Uppsala universitet
On the Use of System Identification
for Design Purposes and Parameter Estimation

Stefano Bigi

Licentiate Thesis, Report UPTEC 95063R, 197pp, April 1995.
Part 1 available as Report UPTEC 95064R 167pp, April 1995

Part 1 of the Thesis available in Pdf.

When digital data are transmitted over dispersive channels, equalizers can be utilized to estimate the transmitted symbols. The theme of Part 1 of the thesis is equalizer design based on short known sequences of training symbols. It investigates the resulting model quality, as well as the use of robust design. Indirect (model-based) strategies are evaluated and compared to the direct adjustment of filter coefficients.

In the first part of the thesis, the use of system identification for the design of a deconvolution estimator is addressed for discrete-time, linear, stable, time-invariant, single-input, single-output systems. A theoretical analysis on suboptimal design solutions in the presence of modeling errors is carried out for the linear deconvolution estimator (LDE) and for the decision feedback equalizer (DFE). A simple expression for the sensitivity of the performance of the Wiener deconvolution estimator with respect to unstructured perturbations of the optimal filter is obtained. The expression seems to be new. For the design of suboptimal filters, the criterion to be considered in order to minimize the loss of performance is obtained as a result.

By means of computer simulations, it is shown that optimal filters of high order can effectively be approximated by suboptimal filters of low-order, with only a small performance degradation. A new principle for the MSE optimal design of DFEs is obtained, which leads to a novel method for suboptimal design. The problem of designing approximate DFEs is clarified and the role played by a constraint on the filter structure can be explained. A filter structure to be used for suboptimal design of DFEs is proposed. Strategies for approximate modeling to serve for LDE and DFE design are investigated and proposed.

An extensive simulation study is carried out to evaluate the theoretical analysis and to draw some general conclusion on differences in performance of various methods for model estimation and filter design. The simulation study provides a basic point of reference for further experiments and indicates directions for further research.

In the second part of the thesis, the problem of estimating continuous-time stochastic processes from discrete-time data is addressed. A direct approach to the parameter estimation is considered. Discrete-time models are parametrized by the continuous-time parameters, using approximations of the differentiation operator. The continuous-time parameters can then be directly estimated, without the use of any transformation as in other approaches. Computationally simple estimator schemes based on an instrumental variable method and on a least-squares method are analyzed, and effective variants are proposed and illustrated by means of computer simulations.

Related publications:
Wiener deconvolution estimator design based on known models (IEEE Trans. ASSP 1989).
Decision Feedback Equalizer design based on exactly known IIR model (IEEE Trans. IT 1990).
Design of robust filters and uncertainty modelling, as described in Automatica 1993.
Robust DFE design, IEEE ICASSP 1993.

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