Estimation of the phase probability density function based on the solve of the inverse problem
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 26 (2023) no. 3, pp. 287-300 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The article considers the problem of calculating the phase probability density function of a phase-shift keying signal received under conditions of distortion and additive noise. This problem is reduced to an inverse problem, namely, to solving an integral equation of the convolution type. The functions included in the integral equation are analyzed. The case of equiprobable symbols, which is important from a practical point of view, is considered separately. Numerical simulation results are presented.
@article{SJVM_2023_26_3_a4,
     author = {M. L. Maslakov and V. V. Egorov},
     title = {Estimation of the phase probability density function based on the solve of the inverse problem},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {287--300},
     year = {2023},
     volume = {26},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2023_26_3_a4/}
}
TY  - JOUR
AU  - M. L. Maslakov
AU  - V. V. Egorov
TI  - Estimation of the phase probability density function based on the solve of the inverse problem
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2023
SP  - 287
EP  - 300
VL  - 26
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SJVM_2023_26_3_a4/
LA  - ru
ID  - SJVM_2023_26_3_a4
ER  - 
%0 Journal Article
%A M. L. Maslakov
%A V. V. Egorov
%T Estimation of the phase probability density function based on the solve of the inverse problem
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2023
%P 287-300
%V 26
%N 3
%U http://geodesic.mathdoc.fr/item/SJVM_2023_26_3_a4/
%G ru
%F SJVM_2023_26_3_a4
M. L. Maslakov; V. V. Egorov. Estimation of the phase probability density function based on the solve of the inverse problem. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 26 (2023) no. 3, pp. 287-300. http://geodesic.mathdoc.fr/item/SJVM_2023_26_3_a4/

[1] Mardia K.V., “Statistics of directional data”, J. of the Royal Statistical Society: Series B (Statistical Methodology), 37:3 (1975), 349–371 | MR

[2] Mardia K.V., Jupp P.E., Directional Statistics, John Wiley Sons, Inc, Chichester, 2000 | MR

[3] Jammalamadaka S.R., SenGupta A., Topics in Circular Statistics, World Scientific Publishing Co, Singapore, 2001 | MR | Zbl

[4] Santamarina J.C., Fratta D., Discrete Signals and Inverse Problems, John Wiley Sons, Ltd, 2005

[5] Levy B.C., Principles of Signal Detection and Parameter Estimation. New York: Springer, 2008

[6] Barkat M., Signal Detection and Estimation, 2nd ed., Artech House, Inc, Norwood, 2005

[7] Xiong F., Digital Modulation Techniques, Artech House, Inc, Boston, 2006 | Zbl

[8] Tikhonov V.I., Statisticheskaya radiotekhnika, Sovetskoe radio, M., 1966

[9] Digital Communications, 5th ed., McGraw-Hill, New York, 2008

[10] Maslakov M.L., Egorov V.V., “Regulyarizatsiya ryadov Fure s priblizhennymi koeffitsientami dlya zadachi otsenki plotnosti raspredeleniya veroyatnostei faz”, Sib. zhurn. vychisl. matematiki, 25:2 (2022), 157–171 | DOI | MR

[11] Zhuk V.V., Approksimatsiya periodicheskikh funktsii, Izd-vo Leningradskogo un-ta, L., 1982

[12] Gubarev V.V., Algoritmy statisticheskikh izmerenii, Energoatomizdat, M., 1985

[13] Sirota A.A., Metody i algoritmy analiza dannykh i ikh modelirovanie v MATLAB, BKhV-Peterburg, SPb., 2016

[14] Tikhonov A.N., Arsenin V.Ya., Metody resheniya nekorrektnykh zadach, Nauka, M., 1979

[15] Tikhonov A.N., “Ob ustoichivykh metodakh summirovaniya ryadov Fure”, Dokl. AN SSSR, 156:2 (1964), 268–271 | Zbl

[16] Arsenin V.Ya., “Ob optimalnom summirovanii ryadov Fure s priblizhennymi koeffitsientami”, Dokl. AN SSSR, 183:2 (1968), 257–260 | Zbl

[17] Tolstov G.P., Ryady Fure, Nauka. Glavnaya redaktsiya fiziko-matematicheskoi literatury, M., 1980

[18] Lu S., Pereverzev S.V., Regularization Theory for Ill-posed Problems, De Gruyter, Berlin, 2013 | MR | Zbl

[19] Tikhonov A.N., Goncharskii A.V., Stepanov V.V., Yagola A.G., Chislennye metody resheniya nekorrektnykh zadach, Nauka, M., 1990

[20] Harris F.J., “On the use of windows for harmonic analysis with the discrete Fourier transform”, Proc. of the IEEE, 66:1 (1978), 51–83 | DOI

[21] Smit S., Tsifrovaya obrabotka signalov. Prakticheskoe rukovodstvo dlya inzhenerov i nauchnykh rabotnikov, Dodeka-XXI, M., 2012

[22] Taylor F.J., Digital Filters: Principles and Applications with MATLAB, John Wiley Sons, New Jersey, 2012

[23] Lemeshko B.Yu., Lemeshko S.B., Postovalov S.N., Chimitova E.V., Statisticheskii analiz dannykh, modelirovanie i issledovanie veroyatnostnykh zakonomernostei. Kompyuternyi podkhod, Izd-vo NGTU, Novosibirsk, 2011