# Mathematical Model Algorithm and Experimental Study of Accuracy Measurement of Deviation Frequency of LFM Signal With Low Spectral Power Density

## DOI:

https://doi.org/10.20535/RADAP.2024.97.12-19## Keywords:

autocorrelation algorithm, frequency deviation, a priori uncertainty, energy hidden signal, correlation method, optimal algorithm, radio monitoring, complex signal, broadband signal## Abstract

**Formulation of the problem in general**. Recently, there has been a tendency to increase the share of radio-electronic systems of various purposes (radiolocation, telecommunications, communication, etc.) with an extended spectrum of emissions. Such radio electronic systems use complex types of signals — with pseudo-random reconfiguration of the operating frequency, noise-like, with linear frequency modulation and others. Due to this, the immunity of radio-electronic systems increases and the hidden mode of their operation is ensured (the last factor is important for dual-purpose radio-electronic systems). The above trend gives rise to problematic issues in the field of creating radio monitoring systems (means). The use of broadband signals in radio electronic systems significantly reduces the spectral power density of radio radiation and their energy availability. Detecting such radio emissions, determining the signals used, measuring their parameters and further processing in a situation where there is no a priori information about the radio-electronic systems to be monitored are complex scientific and technical tasks.

**Analysis of recent researches and publications.** An analysis of frequency deviation measurement methods shows that almost all of them can be used only if the signal-to-noise ratio is sufficiently high. If the power spectral density of a signal with linear frequency modulation decreases, approaching the power spectral density of noise, only autocorrelation methods remain effective. They are implemented by autocorrelation frequency discriminators. If signals are detected, the information about which is not known a priori, then against the background of Gaussian stationary noise (interference) these means are ``optimal'' and therefore are widely used for solving statistical problems during the initial processing of information. Taking into account the stated purpose and the main content of the article is a description of an improved functional node for measuring the frequency deviation of a linear-frequency modulated signal with low power spectral density based on the autocorrelation algorithm of a discrete model of signal detection and processing, taking into account methods of reducing the measurement duration, as well as an experimental study of the accuracy of its operation.

**Presenting the main material**. The article proposes a solution rule for the algorithm for measuring the frequency deviation of a linear-frequency-modulated signal with low power spectral density for a discrete model of an autocorrelation receiver with quadrature processing and considers the option of reducing the duration of the stage of determining the frequency deviation of a radio monitoring session. A functional node for measuring the frequency deviation of a linear-frequency-modulated signal with low power spectral density has been synthesized. The algorithm of the procedure for determining the frequency deviation of a linear-frequency-modulated signal has been developed.

**Conclusion**. An improved functional unit for measuring the frequency deviation of a linear-frequency-modulated signal with low power spectral density was synthesized based on the autocorrelation algorithm of a discrete signal detection and processing model. The task of reducing the time for determining the estimation of the deviation of the signal frequency is solved by introducing the function of zeroing the integrators in the quadrature channels of the autocorrelation receiver with quadrature processing when the output signal reaches the threshold value. The maximum inconsistency of the experimental data with the theoretical curves of the root mean square error is about 7%, which indicates a good agreement between the theoretical calculations and the simulation results. The considered structural scheme can be implemented during the development of new means of radio monitoring.

**The perspectives of future researches**. Further research should be directed to the improvement of the structural scheme of the radio monitoring receiver for measuring the duration of the elementary pulse of an a priori unknown linear-frequency-modulated signal of a signal with a low spectral power density.

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*Visnyk NTUU KPI Seriia - Radiotekhnika Radioaparatobuduvannia*, (97), pp. 12-19. doi: 10.20535/RADAP.2024.97.12-19.

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