• Previous Article
    A derivative-free trust-region algorithm for unconstrained optimization with controlled error
  • NACO Home
  • This Issue
  • Next Article
    Performance evaluation of multiobjective multiclass support vector machines maximizing geometric margins
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 & 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).

[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.

[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.

[4]

S. Haykin, Cognitive radio: brain-empowered wireless communications,, IEEE Journal Selected Areas in Communications, 23 (2005), 201. 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). 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. 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. 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, (2001), 1745.

[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.

[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.

[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.

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, (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. 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. doi: 10.1109/TIT.2008.2011433.

[4]

S. Haykin, Cognitive radio: brain-empowered wireless communications,, IEEE Journal Selected Areas in Communications, 23 (2005), 201. 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). 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. 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. 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, (2001), 1745.

[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.

[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.

[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.

[1]

Radosław Kurek, Paweł Lubowiecki, Henryk Żołądek. The Hess-Appelrot system. Ⅲ. Splitting of separatrices and chaos. Discrete & Continuous Dynamical Systems - A, 2018, 38 (4) : 1955-1981. doi: 10.3934/dcds.2018079

[2]

Lingling Lv, Zhe Zhang, Lei Zhang, Weishu Wang. An iterative algorithm for periodic sylvester matrix equations. Journal of Industrial & Management Optimization, 2018, 14 (1) : 413-425. doi: 10.3934/jimo.2017053

[3]

Fabián Crocce, Ernesto Mordecki. A non-iterative algorithm for generalized pig games. Journal of Dynamics & Games, 2018, 5 (4) : 331-341. doi: 10.3934/jdg.2018020

[4]

Ruiqiang Guo, Lu Song. Optical chaotic secure algorithm based on space laser communication. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1355-1369. doi: 10.3934/dcdss.2019093

[5]

Aiwan Fan, Qiming Wang, Joyati Debnath. A high precision data encryption algorithm in wireless network mobile communication. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1327-1340. doi: 10.3934/dcdss.2019091

[6]

Sébastien Court. Stabilization of a fluid-solid system, by the deformation of the self-propelled solid. Part II: The nonlinear system.. Evolution Equations & Control Theory, 2014, 3 (1) : 83-118. doi: 10.3934/eect.2014.3.83

[7]

Sébastien Court. Stabilization of a fluid-solid system, by the deformation of the self-propelled solid. Part I: The linearized system.. Evolution Equations & Control Theory, 2014, 3 (1) : 59-82. doi: 10.3934/eect.2014.3.59

[8]

Paweł Lubowiecki, Henryk Żołądek. The Hess-Appelrot system. I. Invariant torus and its normal hyperbolicity. Journal of Geometric Mechanics, 2012, 4 (4) : 443-467. doi: 10.3934/jgm.2012.4.443

[9]

Sanming Liu, Zhijie Wang, Chongyang Liu. Proximal iterative Gaussian smoothing algorithm for a class of nonsmooth convex minimization problems. Numerical Algebra, Control & Optimization, 2015, 5 (1) : 79-89. doi: 10.3934/naco.2015.5.79

[10]

Yan Tang. Convergence analysis of a new iterative algorithm for solving split variational inclusion problems. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-20. doi: 10.3934/jimo.2018187

[11]

Xin Li, Ziguan Cui, Linhui Sun, Guanming Lu, Debnath Narayan. Research on iterative repair algorithm of Hyperchaotic image based on support vector machine. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1199-1218. doi: 10.3934/dcdss.2019083

[12]

Pan Zheng, Chunlai Mu, Xuegang Hu. Boundedness and blow-up for a chemotaxis system with generalized volume-filling effect and logistic source. Discrete & Continuous Dynamical Systems - A, 2015, 35 (5) : 2299-2323. doi: 10.3934/dcds.2015.35.2299

[13]

Guangzhou Chen, Guijian Liu, Jiaquan Wang, Ruzhong Li. Identification of water quality model parameters using artificial bee colony algorithm. Numerical Algebra, Control & Optimization, 2012, 2 (1) : 157-165. doi: 10.3934/naco.2012.2.157

[14]

Kien Ming Ng, Trung Hieu Tran. A parallel water flow algorithm with local search for solving the quadratic assignment problem. Journal of Industrial & Management Optimization, 2019, 15 (1) : 235-259. doi: 10.3934/jimo.2018041

[15]

Nicolas Besse, Florent Berthelin, Yann Brenier, Pierre Bertrand. The multi-water-bag equations for collisionless kinetic modeling. Kinetic & Related Models, 2009, 2 (1) : 39-80. doi: 10.3934/krm.2009.2.39

[16]

Sie Long Kek, Mohd Ismail Abd Aziz, Kok Lay Teo, Rohanin Ahmad. An iterative algorithm based on model-reality differences for discrete-time nonlinear stochastic optimal control problems. Numerical Algebra, Control & Optimization, 2013, 3 (1) : 109-125. doi: 10.3934/naco.2013.3.109

[17]

Heping Dong, Deyue Zhang, Yukun Guo. A reference ball based iterative algorithm for imaging acoustic obstacle from phaseless far-field data. Inverse Problems & Imaging, 2019, 13 (1) : 177-195. doi: 10.3934/ipi.2019010

[18]

Ya-Zheng Dang, Zhong-Hui Xue, Yan Gao, Jun-Xiang Li. Fast self-adaptive regularization iterative algorithm for solving split feasibility problem. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-15. doi: 10.3934/jimo.2019017

[19]

Alexander Zeh, Antonia Wachter. Fast multi-sequence shift-register synthesis with the Euclidean algorithm. Advances in Mathematics of Communications, 2011, 5 (4) : 667-680. doi: 10.3934/amc.2011.5.667

[20]

Jiangchuan Fan, Xinyu Guo, Jianjun Du, Weiliang Wen, Xianju Lu, Brahmani Louiza. Analysis of the clustering fusion algorithm for multi-band color image. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1233-1249. doi: 10.3934/dcdss.2019085

 Impact Factor: 

Metrics

  • PDF downloads (5)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]