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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

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

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.
Citation: Simai He, Min Li, Shuzhong Zhang, Zhi-Quan Luo. A nonconvergent example for the iterative water-filling algorithm. Numerical Algebra, Control and 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 "IEEE International Symposium on Information Theory," Yokohama, Japan, 2003.

[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), 2660-2674. doi: 10.1109/TSP.2009.2014275.

[3]

S. Hayashi and Z. Q. Luo, Spectrum management for interference-limited multiuser communication systems, IEEE Transactions on Information Theory, 55 (2009), 1153-1175. doi: 10.1109/TIT.2008.2011433.

[4]

S. Haykin, Cognitive radio: brain-empowered wireless communications, IEEE Journal Selected Areas in Communications, 23 (2005), 201-220. doi: 10.1109/JSAC.2004.839380.

[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), Article ID 24012. doi: 10.1155/ASP/2006/24012.

[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), 1230-1249. doi: 10.1109/TSP.2007.907807.

[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), 1250-1267. doi: 10.1109/TSP.2007.907808.

[8]

S. Shamai and B. M. Zaidel, Enhancing the Cellular Downlink Capacity via Co-Processing at the Transmitting End, in "Proceedings of the 53rd IEEE Vehicular Technology Conference (VTC 01)," Rhodes, Greece, (2001), 1745-1749.

[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), 633-652. doi: 10.1080/1055678042000218975.

[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), 1105-1115. doi: 10.1109/JSAC.2002.1007390.

[11]

W. Yu and R. Lui, Dual methods for nonconvex spectrum optimization of multicarrier systems, IEEE Transcations of Commucations, 54 (2006), 1310-1322. doi: 10.1109/TCOMM.2006.877962.

show all references

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 "IEEE International Symposium on Information Theory," Yokohama, Japan, 2003.

[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), 2660-2674. doi: 10.1109/TSP.2009.2014275.

[3]

S. Hayashi and Z. Q. Luo, Spectrum management for interference-limited multiuser communication systems, IEEE Transactions on Information Theory, 55 (2009), 1153-1175. doi: 10.1109/TIT.2008.2011433.

[4]

S. Haykin, Cognitive radio: brain-empowered wireless communications, IEEE Journal Selected Areas in Communications, 23 (2005), 201-220. doi: 10.1109/JSAC.2004.839380.

[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), Article ID 24012. doi: 10.1155/ASP/2006/24012.

[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), 1230-1249. doi: 10.1109/TSP.2007.907807.

[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), 1250-1267. doi: 10.1109/TSP.2007.907808.

[8]

S. Shamai and B. M. Zaidel, Enhancing the Cellular Downlink Capacity via Co-Processing at the Transmitting End, in "Proceedings of the 53rd IEEE Vehicular Technology Conference (VTC 01)," Rhodes, Greece, (2001), 1745-1749.

[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), 633-652. doi: 10.1080/1055678042000218975.

[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), 1105-1115. doi: 10.1109/JSAC.2002.1007390.

[11]

W. Yu and R. Lui, Dual methods for nonconvex spectrum optimization of multicarrier systems, IEEE Transcations of Commucations, 54 (2006), 1310-1322. doi: 10.1109/TCOMM.2006.877962.

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