Cyclic spectrum power dencity estimation of info-communication signals

Аuthors

Efimov E. N.^1*, Shevgunov T. Y.^**, Kuznetsov Y. V.^2***

1. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia
2. ,

*e-mail: omegatype@gmail.com
**e-mail: shevgunov@gmail.com
***e-mail: kuztetsov@mai-trt.ru

Abstract

The paper introduces cyclic periodogram averaging block algorithm for the estimation of cyclic power spectral density (CPSD) using time-smoothing approach. A brief overview of the cyclostationarity phenomena and the corresponding cyclic characteristic functions are provided; a detailed theoretical description of the proposed algorithm focusing on the task of cyclic power spectral density estimation of the finite length digital infocommunication signals is presented. The structure of the CPSD function on bispectral plane for the case of finite length digital signals is described. The properties of the support region of CPSD on bispectral plane such as resolution element shape and effective width are taken into the consideration in order to avoid significant gaps alongside cyclic frequency axis.

In order to demonstrate the proposed algorithm as well as the advantages of the cyclostationary approach itself, a numerical simulation is carried out. A mixture of two amplitude-modulated signals with wide-sense stationary random processes used as their modulation sequences is chosen for the simulation. The parameters of the simulation such as effective bandwidths of the mixture components and their carrying frequencies are selected in a manner that a significant overlapping in the frequency domain is to occur. The analysis of the estimated cyclic power spectral density as a two-variable function obtained with the proposed algorithm allowed to successfully determine the number of the components in the signal mixture, their carrier frequencies, separated periodograms for each of the components and make the conclusion of the statistical independency of the underlying random processes. The results of the numerical simulation confirm the correct work of the proposed algorithm as well as demonstrate the selective properties of the cyclostationary approach.

Keywords:

cyclostationarity, cyclic spectral power density, nonparametric estimation methods, periodograms, spectral correlation analysis

References

1. Franks L. E. Signal Theory. – Englewood Cliffs, N.J.: Prentice Hall. – 1969.– 318 pp.

2. Gardner W. A., Napolitano A., Paura L. Cyclostationarity: Half a century of research // Signal Processing. – 2006. – Vol. 86, no. 4. – pp. 639–697.

3. Roberts R. S., Brown W. A., Loomis H. H. Computationally efficient algorithms for cyclic spectral analysis // IEEE Signal Processing Magazine. – 1991. – Vol. 8, no. 3. – pp. 38–49.

4. Efimov E.N., Shevgunov T.Ya., Formirovanie ocenki napravlenija prihoda signala s ispolzovaniem iskusstvennyh nejronnyh setej // Trudy MAI. – 2015. – № 82.

5. Efimov E.N., Shevgunov T.Ya., Identifikacija tochechnyh rasseivatelej radiolokacionnyh izobrazhenij s ispolzovaniem nejronnyh setej radialno-bazisnyh funkcij // Trudy MAI. – 2013. – № 68.

6. Bulygin M. L., Mullov K. D., Formirovatel zondirujushhego signala dlja radiolokatora s sintezirovannoj aperturoj // Trudy MAI. – 2015. – № 80.

7. Antoni J., Cyclostationarity by examples // Mechanical Systems and Signal Processing, Elsevier, no. 23, 2009, pp. 987-1036.

8. Martirosov V. E., Alekseev G. A., Kvazikogerentnyj moduljator signala QPSK // Trudy MAI. – 2015. – № 80.

9. Efimov E.N., Shevgunov T.Ya., Ciklostacionarnye modeli radiosignalov s kvadraturnoj amplitudnoj moduljaciej // Elektrosvyaz. – 2016. – № 11. – pp. 65-71.

10. Antciperov V.E., Estimation of renewal point process aftereffect character on the basis of multiscale correlation analysis methods // Journal of Radioelectronics. – № 6, 2015.

11. E. Karami, O. A. Dobre and N. Adnani, Identification of GSM and LTE signals using their second-order cyclostationarity, // 2015 IEEE International Instrumentation and Measurement Technology Conference (I2MTC) Proceedings, Pisa, 2015, pp. 1108-1112.

12. E. Karami, O. A. Dobre, Identification of SM-OFDM and AL-OFDM Signals Based on Their Second-Order Cyclostationarity, // IEEE Transactions on Vehicular Technology, vol. 64, no. 3, pp. 942–953, March 2015.

13. Gardner W., Measurement of spectral correlation // IEEE Trans. on Acoustics, Speech, and Signal Processing. – vol. 34. – no. 5. – 1986. – pp. 1111–1123.

14. Welch P. The use of fast fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms // IEEE Transactions on Audio and Electromagnetics, .– vol. 15. – no. 2. – 1967. – pp. 70-73.

15. Tichonov V.I., Shahtarin B.I., Sizyh V.V., Random processes. Examples and problems. Estimation of signals, their parameters and spectra. Foundation of Information theory. Textbook. – Goryachaya Linia – Telecom. – Moscow. – 2012. – 400 p.

16. Shahtarin B.I., Sizyh V.V., Bulatov A.V., Obnaruzhenie signalov neizvestnoi intensivnosti v gaussovskom shume s neizvestnoi dispersiei (algorithm s obucheniem) // Nauchniy vestnik Moskovskogo Gosudarstvennogo Technicheskogo Universiteta Grazhdanskoy Aviatsii, № 93. – Moscow. – 2005. – P. 36-44.

17. Gardner W.A., Cyclostationarity in Communications and Signal Processing. – IEEE Press, 1994. – 504 p.

18. Marpl-Jnr. S.L. Digital spectral analysis and applications. – M.: Mir, 1990. – 584 p.

19. Shevgunov T.Ya., Efimov E.N., Zhukov D.M., Algoritm 2N-BPF dlja ocenki ciklicheskoj spektral’noj plotnosti moshhnosti // Elektrosvyaz (ISSN 0013-5771), M.: Info-Elektrosvyaz., 2017, № 6, pp. 50–57.

20. Gardner W. A., Statistical Spectral Analysis – A Nonprobabilistic Theory. – Prentice Hall, 1988. – 566 p.

Download