Zhurnal Radioelektroniki - Journal of Radio Electronics. eISSN 1689-1719. 2020. No. 7
ContentsFull text in Russian (pdf)
DOI https://doi.org/10.30898/1684-1719.2020.7.12
UDC 621.396.8
Analysis of the influence of fluctuation modulating noise on the statistical characteristics of the linear filter output distribution
V. M. Artyushenko 1, V. I. Volovach 2
1 Technological University, 42, Gagarin Street, Korolev 141070, Russia
2 Volga Region State University of Service, 4, Gagarin Street, Togliatti 445017, Russia
The paper is received on July 15, 2020
Abstract. The statistical characteristics of the signal distribution in the presence of modulating noise at the output of the linear filter are considered and analyzed. Linear circuits carrying out an integral type conversion are considered. It is shown that a signal distorted by stationary modulating noise is non-stationary. The average value and variance of the output signal are determined for the case of the ideal integrator, The convergence of the distribution of the output signal to two types of normal distributions is determined – the type with a non-oscillating second moment and oscillating second moment – in the presence of modulating noise. An analytical expression is obtained for the probability density of the output signal averaged over the period of the carrier frequency; conditions for its convergence are determined. A quantitative estimate was made of the accuracy of distribution approximation of the output signal with a non-oscillating and oscillating second moment under the influence of modulating noise. The case when the modulating noise is purely phase distortion with a normal distribution and a given variance is considered. It is shown that in order for the distribution of a signal distorted by a stationary random modulating noise to be approximated by a non-oscillating (at the second moment) normal distribution, special conditions must be imposed on the statistical characteristics of the noise modulation function. First of all, the relation module of the non-stationary second moment to the stationary one should be much less than unity. The graphs of the error of the cumulative distribution approximation for the signal distorted by a stationary modulating noise with a normal distribution and an oscillating second moment are obtained.
Key words: linear filter, fluctuation modulating noise, amplitude and phase distortions, central and initial moments of distribution, random stationary process.
References
1. Kremer I.Ya., Vladimirov V.I., Karpuhin V.I. Moduliruyushchie (mul'tip-likativnye) pomekhi i priem radiosignalov. [Modulating (multiplicative) noise and receiving radio signals]. Moscow, Sovetskoye Radio Publ. 1972. 480 p. (In Russian)
2. Vasil'ev K.K. Priem signalov pri mul'tiplikativnyh pomekhah. [Signal reception with multiplicative noise]. Saratov, Saratov State University Publ. 1983. 128 p. (In Russian)
3. Akimov P.S., Bakut P.A., Bogdanovich V.A. et al. Teoriya obnaruzheniya signalov. [Signal detection theory]. Moscow, Radio i Svyaz' Publ. 1984. 440 p. (In Russian)
4. Valeev V.G., Danilov V.A. Optimal signal detection against non-Gaussian correlated radio noise, Izv. vysh. uchebn. zavedenij. Radioelektronika – Bulletin of higher educational institutions. Radio electronic., 1991. No.7. P.30-34. (In Russian)
5. Artyushenko V M., Volovach V.I. Estimation of the measurement error of the scalar information parameter of the signal against the background of multiplicative noise. Zhurnal Radioelektroniki - Journal of Radio Electronics, 2016. No.3. Available at http://jre.cplire.ru/jre/mar16/8/text.pdf (In Russian)
6. Artyushenko V. M., Volovach V. I. Identification of the distribution parameters of additive and multiplicative non-Gaussian noise, Avtometriya – Autometry.2017. Vol.53. No.3. P.36-43. (In Russian)
7. Middleton D. An Introduction to Statistical Communication Theory: an IEEE Press Classic Reissure. Wiley-IEEE Press. 1996. 1184 p.
8. Levin B. R. Teoreticheskie osnovy staticheskoj radiotehniki. [Theoretical foundations of radio engineering static]. 3rd ed. Moscow, Sovetskoye Radio Publ. 1989. 656 p. (In Russian)
9. Tihonov V.I. Statisticheskaya radiotekhnika. [Statistical radio engineering]. Moscow, Radio i Svyaz' Publ. 1982. 624 p. (In Russian)
10. Tihonov V.I., Kul'man N.K. Nelinejnaya fil'traciya i kvazioptimal'nyj priem signalov. [Nonlinear filtering and quasi-optimal signal reception]. Moscow, Sovetskoye Radio Publ. 1975. 704 p. (In Russian)
11. Artyushenko V.M., Volovach V.I. Statistical characteristics of the signal distribution at the output of the linear filter in the presence of fluctuation modulating noise. Proceedings of the ÕIII All-Russian conference «Radiolokatsyya i radiosvyaz'» [«Radar and Radio Communication»]. Moscow, Kotelnikov IRE RAS. November 25-27, 2019. P.143-148. (In Russian)
12. Artyushenko V. M., Volovach V. I. Analysis of the effect of multiplicative noise on signal detection against additive noise Proceedings of the ÕIII All-Russian conference «Radiolokatsyya i radiosvyaz'» [«Radar and Radio Communication»]. Moscow, Kotelnikov IRE RAS. November 25-27, 2019. P.149-154. (In Russian)
For citation:
Artyushenko V.M., Volovach V.I. Analysis of the influence of fluctuation modulating noise on the statistical characteristics of the linear filter output distribution. Zhurnal Radioelektroniki - Journal of Radio Electronics. 2020. No. 7. https://doi.org/10.30898/1684-1719.2020.7.12 (In Russian)