V.M. Artyushenko - Dr. Sc. (Eng.), Professor, Head of Department of Information Technology and Management Systems, Technological University (Korolyov, Moscow region) E-mail: artuschenko@mail.ru V.I. Volovach - Dr. Sc. (Eng.), Associate Professor, Head of Department of Information and Electronic Service, Volga Region State University of Service (Togliatti) E-mail: volovach.vi@mail.ru

The statistical characteristics of the mixture of the processed signal and non-Gaussian additive-multiplicative noise are considered and analyzed. It is noted that in real cases, as a rule, observed random processes have non-Gaussian nature of distribution. For the solve problems of synthesis and analysis of electronic systems and devices, it is necessary to adequately choose the mathematical model of the random effects, their probability density function (PDF) and statistical characteristics. Statistical characteristics of the PDF of instantaneous values of the signal under the influence of the multiplicative noise, leading to amplitude and phase distortion are considered. The model PDF of the amplitude (PDFA) of radio waves used for a wide class non-Gaussian signals, particularly for signals having PDFA Rayleigh, Rice and Nakagami. Statistical characteristics of the envelope of the mixture of additive Gaussian noise and the signal under the influence of the multiplicative noise with Nakagami PDF are considered. Such combination is typical for many practically important cases. Statistical characteristics of the envelope of the additive mixture of a deterministic signal and non-Gaussian noise are considered. The expressions of generalized conditional and unconditional PDF of the envelope of the additive mixture are given. The PDFA expression of non-Gaussian signal in the presence of non-Gaussian noise is given. It is determined by three parameters of the depth of signal fluctuations and two noise parameters. The PDFA expression is obtained when deterministic signal amplitude is absent. For these PDFs a family of curves is presented; impact of the distribution parameters on their shape is analyzed. The expression to determine the ν-th initial moments of PDFA is presented. The expressions for PDFA for two frequent cases are obtained and analyzed: Gaussian signal with a Rayleigh PDF of the envelope and the envelope of non-Gaussian noise with Nakagami PDF; PDF of the envelope of noise and the signal, described by the Nakagami distribution. The analysis showed that the statistical characteristics of the PDF of instantaneous values and envelopes of the mixture of the additive noise and the signal influenced by multiplicative noise, have in general case non-Gaussian nature of distribution. It is shown that the PDFA of the mixture of non-Gaussian signal and additive-multiplicative noise is fully determined by the distribution parameters characterizing depth of fluctuations of the signal and additive noise.

 

1. Levin B.R. Teoreticheskie osnovy statisticheskojj radiotekhniki. M.: Radio i svjaz. 1989. 656 s.
2. Tikhonov V.I. Nelinejjnoe preobrazovanie sluchajjnykh processov. M.: Radio i svjaz. 1986. 296 c.
3. Tikhonov V.I. Statisticheskaja radiotekhnika. Izd. 2-e, pererab. i dop. M.: Sov. radio. 1982. 624 s.
4. Falkovich S.E., KHomjakov EH.N. Statisticheskaja teorija izmeritelnykh radiosistem. M.: Sov. radio. 1981. 288 s.
5. Kremer I.JA., Vladimirov V.I., Karpukhin V.I. Modulirujushhie (multiplikativnye) pomekhi i priem radiosignalov / Pod red. I.JA. Kremera. M.: Sov. radio. 1972. 480 s.
6. Vasilev K.K. Priem signalov pri multiplikativnykh pomekhakh. Saratov: Izd-vo Saratovskogo un-ta. 1983. 128 s.
7. Kassam S.A. Signal Detection in Non-Gaussian Noise. New York: Springer Verlag. 1989. 242 r.
8. Akimov P.S., Bakut P.A., Bogdanovich V.A. i dr. Teorija obnaruzhenija signalov / Pod red. P.A. Bakuta. M.: Radio i svjaz. 1984. 440 s.
9. Artjushenko V.M., Volovach V.I. Kvazioptimalnaja diskretnaja demoduljacija signalov na fone korrelirovannykh negaussovskikh fljuktuacionnykh multiplikativnykh pomekh // Radiotekhnika. 2016. № 6. S. 106−112.
10. Artjushenko V.M., Volovach V.I. Kvazioptimalnaja obrabotka signalov na fone uzkopolosnykh korrelirovannykh negaussovskikh pomekh // Radiotekhnika. 2016. № 7. S. 125−132.
11. Valeev V.G., Danilov V.A. Optimalnoe obnaruzhenie signalov na fone negaussovskikh korrelirovannykh radiopomekh // Izvestija VUZov. Ser. Radioehlektronika. 1991. № 7. S. 30−34.
12. Lu N.H., Eisenstein Bruce A. Detection of weak signals in non-Gaussian noise // IEEE Trans. Microwave Theory Tech. November 1981. V. 27. № 6. P. 755−771.
13. Artjushenko V.M., Volovach V.I. Izmerenie informacionnykh parametrov signala v uslovijakh vozdejjstvija additivnykh negaussovskikh korrelirovannykh pomekh // Avtometrija. 2016. T. 52. № 6. S. 22−28.
14. Artjushenko V.M., Volovach V.I. Ispolzovanie ehllipticheski simmetrichnojj modeli plotnosti raspredelenija verojatnosti dlja opisanija negaussovskikh pomekh // Radiotekhnika. 2016. № 6. S. 113−117.
15. Artjushenko V.M., Volovach V.I., Ivanov V.V. Statisticheskie kharakteristiki dlitelnostejj vybrosov ogibajushhikh signalov, otrazhennykh ot protjazhennykh obektov // Radiotekhnika. 2015. № 2. S. 54−61.
16. Artjushenko V.M., Volovach V.I., Ivanov V.V. Statisticheskie kharakteristiki signalov i pomekh radiotekhnicheskikh ustrojjstv blizhnego dejjstvija // Izvestija VUZov. Ser. Priborostroenie. 2014. T. 57. № 7. S. 46−50.
17. Artjushenko V.M., Volovach V.I. Kvazioptimalnaja obrabotka signalov na fone additivnojj i multiplikativnojj negaussovskikh pomekh // Radiotekhnika. 2016. № 1. S. 124−130.
18. Artjushenko V.M., Volovach V.I. Modelirovanie plotnosti verojatnosti signala i additivnogo shuma pri vozdejjstvii multiplikativnykh pomekh // Radiotekhnika. 2016. № 12. S. 28−36.
19. Melitickijj V.A., Akishin N.S., Mikhajjlov A.V. Verojatnostnaja model negaussovskogo signala i ee kharakteristiki // Radiotekhnika. 1983. № 9. S. 49−51.
20. Nakagami M. The m‑distribution-A-general formula of intensity of rapid fading // Proceedings of a Symposium «Statistical Methods in Radio Wave Propagation». Held at the University of California, Los Angeles. 18−20 June 1958. New York: Pergamon Press. 1960. P. 3−36.
21. Pozdnjak S.I., Melitickijj V.A. Vvedenie v statisticheskuju teoriju poljarizacii radiovoln. M.: Sov. radio. 1974. 479 s.
22. Artjushenko V.M., Volovach V.I. Ocenka pogreshnosti vektornogo informacionnogo parametra signala na fone multiplikativnykh pomekh // Radiotekhnika. 2016. № 2. S. 72−82.