Conducting numerical experiments to evaluate detection characteristics with the aid of a mathematical radar model

The task of detecting and observing targets has always been relevant. One of the most important objectives of radar development is to improve target recognition. There are two ways to achieve this – firstly, the installation of more powerful radar systems, which is very expensive and hard to implement under the conditions of limited space, for example, on airplanes; secondly, the quality of the received signal can be enhanced with the aid of mathematical methods, which allows to considerably save on setting up additional equipment. One of the main problems of recognition is the fact that the number and angular location of targets can be difficult to determine from the signal received by the radar system. This problem can be addressed by employing a wavelet transform. This method enables to overcome the Rayleigh criterion, that makes it possible to obtain an angular super-resolution (to surmount the classical diffraction limit of the spatial resolution of an image focused by a lens that is less than half the radiation wavelength). The article uses a mathematical model of a radar station to present the results of numerical experiments to achieve super-resolution by means of algebraic methods at a significant noise level. We examine the suitability of utilizing different types of wavelets, namely the Haar wavelet, the symmetric Haar wavelet, and the Wave wavelet.

1. Lagovsky B.A., Samokhin A.B., Shestopalov Y.V. Regression Methods of Obtaining Angular Superresolution. 2019 URSI Asia-Pacific Radio Science Conference (AP-RASC). 2019

2. Lagovsky B.A., Samokhin A.B. Stability of algebraic methods for restoring images of sources with increased angular resolution. Elektromagnitnyye volny i elektronnyye sistemy = Electromagnetic Waves and Electronic Systems. 2011;16(4):6–12. (In Russ.)

3. Lagovsky B.A., Samokhin A.B., Samokhina A.S. Formation of images of radar targets with super-resolution by algebraic methods. Uspekhi sovremennoy radioelektroniki = Achievements of Modern Radioelectronics. 2014;8:23–27. (In Russ.)

4. Lagovsky B.A., Сhikina A.G. Regression methods for obtaining superresolution for a group target. Uspekhi sovremennoy radioelektroniki = Achievements of Modern Radioelectronics. 2020;1:69–76. (In Russ.)

5. Lagovsky B.A., Сhikina A.G. Solution of inverse problems of obtaining superresolution based on data symmetrization. Aktual'nye problemy gumanitarnykh i estestvennykh nauk. 2015;4(1):20–23. (In Russ.)

6. Lagovsky B.A. Methods for improving the effective angular resolution of small-sized targets in radio navigation and radar problems. Antenny = Antennas. 2007;9(124):50–55. (In Russ.)

7. Lagovsky B.A., Samokhin A.B. Algebraic methods for image reconstruction of radio sources with increased angular resolution. Elektromagnitnyye volny i elektronnyye sistemy = Electromagnetic Waves and Electronic Systems. 2009;14(9):7–18. (In Russ.)

8. Kozhanova E.R., Zakharov A.A. Application of the modernized French hat wavelet function for approximation of the longitudinal distribution of the magnetic field in magnetic reverse focusing systems. Molodoi uchenyi. 2012;1(9):25–29. (In Russ.)

9. Lagovsky B.A., Shumov I.Y. Restoration of two-dimensional images of radiation sources with super-resolution. Antenny = Antennas. 2013;4:60–65. (In Russ.)

10. Lagovsky B.A. Restoring the image of a group target with digital antenna arrays. Antenny = Antennas. 2011;2(165):40–46. (In Russ.)

11. Holami G., Mehrpourbernety H., Zakeri B. UWB Phased Array Antennas for High Resolution Radars. Proc. of the 2013 International Symposium on Electromagnetic Theory. 2013:532–535.

12. Khan H. A., Edwards D. J., Malik W. Q. Ultra wideband MIMO radar. Proc. IEEE Intl. Radar Conf. Arlington. 2005.

13. Zhou Yuan; Law Choi Look; Xia Jingjing. Ultra low-power UWB-RFID system for precise location-aware applications. 2012 IEEE Wireless Communications and Networking Conference. 2012:154–158.

14. Terrence W. Barrett. History of UWB Radar and Communications: Pioneers and Innovators. Progress in Electromagnetics Symposium (PIERS). 2000.

15. Herman M. A., Strohmer T. High-resolution radar via compressed sensing. IEEE Trans. Signal Processing. 2009;57(6):2275–2284.

16. Bajwa W. U., Gedalyahu K., Eldar Y. C. Identification of Parametric Underspread Linear Systems and Super-Resolution Radar. IEEE Transactions on Signal Processing. 2011;52(5):2548–2561.