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# Recursive estimation in time-varying communication systems

thesis

posted on 2023-05-27, 16:00 authored by Nicholson, GrantThis thesis considers applications of minimum mean-square error, recursive estimators to equalization of time-varying digital communication channels. The equalization of the channel is framed as a linear state estimation problem to which the discrete Kalman filter is applied. The resultant equalizer, called the message estimator, yields an unbiased, linear, minimum mean-square error estimate of the message sequence. The message estimator models the channel as a vector, whose elements are the sampled channel impulse response. An adaptive Kalman filter is used in a decision feedback arrangement to estimate on line the channel vector, and so adapt the message estimator to a time-varying channel. A tapped-delay-line equalizer is also investigated for minimum mean-square error estimation of the message sequence. Recursive least squares is modified to adaptively estimate the tap weights of the equalizer on a time-varying channel. Recursive estimators are considered for minimum variance of the tap weights. The recursive least-squares equalizer, as well as a conventional steepest-descent tapped-delay-line equalizer, are compared with the adaptive message estimator. The message estimator and tapped-delay-line equalizer are two different equalization approaches for a minimum mean-square error estimate. The relation between mean-square error and error rate at typical signal-to-noise ratios is discussed. Expressions are developed to describe the amplitude probability distribution of the message estimates for each scheme. The distributions are shown to have similar properties of bias and residual intersymbol interference, yet different error rates. The error rate of the message estimator compares favourably with a transversal equalizer, but is significantly higher than for a decision feedback equalizer of similar complexity. An upper bound on the error rate for the message estimator is derived which is simple to apply. Computer simulation is used to test the proposed adaptive equalizers on a time-varying channel. The convergence of the adaptive message estimator is significantly quicker than for the recursive least-squares equalizer, and an order of magnitude faster than for the steepest-descent equalizer. The degradation in steady-state performance from making the message estimator adaptive is small. The adaptive message estimator should be particularly effective when the channel is rapidly time-varying or the training period is restricted.

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## Publication status

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## Rights statement

Copyright 1978 the author - The University is continuing to endeavour to trace the copyright owner(s) and in the meantime this item has been reproduced here in good faith. We would be pleased to hear from the copyright owner(s). Thesis (M.Eng.Sc.)--University of Tasmania, 1978. Bibliography: leaves 158-163## Repository Status

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