DocumentCode :
1151687
Title :
Maximum likelihood and lower bounds in system identification with non-Gaussian inputs
Author :
Shalvi, Ofir ; Weinstein, Ehud
Author_Institution :
Dept. of Electr. Eng., Tel Aviv Univ., Israel
Volume :
40
Issue :
2
fYear :
1994
fDate :
3/1/1994 12:00:00 AM
Firstpage :
328
Lastpage :
339
Abstract :
We consider the problem of estimating the parameters of an unknown discrete linear system driven by a sequence of independent identically distributed (i.i.d.) random variables whose probability density function (PDF) may be non-Gaussian. We assume a general system structure that may contain causal and noncausal poles and zeros. The parameters characterizing the input PDF may also be unknown. We derive an asymptotic expression for the Cramer-Rao lower bound, and show that it is the highest (worst) in the Gaussian case, indicating that the estimation accuracy can only be improved when the input PDF is non-Gaussian. It is further shown that the asymptotic error variance in estimating the system parameters is unaffected by lack of knowledge of the PDF parameters, and vice verse. Computationally efficient gradient-based algorithms for finding the maximum likelihood estimate of the unknown system and PDF parameters, which incorporate backward filtering for the identification of non-causal parameters, are presented. The dual problem of blind deconvolution/equalization is considered, and asymptotically attainable lower bounds on the equalization performance are derived. These bounds imply that it is preferable to work with compact equalizer structures characterized by a small number of parameters as the attainable performance depend only on the total number of equalizer parameters
Keywords :
equalisers; filtering and prediction theory; identification; linear systems; maximum likelihood estimation; parameter estimation; probability; random processes; Cramer-Rao lower bound; asymptotic error variance; backward filtering; blind deconvolution/equalization; discrete linear system; equalization performance; equalizer parameters; estimation accuracy; gradient-based algorithms; independent identically distributed random variables; maximum likelihood estimate; nonGaussian inputs; noncausal parameters; poles; probability density function; system identification; system parameters; zeros; Blind equalizers; Deconvolution; Filtering algorithms; Linear systems; Maximum likelihood estimation; Parameter estimation; Poles and zeros; Probability density function; Random variables; System identification;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/18.312156
Filename :
312156
Link To Document :
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