# Implementation of Method of Minimizing the Side Lobe Level of Autocorrelation Functions of Signals With Nonlinear Frequency Modulation

## Keywords:

nonlinear frequency modulation, autocorrelation function, minimization the side lobes level## Abstract

An important problem that is solved during the creation of new and modernization of existing radar equipment is to ensure the maximum range of detection of air targets, which requires increasing the radiated power while maintaining the required range resolution. Since the generating devices, which are now widely used as semiconductor elements, have limited peak power, the required energy is emitted by increasing the duration of the sensing radio pulse, and the requirements for resolution are met by using so-called complex signals, the product of the spectrum width of which and their duration (signal base) is greater than one.

One of the types of complex signals is multifragment signals with nonlinear frequency modulation, which, unlike the well-known linear frequency modulated signals, have a significantly lower peak side lobes level of autocorrelation functions, but the value of this level depends significantly on the frequency and time parameters of the signal. Finding parameters that minimize the side lobes level of the autocorrelation function of nonlinear frequency modulated signals, which include fragments with linear frequency modulation, is an important scientific and technical problem, the solution of which is the subject of this article. The peculiarity of considering this issue is that, in contrast to the previously proposed implementation of the method of minimizing the side lobes level for mathematical models with a current time change, the paper develops models of shifted time, that is, when the time count of each subsequent signal fragment is shifted to zero. The first section of the paper analyzes the known publications, which shows that the method of minimizing the side lobes level of correlation functions has not been considered before for mathematical models of the shifted. Given this circumstance, the second section of the paper formulates the research objectives. The theoretical justification of a new variant of the proposed method by developing mathematical time-shifted models for two- and three-fragment nonlinear frequency-modulated signals, as well as the modeling results, are presented in Section 3. In further research, it is planned to develop an algorithm for optimizing the time-frequency parameters of signals with nonlinear frequency modulation based on mathematical models of current and shifted time.

## References

**References**

Skolnik M. I. (1981). *Introduction to Radar Systems*. Second Edition. Singapore: McGraw-Hill Book Co., 581 p.

Richards M. A., Scheer J. A., Holm W. A. (2010). *Principles of modern radar*, Vol. I: Basic Principles, Chelsea: Sheridan Books, Inc., 962 p.

Meikle H. (2008). *Modern Radar Systems*. Second Edition. Norwood: Artech House, Inc, 701 p.

Kwok Tom, Kenneth Ranney (2020). Survey of Methodology and Features for Radar Waveform Modulation Classification. *CCDC Army Research Laboratory*, Sensors and Electron Devices Directorate, ARL-TR-9062, 42 p.

Levanon N., and Mozeson E. (2004). *Radar Signals*. Wiley IEEE Press.

Cook C. E., and Bernfeld M. (1993). *Radar Signals: An Introduction to Theory and Appli-cation*. Artech House, 552 p.

Heinzel G., Rüdiger A., and Schilling R. (2002). Spectrum and spectral density estimation by the Discrete Fourier transform (DFT), including a comprehensive list of window functions and some new flat-top windows. Technical Report. *Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut)*, Germany, 84 p.

Valli N. A., Rani D. E., Kavitha C. (2019). Windows for Reduction of ACF Sidelobes of Pseudo-NLFM Signal. *International Journal of Scientific & Technology Research*, Vol. 8, Iss. 10, pp. 2155-2161.

Doerry A. W. (2017). Catalog of Window Taper Functions for Sidelobe Control. Technical Report SAND2017-4042. *U.S. Department of Energy Office of Scientific and Technical Information*, 208 p. doi: 10.2172/1365510.

Swiercz E., Janczak D., and Konopko K. (2022). Estimation and Classification of NLFM Signals Based on the Time-Chirp Representation. *Sensors*, Vol. 22, 8104. doi: 10.3390/s22218104.

Alphonse S., Williamson G. A. (2014). Novel radar signal models using nonlinear frequency modulation. *22nd European Signal Processing Conference (EUSIPCO)*, doi:10.5281/ZENODO.44184.

Song Chen, et al. (2022). A Novel Jamming Method against SAR Using Nonlinear Frequency Modulation Waveform with Very High Sidelobes. *Remote Sensing*, Vol. 14, Iss. 21, 5370. doi:10.3390/rs14215370.

Chukka A. and Krishna B. (2022). Peak Side Lobe Reduction analysis of NLFM and Improved NLFM Radar signal. *Aiub Journal of Science and Engineering (AJSE)*, Vol. 21, Iss. 2, pp. 125-131. doi: 10.53799/ajse.v21i2.440.

Fan Z., Meng H. (2020). Coded excitation with Nonlinear Frequency Modulation Carrier in Ultrasound Imaging System. * IEEE Far East NDT New Technology & Application Forum (FENDT)*. doi:10.1109/FENDT50467.2020.9337517.

