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T-Comm_Article 7_11_2021

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USING TWO-DIMENSIONAL FAST FOURIER TRANSFORM FOR ESTIMATING SPECTRAL CORRELATION FUNCTION

Timofey Ya. Shevgunov, Moscow Aviation Institute (National Research University), Moscow, Russia, shevgunov@gmail.com
Oksana A. Gushchina, Moscow Aviation Institute (National Research University), Moscow, Russia, shevgunov@gmail.com

Abstract
The paper presents the algorithm for estimating spectral correlation function (SCF) of a wide-sense cyclostationary random process. SCF provides the quantitative representation of the correlation in frequency domain and relates to cyclic autocorrelation function via Fourier transform. The algorithm is based on two-dimensional Fourier transform, which is being applied to the discrete diadic correlation function weighted by a two-dimensional windowing function, chosen rectangular in the direction orthogonal to the current-time axis. This transform can be implemented by means of the fast Fourier transform (FFT) algorithm, which is built-in in a variety of modern mathematical platforms. A pulse-amplitude modulated process masked by the additive stationary Gaussian noise was considered as an example of a random process exhibiting strong cyclostationarity. The numerical simulation where the estimation of spectral correlation function of such process is conducted, and it proved the effectiveness of the proposed algorithm.

Keywords: Cyclostationarity, Cyclic frequency, Spectral correlation function, Spectral correlation density, Two-dimensional FFT, Fast Fourier transform, Pseudo-power

References

  1. Napolitano (2019). Cyclostationary Processes and Time Series: Theory, Applications, and Generalizations. Academic Press. DOI: https://doi.org/10.1016/C2017-0-04240-4.
  2. A. Gardner (1994). Cyclostationarity in communications and signal processing. IEEE Press. 506 p.
  3. Gardner (1986). Measurement of spectral correlation, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 34, no. 5. pp. 1111-1123, DOI: https://doi.org/10.1109/TASSP.1986.1164951.
  4.  Roberts, W.A. Brown, H.H. Loomis (1991). Computationally efficient algorithms for cyclic spectral analysis, IEEE Signal Processing Magazine, vol. 8, no. 2, pp. 38-49, DOI: https://doi.org/10.1109/79.81008.
  5. A. Brown, H.H. Loomis (1993). Digital implementations of spectral correlation analyzers, IEEE Transaction on Signal Processing, vol. 41, no. 2, pp. 703-720 (1993), DOI: https://doi.org/10.1109/78.193211.
  6. Shevgunov, E. Efimov, D. Zhukov (2017). Algorithm 2N-FFT for estimation cyclic spectral density, Electrosvyaz, no. 6, pp. 50-57.
  7. Shevgunov, E. Efimov, D. Zhukov (2018). Averaged absolute spectral correlation density estimator, Proceedings of Moscow Workshop on Electronic and Networking Technologies (MWENT), pp. 1-4 DOI: https://doi.org/10.1109/MWENT.2018.8337271.
  8.  M. Kay, S. L. Marple (1981). Spectrum analysis – A modern perspective, Proceedings of the IEEE, vol. 69, no. 11, pp. 1380-1419, DOI: https://doi.org/10.1109/PROC.1981.12184.
  9. C. Gonzalez, R.E. Woods (2018). Digital Image Processing, 4th ed. Pearson, 1192 p.
  10. J. Marks (2009). Handbook of Fourier Analysis & Its Applications, Oxford University Press, 800 p., DOI: https://doi.org/10.1093/oso/9780195335927.001.0001
  11. Samorodnitsky, M.S. Taqqu (1994). Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance, Chapman and Hall/CRC, 632 p.
  12. Lindgren (2012). Stationary Stochastic Processes: Theory and Applications. Chapman and Hall/CRC, 375 p.
  13. A.H. Zemanian (1987). Distribution Theory and Transform Analysis: An Introduction to Generalized Functions, with Applications, Dover Publications, 387 p.
  14. Lenart (2011). Asymptotic distributions and subsampling in spectral analysis for almost periodically correlated time series, Bernoulli, vol. 17, no. 1, pp. 290–319, DOI: https://doi.org/10.3150/10-BEJ269.
  15. Shevgunov (2019). A comparative example of cyclostationary description of a non-stationary random process, Journal of Physics: Conference Series, vol. 1163, 012037, DOI: https://doi.org/10.1088/1742-6596/1163/1/012037
    16. E. Efimov, T. Shevgunov, Y. Kuznetsov (2018). Time delay estimation of cyclostationary signals on PCB using spectral correlation function, Proceedings of Baltic URSI Symposium, pp. 184–187, DOI: https://doi.org/10.23919/URSI.2018.8406726.

Information about authors:

Timofey Ya. Shevgunov, Ph.D. (candidate of technical sciences), associate professor, Theoretical Radio Engineering department, Moscow Aviation Institute (National Research University) «MAI», Moscow, Russia
Oksana A. Gushchina, Graduate student, Theoretical Radio Engineering department, Moscow Aviation Institute (National Research University) «MAI», Moscow, Russia