. Palomar and S. Barbarossa, Optimal linear precoding/multiplexing for wideband multipoint-to-multipoint systems based on game theory-part I: Nash equilibria,, IEEE Transactions on Signal Processing, 56 (2008), 1230. doi: 10.1109/TSP.2007.907807. Google Scholar
[7]	G. Scutari, D. P. Palomar and S. Barbarossa, Optimal linear precoding/multiplexing for wideband multipoint-to-multipoint systems based on game theory-part II: algorithms,, IEEE Transactions on Signal Processing, 56 (2008), 1250. doi: 10.1109/TSP.2007.907808. Google Scholar
[8]	S. Shamai and B. M. Zaidel, Enhancing the Cellular Downlink Capacity via Co-Processing at the Transmitting End,, in, (2001), 1745. Google Scholar
[9]	N. Yamashita and Z. Q. Luo, A nonlinear complementarity approach to multi-user power control for digital subscriber lines,, Optimization Methods and Software, 19 (2004), 633. doi: 10.1080/1055678042000218975. Google Scholar
[10]	W. Yu, G. Ginis and J. M. Cioffi, Distributed multi-user power control for digital subscriber lines,, IEEE Journal on Selected Areas in Communications, 20 (2002), 1105. doi: 10.1109/JSAC.2002.1007390. Google Scholar
[11]	W. Yu and R. Lui, Dual methods for nonconvex spectrum optimization of multicarrier systems,, IEEE Transcations of Commucations, 54 (2006), 1310. doi: 10.1109/TCOMM.2006.877962. Google Scholar

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