Nonlinear channel equalizer design using directional evolutionary multi-objective optimization

Abstract

In this paper, a new equalizer learning scheme is introduced based on the algorithm of the directional evolutionary multi-objective optimization (EMOO). Whilst nonlinear channel equalizers such as the radial basis function (RBF) equalizers have been widely studied to combat the linear and nonlinear distortions in the modern communication systems, most of them do not take into account the equalizers’ generalization capabilities. In this paper, equalizers are designed aiming at improving their generalization capabilities. It is proposed that this objective can be achieved by treating the equalizer design problem as a multi-objective optimization (MOO) problem, with each objective based on one of several training sets, followed by deriving equalizers with good capabilities of recovering the signals for all the training sets. Conventional EMOO which is widely applied in the MOO problems suffers from disadvantages such as slow convergence speed. Directional EMOO improves the computational efficiency of the conventional EMOO by explicitly making use of the directional information. The new equalizer learning scheme based on the directional EMOO is applied to the RBF equalizer design. Computer simulation demonstrates that the new scheme can be used to derive RBF equalizers with good generalization capabilities, i.e., good performance on predicting the unseen samples.

Keywords:

• Channel equalization
• RBF network
• Multi-objective optimization
• Evolutionary algorithms
• Gradient descent

Acknowledgements

The authors gratefully acknowledge that part of this work was supported by UK EPSRC. The authors also wish to thank the referees for their valuable comments and helpful suggestions which greatly improved the paper's quality.

Ning Zong received the first degree (B.Eng.) in Industrial Automation from East China Shipbuilding Institute, P.R. China, in 1997 and his Master's degree (M.Eng.) in Control System and Control Engineering from Xi’an JiaoTong University, P.R. China, in 2000. He has also worked as a software engineer in the telecommunication field for almost 3 years (2000–2002). He started his Ph.D. in January 2003 and is now under the supervision of Dr. Xia Hong. His research interest is in the nonlinear system model design and algorithms.

Xia Hong received her university education at the National University of Defense Technology, P.R. China (B.Sc., 1984, M.Sc., 1987), and the University of Sheffield, UK (Ph.D., 1998), all in automatic control. She worked as a research assistant in Beijing Institute of Systems Engineering, Beijing, China from 1987–1993. She worked as a research fellow in the Department of Electronics and Computer Science at the University of Southampton from 1997–2001. She is currently a lecturer at Department of Cybernetics, University of Reading, UK. She is actively engaged in research into data modelling and learning theory, neurofuzzy systems and their applications. Her research interests include system identification, estimation, neural networks, intelligent data modelling and control. She has published over 50 research papers, and coauthored a research book. She was awarded a Donald Julius Groen Prize by IMechE in 1999.