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Potential accuracy of estimation of a delay of arrival of radio signals in the presence of a frequency mismatch of signals on the basis of calculation of cross-correlation function of the modified complex envelope signals

Keywords:

K.L. Ovcharenko – Adjunct, Military Space Academy named after A.F. Mozhajskij (St. Petersburg)
E-mail: kostao@ya.ru


Now one of the tasks solved in radio engineering systems is estimation of a delay of arrival of radio signals. In communication systems, navigation and radiolocating estimating of time delay of arrival of signals is carried out by search of a maximum of cross-correlation function. However at practice along with a time delay of arrival of signals there is also a Doppler shift which existence significantly complicates search of a maximum of the cross-correlation function and leads to decline in production of devices of estimation of a delay of arrival of signals.

For the purpose of elimination of aprioristic uncertainty of a frequency mismatch by the author the method of computing and effective estimation of a delay on the basis of calculation of cross-correlation function of the modified complex envelope signals is offered.
In this article dependence of accuracy of search of a time delay of arrival by method of computing and effective estimation from the signal-to-noise ratio is investigated.
For this method the assessment of a delay of arrival corresponds to the provision of a maximum of cross-correlation function of the modified complex envelope signals which search is carried out by decomposition of cross-correlation function in a Taylor series.
Equality to zero mean of white noise allows to draw a conclusion on not shift of dispersion of an assessment of a delay of arrival. Taking into account it dispersion of an assessment of a delay will meet mean of a square of an assessment of the time delay of arrival found method on the basis of calculation of cross-correlation function of the modified complex envelope signals.
Results of imitating modeling in the multi-paradigm numerical computing environment of Matlab have confirmed a correctness of the received analytical dependence.
Thus, the received analytical expression of potential accuracy of a method of computing and effective estimation of a delay of arrival of signals in the presence of a frequency mismatch of signals on the basis of calculation of cross-correlation function of the modified complex envelope signals allows to estimate the lower bound of dispersion of a delay depending on the signal-to-noise ratio for the any kinds of the signals set as analytically, and accepted from a radio channel.

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May 29, 2020

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