Uppsala universitet
A Wiener Filtering Approach to the Design of Tracking Algorithms
With Applications in Mobile Radio Communications

Lars Lindbom

PhD Thesis, Uppsala University, 255pp, ISBN 91-506-1126-7, November 1995.

Chapter 1 of the Thesis available in Pdf.

Paper copies of the whole thesis can be obtained from Ylva Johansson, Signals and Systems Group, Uppsala University, Box 534, SE-75121 Uppsala, Sweden.

Adaptation algorithms are used for adjusting the coefficients of models, filters and controllers. When fast parameter changes are required, present-day algorithms such as LMS and RLS are severely challenged. The thesis provides a novel framework for the systematic design of adaptation laws, in which both performance and complexity is taken into account.

A Wiener filtering approach to the design of parameter adaptation algorithms is developed. It constitutes a systematic approach to the tracking of parameters of multivariate linear regression models.

The methodology is founded on the concept of stochastic hypermodeling: The dynamics of the time-varying parameters is assumed to be described by linear stochastic models. It provides simple means for both analysis and synthesis of predictors and smoothers with arbitrary lags. Expressions for the tracking performance are derived for both slow and fast parameter variations. The adaptation schemes offer a unique combination of efficient tracking, low computational complexity and robustness against uncertain hypermodels.

The utility of the proposed class of tracking algorithms is investigated by means of a case study, in which tracking and equalization of a mobile radio channel, specified by the D-AMPS standard (IS-54), is considered. Both indirect and direct decision feedback equalization and Viterbi schemes are considered. It is shown that a hypermodel based algorithm of LMS complexity, called the Wiener least mean squares (WLMS) algorithm, will attain superior performance as compared to what can be obtained by considering LMS tracking.

1. Summary and Introduction
2. Algorithms with Time-Varying Gains
3. Design of Tracking Algorithms with Time-Invariant Gains
4. Analysis: Stability and Performance
5. Analysis of the LMS Algorithm from a Filtering Perspective
6. Modeling of a Mobile Radio Channel
7. Equalization of Mobile Radio Channels
8. A Case Study: D-AMPS

Related publications:
Paper 1 on design of general constant-gain adaptation algorithms.
Paper 2 on analysis of stability and performance.
Paper 3 on the Wiener LMS adaptation algorithm (a special case).
Paper 4 on a case study on IS-136 1900MHz channels.

Licentate Thesis by Lars Lindbom, 1992
Conference paper on the simplest variant, SWLMS, and a channel tracking example.
Conference paper in IEEE ICASSP'93 on an early version of algorithm.
Master Thesis on the use of a fixed grid of algorithms in IS-136 1900MHz.
Deterministic modelling of time-variations in digital mobile radio channels.
PhD Thesis by Kenth Öhrn, May 1996, on robust filtering and Kalman tracking.

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