Zhao Y., et al. (2020). Non-continuous piecewise nonlinear frequency modulation pulse with variable sub-pulse duration in a MIMO SAR Radar System. *Remote Sensing Letters*, Vol. 11(3), pp. 283-292. doi:10.1080/2150704X.2019.1711237.

Jin G. et al. (2019). An Advanced Nonlinear Frequency Modulation Waveform for Radar Imaging With Low Sidelobe. *IEEE Transactions on Geosciences and Remote Sensing*, Vol. 57, Iss. 8, pp. 6155–6168. doi:10.1109/TGRS.2019.2904627.

Saleh M., Omar S.-M., Grivel E., Legrand P. (2021). A Variable Chirp Rate Stepped Frequency Linear Frequency Modulation Waveform Designed to Approximate Wideband Non-Linear Radar Waveforms. *Digital Signal Processing*, Vol. 109. doi: 10.1016/j.dsp.2020.102884.

Xu, Z.; Wang, X.; Wang, Y. (2022). Nonlinear Frequency-Modulated Waveforms Modeling and Optimization for Radar Applications. *Mathematics*, Vol. 10(21), 3939, pp. 1-11. doi: 10.3390/math10213939.

Kavitha C., Valli N. A., Dasari M. (2020). Optimization of two-stage NLFM signal using Heuristic approach. *Indian Journal of Science and Technology (INDJST)*, Vol. 13(44), pp. 4465-4473. doi:10.17485/IJST/v13i44.1841.

Kostyria O. O., Hryzo A. A., Dodukh O. M., Nariezhnii O. P. & Fedorov, A. V. (2023). Mathematical model of the current time for three-fragment radar signal with non-linear frequency modulation. *Radio Electronics, Computer Science, Control*, Vol. 3(63), pp. 17-26. doi: 10.15588/1607-3274-2023-3-2.

Kostyria O. O., Hryzo A. A., Dodukh O. M., Lisohorskyi B. А., & Lukianchykov А. А. (2023). Method of minimization sidelobes level autocorrelation functions of signals with non-linear frequency modulation. *Radio Electronics, Computer Science, Control*, Vol. 4(67), pp. 39-48. doi: 10.15588/1607-3274-2023-4-4.

Prakash B. L., Sajitha G., and Rajeswari K. R. (2016). Generation of Random NLFM Signals for Radars and Sonars and their Ambiguity Studies. *Indian Journal of Science and Technology*, Vol. 9, Iss. 29, pp. 1-7. doi:10.17485/ijst/2016/v9i29/93653.

Kurdzo J. M., et al. (2019). A Neural Network Approach for Waveform Generation and Selection with Multi-Mission Radar. * IEEE Radar Conference*, pp. 1-6. doi:10.1109/RADAR.2019.8835803.

Bayındır C. (2015). A Novel Nonlinear Frequency Modulated Chirp Signal for Synthetic Aperture Radar and Sonar Imaging. *Journal of Naval Science and Engineering*, Vol. 11, No. 1, pp.68-81.

Valli N. A., Rani D. E., Kavitha C. (2019). Modified Radar Signal Model using NLFM. *International Journal of Recent Technology and Engineering (IJRTE)*, Vol. 8, Iss. 2S3, pp. 513-516. doi: 10.35940/ijrte.B1091.0782S319.

Jeevanmai R., Rani N. D. (2016). Side lobe Reduction using Frequency Modulated Pulse Compression Techniques in Radar. *International Journal of Latest Trends in Engineering and Technology*, Vol. 7, Iss. 3, pp. 171-179. doi: 10.21172/1.73.524.

Adithyavalli N., Rani D. E., Kavitha C. (2019). An Algorithm for Computing Side Lobe Values of a Designed NLFM function. *International Journal of Advanced Trends in Computer Science and Engineering*, Vol. 8(4), pp. 1026-103. doi:10.30534/ijatcse/2019/07842019.

Galati G., Pavan G., and De Palo F. (2017). Chirp Signals and Noisy Waveforms for Solid-State Surveillance Radars. *Aerospace*, Vol. 4(1), 15, 14 p. doi:10.3390/aerospace4010015.

Leśnik C. (2009). Nonlinear Frequency Modulated Signal Design. *Acta Physica Polonica A*, Optical and Acoustical Methods in Science and Technology, Vol. 116, No. 3, pp. 351-354. doi:10.12693/APhysPolA.116.351.

## Downloads

## Published

## How to Cite

*Visnyk NTUU KPI Seriia - Radiotekhnika Radioaparatobuduvannia*, (95), pp. 16-22. Available at: https://radap.kpi.ua/radiotechnique/article/view/1976 (Accessed: 22April2024).

## Issue

## Section

## License

Copyright (c) 2024 Олександр Костиря, Андрій Гризо, Ірина Хижняк, Андрій Федоров , Андрій Лук'янчиков

This work is licensed under a Creative Commons Attribution 4.0 International License.

Authors who publish with this journal agree to the following terms:

- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).