Nonlinear Adaptive Filtering
The classic adaptive filtering algorithms, such as those discussed in the remaining chapters of this book, consist of adapting the coefficients of linear filters in real time. These algorithms have applications in a number of situations where the signals measured in the environment can be well modeled as Gaussian noises applied to linear systems, and their combinations are of additive type. In digital communication systems, most of the classical approaches model the major impairment affecting the transmission with a linear model. For example, channel noise is considered additive Gaussian noise, intersymbol and co-channel interferences are also considered of additive type, and channel models are assumed to be linear frequency selective filters. While these models are accurate, there is nothing wrong with the use of linear adaptive filters 1 to remedy these impairments. However, the current demand for higher-speed communications leads to the exploration of the channel resources beyond the range their models can be considered linear. For example, when the channel is the pair of wires of the telephone system, it is widely accepted that linear models are not valid for data transmission above 4.8 kb/s. Signal companding, amplifier saturation, multiplicative interaction between Gaussian signals, and nonlinear filtering of Gaussian signals are typical phenomena occurring in communication systems that cannot be well modeled with linear adaptive systems.
KeywordsRadial Basis Function Radial Basis Function Network Adaptive Filter Volterra Series Convergence Factor
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- 2.V. J. Mathews and G. L. Sicuranza, Polynomial Signal Processing, John Wiley & Sons, New York, NY, 2000.Google Scholar
- 20.D. Gonzaga, M. L. R. de Campos, and S. L. Netto, “Composite squared-error algorithm for training feedforward neural networks,” Proc. of the 1998 IEEE Digital Filtering and Signal Processing Conference, Victoria, B.C., June 1998.Google Scholar
- 22.A. Papoulis, Probability, Random Variables, and Stochastic Processes, Mc-Graw Hill, New York, NY, 3rd edition, 1991.Google Scholar
- 24.B. Widrow and E. Walach, Adaptive Inverse Control, Prentice Hall, Englewood Cliffs, NJ, 1996.Google Scholar
- 26.F.-L. Luo and R. Unbehauen, Applied Neural Networks for Signal Processing, Cambridge University Press, Cambridge, U.K, 1996.Google Scholar
- 28.L.-X. Wang, Adaptive Fuzzy Systems and Control: Design and Stability Analysis, Prentice Hall, Englewood Cliffs, NJ, 1994.Google Scholar