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Robust approaches to remote calibration of a transmitting array

Besson, Olivier and Bidon, Stéphanie and Larue de Tournemine, Cécile Robust approaches to remote calibration of a transmitting array. (2010) Signal Processing, vol. 90 (n° 5). pp. 1373-1381. ISSN 0165-1684

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Official URL: http://dx.doi.org/10.1016/j.sigpro.2009.09.008

Abstract

We consider the problem of estimating the gains and phases of the RF channels of a M-element transmitting array, based on a calibration procedure where M orthogonal signals are sent through M orthogonal beams and received on a single antenna. The received data vector obeys a linear model of the type y ¼ AFg þ n where A is an unknown complex scalar accounting for propagation loss and g is the vector of unknown complex gains. In order to improve the performance of the least-squares (LS) estimator at low signal to noise ratio (SNR), we propose to exploit knowledge of the nominal value of g, viz g. Towards this end, two approaches are presented. First, a Bayesian approach is advocated where A and g are considered as random variables, with a non-informative prior distribution for A and a Gaussian prior distribution for g. The posterior distributions of the unknown random variables are derived and a Gibbs sampling strategy is presented that enables one to generate samples distributed according to these posterior distributions, leading to the minimum mean-square error (MMSE) estimator. A second approach consists in solving a constrained least-squares problem in which h ¼ Ag is constrained to be close to a scaled version of g. This second approach yields a closed-form solution, which amounts to a linear combination of g and the LS estimator. Numerical simulations show that the two new estimators significantly outperform the conventional LS estimator, especially at low SNR.

Item Type:Article
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National des Etudes Spatiales - CNES
Université de Toulouse > Ecole Nationale de l'Aviation Civile - ENAC
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT
Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE
Other partners > Rockwell Collins (FRANCE)
Other partners > Thales (FRANCE)
Other partners > Telecom ParisTech (FRANCE)
Other partners > Direction Générale de l’Aviation Civile - DGAC (FRANCE)
Laboratory name:
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Deposited By: Olivier Besson

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