Single-channel doppler frequency detector of coherent synchronously fluctuating signal packets under gaussian noise

Igor Tsevukh; Anastasia Sakovich

doi:10.15222/TKEA2025.1-2.03

Igor Tsevukh Odesа Polytechnic National University, Odesа, Ukraine https://orcid.org/0000-0002-8906-710X
Anastasia Sakovich Odesа Polytechnic National University, Odesа, Ukraine https://orcid.org/0009-0000-3681-9956

DOI: https://doi.org/10.15222/TKEA2025.1-2.03

Keywords: likelihood ratio, sufficient statistics, synchronous fluctuations, correlated and uncorrelated noise, improvement index, additive mixture of noise

Abstract

The need to further simplify the systems for detecting useful signals against a background of complex noises calls for the development of simple algorithms subject to certain restrictions on the detector structure and the type of input signal.
This article presents the developed optimal detection algorithm invariant to Doppler phase shifts of the signal for the class of single-channel Doppler frequency detectors of a Gaussian signal against the background of an additive mixture of uncorrelated and correlated Gaussian noises and under restrictions on synchronous fluctuations of pulses in a packet. The authors prove that the synthesized algorithm is optimal according to the criterion of the likelihood ratio averaged over the signal phase φс , as well as according to the criterion of the maximum of the “detection quality indicator” averaged over φс when solving the problem of detecting a Gaussian signal that fluctuates synchronously under Gaussian noise. The authors prove that the synthesised algorithm is optimal according to the criterion of the signal phase-averaged likelihood ratio,
A comparative analysis of the efficiency of the developed algorithm with the efficiency of the optimal multi-channel algorithm for a completely defined signal and with the potential efficiency of the algorithm forming the Hotelling statistics for various spectral-correlation parameters of the additive mixture of correlated and uncorrelated noise, both in terms of probabilistic characteristics — the probability of correct detection at a given probability of false alarm depending on the signal / uncorrelated noise ratio at the input of the system, and in terms of the "improvement index", which is the fraction of the signal/noise ratio at the output of the nonlinear system to the signal/noise ratio at its input, averaged over all possible radial velocities of the target. The research established the parameters of the signal and the additive mixture of uncorrelated and correlated noise for which the potential efficiency of the developed algorithm turns out to be higher than the efficiency of the algorithm implementing the known Hotelling statistics.
The obtained results allow us to determine the theoretical limit of improvement of real systems of this class and directions of search for new systems for practical application. In particular, they can be used to analyse the efficiency in designing coherent-pulse radar systems for detecting signals of moving targets against the background of an additive mixture of uncorrelated and correlated noises.

References

Skolnik M. I. Radar Handbook. New York: McGraw — Hill, 2008, 1352 p.

Melvin W. L., Scheer J. A. Principles of Modern Radar: Advanced Techniques. New York : SciTech Publishing, IET, Edison, 2013, 846 p.

Richards M. A. Fundamentals of Radar Signal Processing, Second Edition. New York : McGraw — Hill Education, 2014, 618 p.

Diao P.S., Alves T., Poussot B., Azarian S. A review of radar detection fundamentals. IEEE Aerospace and Electronic Systems Magazine, 2024, vol. 39, no. 9, pp. 4–24, https://doi.org/10.1109/MAES.2022.3177395

Besson O., Chaumette E., Vincent F. Adaptive detection of a Gaussian signal in Gaussian noise, 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), Cancun, Mexico, 2015, pp. 117–120, https://doi.org/10.1109/CAMSAP.2015.7383750

Liu W., Liu J., Hao C. et al. Multichannel adaptive signal detection: Basic theory and literature review. Science China: Information Sciences, 2022, vol. 65, 121301. https://doi.org/10.1007/s11432-020-3211-8

Zhou Z., Wei G., Liu X. et al. Noise and Gaussian clutter background descending dimensional subspace signal detector, 2023 IEEE SENSORS, Vienna, Austria, 2023, pp. 1–4, https://doi.org/10.1109/SENSORS56945.2023.10324948

