American Institute of Mathematical Sciences

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

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

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).   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

[1]

Mohammed Abdulrazaq Kahya, Suhaib Abduljabbar Altamir, Zakariya Yahya Algamal. Improving whale optimization algorithm for feature selection with a time-varying transfer function. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 87-98. doi: 10.3934/naco.2020017
[2]

Hirokazu Ninomiya. Entire solutions of the Allen–Cahn–Nagumo equation in a multi-dimensional space. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 395-412. doi: 10.3934/dcds.2020364
[3]

Shun Zhang, Jianlin Jiang, Su Zhang, Yibing Lv, Yuzhen Guo. ADMM-type methods for generalized multi-facility Weber problem. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020171
[4]

A. M. Elaiw, N. H. AlShamrani, A. Abdel-Aty, H. Dutta. Stability analysis of a general HIV dynamics model with multi-stages of infected cells and two routes of infection. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020441
[5]

Zongyuan Li, Weinan Wang. Norm inflation for the Boussinesq system. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020353
[6]

Neng Zhu, Zhengrong Liu, Fang Wang, Kun Zhao. Asymptotic dynamics of a system of conservation laws from chemotaxis. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 813-847. doi: 10.3934/dcds.2020301
[7]

Craig Cowan, Abdolrahman Razani. Singular solutions of a Lane-Emden system. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 621-656. doi: 10.3934/dcds.2020291
[8]

Abdelghafour Atlas, Mostafa Bendahmane, Fahd Karami, Driss Meskine, Omar Oubbih. A nonlinear fractional reaction-diffusion system applied to image denoising and decomposition. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020321
[9]

Manil T. Mohan. First order necessary conditions of optimality for the two dimensional tidal dynamics system. Mathematical Control & Related Fields, 2020  doi: 10.3934/mcrf.2020045
[10]

Sumit Arora, Manil T. Mohan, Jaydev Dabas. Approximate controllability of a Sobolev type impulsive functional evolution system in Banach spaces. Mathematical Control & Related Fields, 2020  doi: 10.3934/mcrf.2020049
[11]

Helmut Abels, Andreas Marquardt. On a linearized Mullins-Sekerka/Stokes system for two-phase flows. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020467
[12]

Adel M. Al-Mahdi, Mohammad M. Al-Gharabli, Salim A. Messaoudi. New general decay result for a system of viscoelastic wave equations with past history. Communications on Pure & Applied Analysis, 2021, 20 (1) : 389-404. doi: 10.3934/cpaa.2020273
[13]

Yuxin Zhang. The spatially heterogeneous diffusive rabies model and its shadow system. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020357
[14]

Hai Huang, Xianlong Fu. Optimal control problems for a neutral integro-differential system with infinite delay. Evolution Equations & Control Theory, 2020  doi: 10.3934/eect.2020107
[15]

Hao Wang. Uniform stability estimate for the Vlasov-Poisson-Boltzmann system. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 657-680. doi: 10.3934/dcds.2020292
[16]

Yichen Zhang, Meiqiang Feng. A coupled $ p $-Laplacian elliptic system: Existence, uniqueness and asymptotic behavior. Electronic Research Archive, 2020, 28 (4) : 1419-1438. doi: 10.3934/era.2020075
[17]

Youshan Tao, Michael Winkler. Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 439-454. doi: 10.3934/dcds.2020216
[18]

Jianquan Li, Xin Xie, Dian Zhang, Jia Li, Xiaolin Lin. Qualitative analysis of a simple tumor-immune system with time delay of tumor action. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020341
[19]

Denis Bonheure, Silvia Cingolani, Simone Secchi. Concentration phenomena for the Schrödinger-Poisson system in $ \mathbb{R}^2 $. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020447
[20]

Xavier Carvajal, Liliana Esquivel, Raphael Santos. On local well-posedness and ill-posedness results for a coupled system of mkdv type equations. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020382

 Impact Factor: 

Tools

Metrics

  • PDF downloads (34)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences