Wiener Design of Adaptation Algorithms with Time-invariant Gains.

IEEE Transactions on Signal Processing, vol. 50, August 2002, pp 1895-1907.
  © IEEE

Mikael Sternad, , Uppsala University
Lars Lindbom, , Ericsson Infotech and
Anders Ahlén , Uppsala University

Presentation slides (pdf).

A brief version of the paper,
Iterative Wiener Design of Adaptation Laws with Constant Gains
by A. Ahlén, M. Sternad and L. Lindbom, is published at
IEEE International Conference on Acoustics, Speech and Signal Processing,
Salt Lake City, May 7-11 2001, pp. 3861-3864. © IEEE

Outline:

When tracking time-varying parameters of linear regression models, LMS is one of the simplest adaptation laws, while Kalman algorithms are the most powerful linear estimators. A third, intermediate, alternative is proposed here: The integration of the instantaneous gradient vector used in LMS is generalized to a linear time-invariant filter. Well-tuned filters provide estimates with an appropriate amount of coupling and inertia, resulting in high performance at low computational complexity.

We will here present a novel Wiener optimization of the structure and the gains of such adaptation laws, while Part II presents results for the analysis of stability, performance and convergence in MSE.

The paper includes an example on tracking of time-varying radio channels in a 2 by 2 MIMO system. The difficult problem of accurately tracking time-varying radio channels in IS-136 cellular systems was an original motivating application. Here, LMS and RLS adaptation provide inadequate performance while the use of Kalman algorithms has so far been precluded, due to their computational complexity. An early version of the proposed algorithm has successfully been used on IS 136 1900MHz channels and a case study on this application can be found in a related paper.

Abstract:

A design method that extends LMS adaptation by including general time-invariant filters is presented. The aim is to track time-varying parameters of linear regression models, in situations where the regressors are stationary or have slowly time-varying properties.

The structure and gain of the adaptation law is optimized for time-variations modeled as vector-ARIMA processes. The method can systematically use such prior information to provide filtering, prediction or fixed lag smoothing estimates for arbitrary lags. A linear time-invariant filter that operates on the instantaneous gradient vector is optimized with respect to the steady-state parameter error covariance matrix. Compared to Kalman estimators, the channel tracking performance becomes nearly the same in mobile radio applications, while the complexity is much lower.

The design method is based on a novel transformation of the adaptation problem into a Wiener filter design problem. The filter works in open loop for slow parameter variations while a time-varying closed loop is important for fast variations, where the filter design is performed iteratively.

The general form of the solution at each iteration is obtained by a bilateral Diophantine polynomial matrix equation and a spectral factorization. For white gradient noise, the Diophantine equation has a closed form solution. Further structural constraints result in very simple design equations.

Related publications:

Analysis of stability and performance, for slow and fast variations.

The Wiener LMS adaptation algorithm, a special case with low complexity.

A Case Study on IS-136 channels.

PhD Thesis by Lars Lindbom.

Licenciate Thesis by Lars Lindbom, on averaged Kalman designs (KLMS)
and on deterministic sinusoid modelling of fading channels.

Conference paper (IFAC Como 2001) on averaged robust design for uncertain fading models.

Sources:

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Conference version (ICASSP 2001): Postscript, 111K ; Pdf, 317K

Paper (final version): Postscript, 390K ; Pdf, 446K

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Technical Report R001, September 2000:
Tracking of Time-varying Systems.
Part I: Wiener Design of Adaptation Algorithms with Time-invariant Gains.

Postscript, 353K ; Pdf, 331K