Title:
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Second-order parameter estimation
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Author:
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Villares Piera, Nemesio Javier; Vázquez Grau, Gregorio
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Teoria del Senyal i Comunicacions; Universitat Politècnica de Catalunya. SPCOM - Grup de Recerca de Processament del Senyal i Comunicacions |
Abstract:
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This work provides a general framework for the design of second-order blind estimators without adopting any
approximation about the observation statistics or the a priori
distribution of the parameters. The proposed solution is obtained
minimizing the estimator variance subject to some constraints on
the estimator bias. The resulting optimal estimator is found to
depend on the observation fourth-order moments that can be calculated
analytically from the known signal model. Unfortunately,
in most cases, the performance of this estimator is severely limited
by the residual bias inherent to nonlinear estimation problems.
To overcome this limitation, the second-order minimum variance
unbiased estimator is deduced from the general solution by assuming
accurate prior information on the vector of parameters.
This small-error approximation is adopted to design iterative
estimators or trackers. It is shown that the associated variance
constitutes the lower bound for the variance of any unbiased
estimator based on the sample covariance matrix.
The paper formulation is then applied to track the angle-of-arrival
(AoA) of multiple digitally-modulated sources by means of
a uniform linear array. The optimal second-order tracker is compared
with the classical maximum likelihood (ML) blind methods
that are shown to be quadratic in the observed data as well. Simulations
have confirmed that the discrete nature of the transmitted
symbols can be exploited to improve considerably the discrimination
of near sources in medium-to-high SNR scenarios. |
Abstract:
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Peer Reviewed |
Subject(s):
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-Àrees temàtiques de la UPC::Enginyeria de la telecomunicació::Processament del senyal -Signal processing -Numerical analysis -Simulation -A priori distribution -Angle-of-arrival estimation -Blind estimator -Covariance matrices -direction-of-arrival estimation -Iterative estimator -Iterative methods -Maximum likelihood blind method -Maximum likelihood estimation -Nonlinear estimation -Second-order minimum variance unbiased estimator -Second-order parameter estimation -Signal processing -Small-error approximation -Uniform linear array -Processament del senyal -Anàlisi numèrica -Simulació de sistemes |
Rights:
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Document type:
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Article |
Published by:
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IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
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