Design of pseudo-random discrete signals with fractional power-law angular modulation

P. Yu. Kostenko; V. V. Slobodyanuk; O. V. Shapovalov

doi:10.3103/S0735272721100034

Authors

P. Yu. Kostenko Ivan Kozhedub Kharkiv National Air Force University, Kharkiv, Ukraine https://orcid.org/0000-0002-3382-0684
V. V. Slobodyanuk Ivan Kozhedub Kharkiv National Air Force University, Kharkiv, Ukraine http://orcid.org/0000-0002-8291-8194
O. V. Shapovalov Ivan Kozhedub Kharkiv National Air Force University, Kharkiv, Ukraine http://orcid.org/0000-0002-9744-9431

DOI:

https://doi.org/10.3103/S0735272721100034

Keywords:

pseudo-random discrete signal, angular modulation, ambiguity function

Abstract

The design approach of pseudo-random discrete signals with fractional power-law angular modulation (FM/PM) is considered in the article. These signals as a discrete set of time values with the uniform sample spacing acquire the properties of pseudo-random sequences. The envelope and phase are defined for the constructed signals using the analytical signal concept. It is found that the time discretization of the oscillation representation by the product of two functions, using the WKB-approximation (Wentzel–Kramers–Brillouin) to solve the parametric oscillator equation, violates the condition of its frequency change slowness (physical feasibility of the solution). The appearance mechanism of pseudo-random behavior of discrete signals with the fractional power-law FM/PM is based on the properties of algebraic irrational numbers sequences. The ambiguity and autocorrelation functions of the Fourier spectra of the designed signals are investigated. The designed signals stealthiness is considered, from the point of view of their disguising as noise, based on the calculation of nonparametric BDS statistics (Brock–Dechert–Scheinkman). The BDS statistics values for different durations of the designed signals are estimated. The method to increase the designed signals stealthiness is proposed.

References

S. E. Falkovich, P. Y. Kostenko, Foundations of Statistical Theory of Radio Systems, [in Russian]. Kharkov: NAU KhAI, 2005.

I.-C. Vizitiu, “Sidelobe reduction in the pulse-compression radar using synthesis of NLFM laws,” Int. J. Antennas Propag., vol. 2013, pp. 1–9, 2013, doi: https://doi.org/10.1155/2013/605604.

S. Alphonse, G. A. Williamson, “Evaluation of a class of NLFM radar signals,” EURASIP J. Adv. Signal Process., vol. 2019, no. 1, p. 62, 2019, doi: https://doi.org/10.1186/s13634-019-0658-9.

H. Milczarek, A. Kawalec, “Instantaneous frequency estimation for radar NLFM signal using combined STFT and TFD ridge smoothing technique,” in XII Conference on Reconnaissance and Electronic Warfare Systems, 2019, p. 9, doi: https://doi.org/10.1117/12.2524516.

D. Massaro, R. Ardoino, M. Grazzini, “An efficient processing architecture for range profiling using noise radar technology,” Aerospace, vol. 5, no. 1, p. 4, 2018, doi: https://doi.org/10.3390/aerospace5010004.

S. Prager, D. Hawkins, M. Moghaddam, “Arbitrary nonlinear FM waveform construction and ultra-wideband synthesis,” in IGARSS 2020 - 2020 IEEE International Geoscience and Remote Sensing Symposium, 2020, pp. 7037–7040, doi: https://doi.org/10.1109/IGARSS39084.2020.9323283.

S. Alphonse, G. A. Williamson, “On estimating nonlinear frequency modulated radar signals in low SNR environments,” IEEE Trans. Aerosp. Electron. Syst., vol. 57, no. 3, pp. 1793–1802, 2021, doi: https://doi.org/10.1109/TAES.2021.3050649.

N. Tai, Y. J. Pan, N. C. Yuan, “Quasi-coherent noise jamming to LFM radar based on pseudo-random sequence phase-modulation,” Radioengineering, vol. 24, no. 4, pp. 1013–1024, 2015, doi: https://doi.org/10.13164/re.2015.1013.

