Nonparametric method of Doppler frequency estimation taking into account deformation of envelope and center frequency shift of signal distorted by multiplicative interference

Pavlo Kostenko; Valeriy Slobodyanuk

doi:10.3103/S0735272723090017

Authors

Pavlo Kostenko Ivan Kozhedub Kharkiv National Air Force University, Kharkiv, Ukraine https://orcid.org/0000-0002-3382-0684
Valeriy Slobodyanuk Ivan Kozhedub Kharkiv National Air Force University, Kharkiv, Ukraine https://orcid.org/0000-0002-8291-8194

DOI:

https://doi.org/10.3103/S0735272723090017

Keywords:

BDS statistics, Cauchy distribution, BPSK signal, multiplicative interference, estimation of parameters

Abstract

The paper considers a nonparametric method for estimating the Doppler frequency of a broadband signal with code (digital) phase manipulation distorted by multiplicative interference. The estimation of the Doppler frequency, which leads to the deformation of the envelope and shift of carrier frequency, was carried out in the absence of a priori information about the probability density function of the noise component in the model of the received signal (observation). An assumption is made that the noise component is an independent and identically distributed (IID) process with independent and identically distributed random quantities (“white” noise). The objective function (OF) is proposed that uses BDS statistics of discrepancies, i.e., the difference between an observation and the expected signal model, to estimate the Doppler frequency. The OF minimum is adopted as an estimate of the parameter. Quality characteristics of the Doppler frequency estimation are investigated in the case of additive noise when observing a signal with different probability distributions: Gaussian, uniform, logistic, and Cauchy. Special attention is paid to the case when the probability density function of multiplicative interference is characterized by “heavy tails.” The statistical modeling of the Doppler frequency estimation algorithm that implements the numerical minimization of the proposed objective function has been carried out. It is shown that the use of BDS statistics and the proposed objective function based on it allows us to avoid specifying the distribution density of the multiplicative interference when determining the Doppler frequency.

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