A new spectral measure of complexity and its capabilities for detecting signals in noise

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Abstract

This article is devoted to the improvement of signal recognition methods based on the information characteristics of the spectrum. A discrete function of the normalized ordered spectrum is established for a single window function included in the DFT. Lemmas on estimates of entropy, imbalance and statistical complexity in processing a time series of independent Gaussian quantities are proved. New concepts of one-dimensional and two-dimensional spectral complexities are proposed. The theoretical results obtained were verified by numerical experiments, which confirmed the effectiveness of the new information characteristic when detecting a signal mixed with white noise at low signal-to-noise ratios.

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About the authors

A. A. Galyaev

Institute of Control Sciences of RAS

Author for correspondence.
Email: galaev@ipu.ru

Corresponding Member of the RAS

Russian Federation, Moscow

V. G. Babikov

Institute of Control Sciences of RAS

Email: babikov@ipu.ru
Russian Federation, Moscow

P. V. Lysenko

Institute of Control Sciences of RAS

Email: pavellysen@ipu.ru
Russian Federation, Moscow

L. M. Berlin

Institute of Control Sciences of RAS

Email: berlin.lm@phystech.edu
Russian Federation, Moscow

References

  1. Amigo J.M. Ordinal methods: Concepts, applications, new developments, and challengesIn memory of Karsten Keller (19612022) / J. M. Amigo, O. A. Rosso // Chaos: An Interdisciplinary Journal of Nonlinear Science. 2023. Vol. 33, no. 8. P. 080401. https://pubs.aip.org/cha/article/33/8/080401/2905538/ Ordinal-methods-Concepts-applications-new.
  2. Distinguishing Noise from Chaos / O.A. Rosso, H.A. Larrondo, M. T. Martin et al. // Phys. Rev. Lett. 2007. Oct. V. 99. P. 154102. https://link.aps.org/doi/10.1103/PhysRevLett.99.154102.
  3. Perkey S. Using Fourier Coefficients and Wasserstein Distances to Estimate Entropy in Time Series / S. Perkey, A. Carvalho, A. Krone-Martins // 2023 IEEE 19th International Conference on e-Science (e-Science). Limassol, Cyprus: IEEE, 2023. P. 1–2. https://ieeexplore.ieee.org/document/10254949/.
  4. Statistical Distributions / C. Forbes, M. Evans, N. Hastings, B. Peacock. 1 edition. Wiley, 2010. https: //onlinelibrary.wiley.com/doi/book/10.1002/9780470627242.
  5. Klenke A. Probability Theory: A Comprehensive Course / A. Klenke. Universitext. London: Springer London, 2014. https://link.springer.com/10.1007/978-1-4471-5361-0.
  6. Галяев А.А. Статистическая сложность как критей рий задачи обнаружения полезного сигнала / А.А. Галяев, П.В. Лысенко, Л.М. Берлин // Автоматика и телемеханика. 2023. С. 121–145.
  7. Distances in Probability Space and the Statistical Complexity Setup / A. M. Kowalski, M. T. Mart’ın, A. Plastino et al. // Entropy. 2011. V. 13. №. 6. P. 1055–1075. http://www.mdpi.com/1099-4300/13/6/1055.
  8. Richards M.A. The Discrete-Time Fourier Transform and Discrete Fourier Transform of Windowed Stationary White Noise / M.A. Richards // Technical Memorandum. 2013. P. 1–24.
  9. Kay S.M. Fundamentals Of Statistical Processing, Volume 2: Detection Theory / S.M. Kay. Prentice-Hall signal processing series. Pearson Education, 2009. https://books.google.ru/books?id=wwmnY9xyt9MC.
  10. Орлов И.Я. Оценка потерь обнаружения сигналов приемнёком с адаптивным порогом на основе метода порядковых статистик / И.Я. Орлов, Е.С. Фитасов // Известия вузов. Радиофизика. 2018. Т. 61. № 7. С. 596–604
  11. Cazelles E. The Wasserstein-Fourier Distance for Stationary Time Series / E. Cazelles, A. Robert, F. Tobar // IEEE Transactions on Signal Processing. 2021. V. 69. P. 709–721. https://ieeexplore.ieee.org/document/9303405/.
  12. Berlin L.M. Comparison of Information Criteria for Detection of Useful Signals in Noisy Environments / L.M. Berlin, A.A. Galyaev, P.V. Lysenko // Sensors. 2023. V. 23. № 4. https://www.mdpi.com/1424-8220/23/4/2133.

Supplementary files

Supplementary Files
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2. Fig. 1. Graphs of the dispersion of a random variable for different values of .

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3. Fig. 2. Explanation of Lemmas 1 and 2. (a) Ordered spectrum and discrete distribution of one realization of a frame of length . (b) The same distributions, horizontal axis on logarithmic scale (standard deviations are shown).

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4. Fig. 3. Dependence of mathematical expectations and standard deviations of entropy and the difference criterion on (illustration of Lemma 3 and Lemma 4). (a) Entropy (b) Imbalance

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5. Fig. 4. Histograms of information characteristics for the average dB value obtained for the signal-noise mixture implementations. (a) Histogram of the distribution of values (b) Histogram of the distribution of values

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6. Fig. 5. ROC curves of information characteristics for the average value of dB, obtained for the realizations of the signal-noise mixture. (a) ROC curve for (b) ROC curve for

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7. Fig. 6. Dependence on .

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