M. Kanevskii, V. P. Litvinenko, G. V. Makarov, Stealth Theory Foundations: Textbook, [in Russian]. Voronezh: VGU, 2006.

P. Y. Kostenko, V. V. Slobodyanuk, A. N. Barsukov, “Stealthiness of analytical chaotic signals,” Radioelectron. Commun. Syst., vol. 60, no. 3, pp. 132–140, 2017, doi: https://doi.org/10.3103/S0735272717030050.

P. Y. Kostenko, A. N. Barsukov, “Use of discrete mapping derived from difference scheme of McKay-Glass differential equation for stealth transmission in binary message,” Radioelectron. Commun. Syst., vol. 52, no. 3, pp. 137–141, 2009, doi: https://doi.org/10.3103/S0735272709030042.

I. Gladkova, “Design of frequency modulated waveforms via the zak transform,” IEEE Trans. Aerosp. Electron. Syst., vol. 40, no. 1, pp. 355–359, 2004, doi: https://doi.org/10.1109/TAES.2004.1292174.

A. M. Ridwan, A. Faroqi, H. Nusantara, A. Munir, “DDS-based 13.56MHz sine wave generator for wireless charging system,” in 2018 International Conference on Applied Electromagnetics, Signal Processing and Communication (AESPC), 2018, pp. 1–4, doi: https://doi.org/10.1109/AESPC44649.2018.9033236.

V. K. Ignatjev, A. V. Nikitin, S. V. Yushanov, “About the uniqueness of quasiharmonious representation,” Sci. J. Volgogr. State Univ. Math. Phys., no. 13, pp. 137–150, 2010, uri: https://mp.jvolsu.com/index.php/en/archive-en/150-science-journal-of-volsu-mathematics-physics-2010-13/radio-physics/327-about-the-uniqueness-of-quasiharmonious-representation.

P. Guha, A. G. Choudhury, “Integrable time-dependent dynamical systems: Generalized Ermakov-Pinney and Emden-Fowler equations,” Nonlinear Dyn. Syst. Theory, vol. 14, no. 4, pp. 355–370, 2014.

N. T. Safiullin, S. V. Porshnev, “Comparative analysis of computation the instantaneous frequency with Hilbert transform and direct quadrature,” Comput. Telecommun. Control, no. 5, pp. 18–24, 2011, uri: https://infocom.spbstu.ru/en/article/2011.22.3/.

A. Venkitaraman, S. Chatterjee, P. Händel, “On Hilbert transform, analytic signal, and modulation analysis for signals over graphs,” Signal Process., vol. 156, pp. 106–115, 2019, doi: https://doi.org/10.1016/j.sigpro.2018.10.016.

S. V. Porshnev, “Physical content of concepts ‘envelope’ and «instantaneous frequency of broadband analytical signal,” Electromagn. Waves Electron. Syst., vol. 6, no. 1, pp. 48–55, 2001.

L. Y. Varakin, Theory of Complex Signals, [in Russian]. Moscow: Ripol Classic, 1970.

N. М. Korobov, Trigonometric Sums and Their Applications, [in Russian]. Moscow: Nauka, 1989.

S. B. Gashkov, V. N. Chubarikov, Arithmetic. Algorithms. Computational Complexity, [in Russian]. Moscow: Drofa, 2005.

R. R. Aidagulov, “Uniformity,” E-Scio, no. 3, pp. 1–26, 2019, uri: https://cyberleninka.ru/article/n/ravnomernost.

G. Weil, “On uniform distribution of numbers modulo 1,” in Selected Works, Moscow: Nauka, 1984, pp. 58–93.

V. V. Krasil’shchikov, “The spectrum of one-dimensional quasilattices,” Sib. Math. J., vol. 51, no. 1, pp. 53–56, 2010, doi: https://doi.org/10.1007/s11202-010-0007-6.

Y. N. Gorbunov, G. V. Kulikov, A. V. Shpak, Radar: Stochastic Approach. Moscow: Goryachaya Liniya-Telekom, 2016.

P. Y. Kostenko, K. S. Vasiuta, S. N. Symonenko, “Improving communication security by complicating chaotic process attractor using linear transform with mandelbrot kernel,” Radioelectron. Commun. Syst., vol. 53, no. 12, pp. 636–643, 2010, doi: https://doi.org/10.3103/S0735272710120022.