Dulek B. On GLRT-based detection of one-sided composite signal in unimodal noise, IEEE Transactions on Aerospace and Electronic Systems, 2023, vol. 59, no. 1, pp. 695–700. https://doi.org/10.1109/TAES.2022.3188595

Chen C., Xu W., Pan Y. et al. A nonparametric approach to signal detection in non-Gaussian noise, IEEE Signal Processing Letters, 2022, vol. 29, pp. 503–507. https://doi.org/10.1109/LSP.2022.3143031

Chmelov V. O., Tereshchenko О. V., Oliinyk M. V. Decorrelation method for passive interference signals in the selection system of slow-moving targets, Visnyk of Vinnytsia Polytechnical Institute, 2024, no. 2, pp. 109–115. https://doi.org/10.31649/1997-9266-2024-173-2-109-115 (Ukr)

Altunin S., Bondariev A., Maksymiv I. Simulation of artillery ballistic station, 2024 IEEE 17th International Conference on Advanced Trends in Radioelectronics, Telecommunications and Computer Engineering (TCSET), Lviv, Ukraine, 2024, pp. 68–71, https://doi.org/10.1109/TCSET64720.2024.10755634

Lekhovytskiy D. I., Riabukha V. P., Semeniaka A. V. et al. Protection of coherent pulse radars against combined interferences. 1. Modifications of STSP systems and their ultimate performance capabilities // Radioelectronics and Communications Systems. 2019, vol. 62, no. 7, pp. 311–341. https://doi.org/10.3103/S073527271907001X

Finkelstein M. I. [Osnovy radiolokatsii: Uchebnik dlya vuzov] Basics of Radar, M.: Radio i svyaz', 1983. 536 p. (Rus)

Tsevukh I. V. An algorithm of the gaussian signal-processing in the presence of gaussian interference. Radioelectronics, 1988, no. 12, с. 53–54. (Rus)

Monzingo R. A., Haupt R. L., Miller T. W. Introduction to Adaptive Arrays, 2011, 543 p. https://doi.org/10.1049/SBEW046E

Repin V. G., Tartakovsky G. P. [Statisticheskiy sintez pri apriornoy neopredelennosti i adaptatsiya informatsionnykh sistem] Statistical synthesis under a priori uncertainty and adaptation of information systems Statistical analysis with a priori uncertainty and adaptation of information systems. M.: Sov. radio., 1977, 432 p. (Rus)

Bartenev V. G., Shloma A. M. [On the construction of an adaptive detector of impulse signals against the background of normal noise with unknown correlation properties]. Radiotekhnika, 1978, no. 2, pp. 3–8. (Rus)

Averochkin V. O., Troyanskiy O. V. the hotelling detector using quadrature chennals decorrelation. Proceedings of the Odessa Polytechnic University, 2014, vol. 1(43), pp. 225–229. Available at: https://www.semanticscholar.org/reader/9b30f121a8a42dca536197a559e943f523d33d0f (accessed 26.02.2025)

Proskurin V. I. [Probability distribution of a quadratic functional from a Gaussian random process]. Radiotekhnika i elektronika, 1985, no. 7, pp. 1335–1340. (Rus)

Lekhovytskiy D.I., Flekser P.M., Polishko S.V. On calculation of distribution laws of quadratic forms of random complex Gaussian vectors. Applied Radio Electronics, 2011, vol. 10, no. 4, pp. 456–462. Available at: https://openarchive.nure.ua/server/api/core/bitstreams/9a7b5117-411e-4916-8214-7fbb58ede5ce/content (accessed 26.02.2025) (Rus)

Tsevukh I. V., Sakovich A. A., Tsevukh V. I. Index of improvement of nonlinear single-channel signal detection systems under Gaussian noise. Technology and design in electronic equipment, 2023, no. 1–2, pp. 9–13. http://dx.doi.org/10.15222/TKEA2023.1-2.09 (Ukr)