On the Use of System Identification
for Design Purposes and Parameter Estimation
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 Postscript :
In Pdf 6.2M.
Paper copies of the whole thesis can be obtained from
Signals and Systems Group, Uppsala University,
Box 528, SE-75120 Uppsala, Sweden.
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
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
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.
design, IEEE ICASSP 1993.