Optimal choice of test signals for linear channel estimation using second order statistics

Braithwaite, Stephen and Addie, Ronald Geoffrey (2014) Optimal choice of test signals for linear channel estimation using second order statistics. Optimization and Engineering, 15 (1). pp. 93-118. ISSN 1389-4420


A time-varying acoustic channel may be estimated by an appropriate inference using the output from a periodic test signal. In this paper it is shown how to do this in a way that takes full account of the past history of the background noise and the past history of the channel. An explicit formula is obtained for the optimal linear estimator that may be used for rapid channel estimation for a given test signal when we know the autocovariance or power spectrum of the interfering noise and the autocovariance of the echo channel variation.

Given this closed formula for the optimal estimator of the channel
impulse response, an efficient method for determining the optimal test signal, subject to a constraint on the test signal power, given the history of the channel and the noise, is developed. We show that if the second order statistics of the channel or the noise are known, then the optimal test signal is not white. The method includes an explicit formula for the optimal test signal given a fixed estimator. A model of channel variation which is realistic while having less complexity than a full second-order statistical model, and therefore is more amenable to robust estimation, is used in the experiments which illustrate the
performance of the optimal test signals and the channel estimation
method. Matrix calculus identities required for the derivation of this expression for the optimal estimator are stated and proved in the Appendixes 1 and 2.

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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: © 2012 Springer Science+Business Media, LLC. Published online 2 June 2012. Permanent restricted access to published version in accordance with the copyright policy of the publisher.
Faculty/School / Institute/Centre: Current - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences
Date Deposited: 21 Jan 2013 06:03
Last Modified: 15 May 2015 01:48
Uncontrolled Keywords: acoustic; echo; autocovariance; channel estimation; Matlab
Fields of Research : 09 Engineering > 0906 Electrical and Electronic Engineering > 090609 Signal Processing
01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010303 Optimisation
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering
A Defence > 81 Defence > 8101 Defence > 810101 Air Force
E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: 10.1007/s11081-012-9193-3
URI: http://eprints.usq.edu.au/id/eprint/22751

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