Geodesic
Regularization of Fourier series with approximate coefficients for the problem of phase probability density function estimation
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 25 (2022) no. 2, pp. 157-171

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This paper considers the problem of phases probability distribution function estimation for phase-shift-keying signals. The modulating sequence, and, accordingly, the values of the symbols phases, as well as the statistical characteristics of this sequence are unknown. The Fourier coefficients are calculated based on a limited sample for estimation of phases probability distribution function. In this case, the obtained Fourier coefficients are regularized. Application of multiparameter regularization for increasing the estimation accuracy are considered. The numerical simulation results are presented. 
@article{SJVM_2022_25_2_a4,
     author = {M. L. Maslakov and V. V. Egorov},
     title = {Regularization of {Fourier} series with approximate coefficients for the problem of phase probability density function estimation},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {157--171},
     publisher = {mathdoc},
     volume = {25},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2022_25_2_a4/}
}
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M. L. Maslakov; V. V. Egorov. Regularization of Fourier series with approximate coefficients for the problem of phase probability density function estimation. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 25 (2022) no. 2, pp. 157-171. http://geodesic.mathdoc.fr/item/SJVM_2022_25_2_a4/