Abstract
In this paper, we investigate the problem of joint detection and estimation of the duration of an arbitrary waveform. The main problem is the nondifferentiability of the logarithm of the likelihood ratio functional and, consequently, the need to use the mathematical apparatus of Markov processes to find the characteristics of noise immunity. A solution to the Fokker – Planck – Kolmogorov equation with time-dependent coefficients is proposed. After that, simulation of the algorithm was carried out. Based on the simulation results, a comparison was made between the theoretically obtained dependences and those obtained during the experiment, as well as with the dependence for a completely known signal. The case of signal detection in the absence of information about the signal shape is also considered, while assuming that the signal has a rectangular shape. At the end, numerical results are presented, and the further direction of research is determined.
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References
Trifonov, A.P., Korchagin, Yu.E., Linvinov, E.V.: Quasi likelihood detection of the signal with unknown amplitude and duration. [Trifonov A.P., Korchagin Yu.E., Linvinov E.V. Kvazipravdopodobnoe obnarujenie signalov s neizvestnymi amplitudoi i dlitel’nost’yu]. Vestnik Voronezhskogo gosudarstvennogo universiteta. Seriya: Fizika. Matematika — Proceedings of Voronezh State University. Series: Physics. Mathematics, no. 1, pp. 41–49 (2016)
Akimov, I.S., Bakut, P.A., Bogdanovich, V.A., et al.: Theory of detection of signals. [Akimov I.S., Bakut P.A., Bogdanovich V.A. i dr. Teoriya obnaruzheniya signalov]. Radio and communications, Moscow, 440 p. (1984)
Trifonov, A.P., Korchagin, Yu.E.: Receiving the signal of unknown duration. Izvestiya vysshix uchebnyx zavedenij. Radiofizika Radiophy. Quantum Electr. 45(5), 625–637 (2002)
Kulikov, E.I., Trifonov, A.P.: Parametr estimation of signals in noise. [Kulikov E.I., Trifonov A.P. Ocenka parametrov signalov na fone pomekh]. Sov. Radio, Moscow, 296 p. (1978)
Trifonov, A.P., Korchagin, Yu.E., Bespalova, M.B.: Statistical properties of height and provisions of absolute maximum markov processes Bachelier type. [Trifonov A.P., Korchagin Yu.E., Bespalova M.B. Statisticheskie svoistva vysoty i polojeniya absolyutnogo maksimuma markovskogo sluchainogo processa tipa Bashel’e]. Vestnik Voronezhskogo gosudarstvennogo universiteta. Seriya: Fizika. Matematika — Proceedings of Voronezh State University. Series: Physics. Mathematics, no. 4, pp. 54–65 (2014)
Gelgor, A.L., Gorlov, A.I., Popov, E.A.: General theory of communication. Hypothesis testing. Parameter estimation. Optimal signal reception. [Gel’gor A. L., Gorlov A. I., Popov E. A. Obshchaya teoriya svyazi. Proverka statisticheskih gipotez. Ocenivanie parametrov. Optimal’nyj priyom signalov]. Saint Peterburg State Polytechnic University, St. Peterburg, 227 p. (2013)
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Ilchenko, N., Popov, E. (2022). Software Implementation of the Algorithm for Optimal Joint Estimation and Detection of an Arbitrary Waveform. In: Koucheryavy, Y., Balandin, S., Andreev, S. (eds) Internet of Things, Smart Spaces, and Next Generation Networks and Systems. NEW2AN ruSMART 2021 2021. Lecture Notes in Computer Science(), vol 13158. Springer, Cham. https://doi.org/10.1007/978-3-030-97777-1_33
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DOI: https://doi.org/10.1007/978-3-030-97777-1_33
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