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Title: Applications of nonlinear filters with the linear-in-the-parameter structure
Author: Chng, Eng Siong
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 1995
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In particular, the Volterra and the radical basis function (RBF) expansion techniques are considered to implement the nonlinear filter structures. These approaches, however, will generate filters with very large numbers of parameters. As large filter models require significant implementation complexity, they are undesirable for practical implementations. To reduce the size of the filter, the orthogonal least squares (OLS) algorithm is considered to perform model selection. Simulations were conducted to study the effectiveness of subset models found using this algorithm, and the results indicate that this selection technique is adequate for many practical applications. The other aspect of the OLS algorithm studied is its implementation requirements. Although the OLS algorithm is very efficient, the required computational complexity is still substantial. To reduce the processing requirement, some fast OLS methods are examined. Two major applications of nonlinear filters are considered in the thesis. The first involves the use of nonlinear filters to predict time series with possesses nonlinear dynamics. To study the performance of the nonlinear predictors, simulations were conduced to compare the performance of these predictors with conventional linear predictors. The simulation results confirm that nonlinear predictors normally perform better than linear predictors. Within its study, the application of RBF predictors to time series that exhibit homogeneous nonstationarity is also considered. This type of time series possesses the same characteristic throughout the time sequence apart from local variations of mean and trend. The second application involves the use of filters for symbol-decision channel equalisation. The decision function of the optimal symbol-decision equaliser is first derived to show that it is nonlinear, and that it may be realised explicitly using a RBF filter. Analysis is then carried out to illustrate the difference between the optimum equaliser's performance and that of the conventional linear equaliser. In particular, the effects of delay order on the equaliser's decision boundaries and bit error rate (BER) performance are studied. The minimum mean square error (MMSE) optimisation criterion for training the linear equaliser is also examined to illustrate the sub-optimum nature of such a criterion. To improve the linear equaliser's performance, a method which adapts the equaliser by minimising the BER is proposed. Our results indicate that the linear equalisers performance is normally improved by using the minimum BER criterion. The decision feedback equaliser (DFE) is also examined. We propose a transformation using the feedback inputs to change the DFE problem to a feedforward equaliser problem. This unifies the treatment of the equaliser structures with and without decision feedback.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available