A method for forming several minima of the electromagnetic field at required points in space
DOI: 10.21293/1818-0442-2026-29-2-16-23
Abstract: Relevance. The article considers a method for forming several electromagnetic field minima in the required spatial regions in order to reduce the level of interference for sensitive equipment. Purpose of the study. Developing a method for calculating the complex amplitudes of emitted signals to form several specified regions of reduced electric field amplitude while simultaneously setting field levels at other reception points using Tikhonov regularization. Methods. A system of linear algebraic equations was balanced by introducing Tikhonov regulariza tion, ensuring the uniqueness of the solution. An optimization problem was also formulated to minimize the quadratic residual between the required and obtained electric field distributions. The theoretical results were verified using mathematical modeling. Scientific novelty. The relationship between complex amplitudes at reception points and complex amplitudes of emitted signals was exploited via the S‑parameter matrix. It is noted that calculating the complex amplitudes of emitted may lead to an underdetermined system of linear algebraic equations, resulting in unstable solutions: there may be an infinite number of them, or there may be no solution at all. Results. Three electric field configurations are proposed, and for each of them the complex amplitudes of the emitted signals are determined. The results of mathematical modeling confirmed the obtained theoretical findings. Practical significance. The obtained results can be used to generate the required electromagnetic field distributions with several minima in specified regions of space.
Keywords: antenna arrays, optimization, system of linear equations, electromagnetic field, electric field minima
For citation:
Yuzvik D. A., Stepanov M. A. A method for forming several minima of the electromagnetic field at required points in space. Doklady Tomskogo gosudarstvennogo universiteta sistem upravleniya i radioelektroniki, 2026, vol. 29, no. 2, pp. 16–23. DOI: 10.21293/1818-0442-2026-29-2-16-23
Authors and copyright holders:
- Yuzvik D. A. , Novosibirsk State Technical University
- Stepanov M. A. , Novosibirsk State Technical University
- 1. Voudoukis N. Performance analysis, characteristics, and simulation of digital QAM. European Journal of Electrical Engineering and Computer Science, 2017, vol. 1, no. 1, pp. 1–7.
- 2. Svensson A. An introduction to adaptive QAM modulation schemes for known and predicted channels. Proceedings of the IEEE, 2007, vol. 95, no. 12, pp. 2322–2336.
- 3. Hansen R. Focal region characteristics of focused array antennas. IEEE Transactions on Antennas and Propagation, 2003, vol. 33, no. 12, pp. 1328–1337.
- 4. Iuzvik D., Stepanov M. Formation of the maximum amplitude of the electric field strength using two one-dimensional linear antenna arrays located orthogonal to each other. Journal of Electromagnetic Waves and Applications, 2024, vol. 38, no. 18, pp. 2106–2123.
- 5. Iuzvik D., Stepanov M. Ensuring the maximum amplitude of the electric field strength in given coordinates using a linear antenna array focused on a finite distance. Journal of Electromagnetic Waves and Applications, 2024, vol. 38, no. 4, pp. 411–427.
- 6. Iuzvik D., Stepanov M. Focusing of the electromagnetic field in several given areas of space. Progress in Electromagnetics Research M, 2022, vol. 113, pp. 11–22.
- 7. Skolnik M.I. Radar handbook. 3rd ed. New York, McGraw-Hill, 2008, 1328 p.
- 8. Strang G. Linear algebra and its applications. 4th ed. Belmont, Thomson Brooks/Cole, 2006, 487 p.
- 9. Gantmakher F.R. Teoriya matrits [The theory of matrices], textbook, M., FIZMATLIT, 2010, 560 p. (in Russ.).
- 10. Ben-Israel A., Greville T.N.E. Generalized inverses: theory and applications. 2nd ed. New York, Springer, 2003, 420 p.
- 11. Tikhonov A.N., Arsenin V.Y. Solutions of ill-posed problems. Washington, V.H. Winston & Sons, 1977, 258 p.
- 12. Brandwood D.H. A complex gradient operator and its application in adaptive array theory. IEE Proceedings F – Communications, Radar and Signal Processing, 1983, vol. 130, no. 1, pp. 11–16.
- 13. Ni H. et al. Energy-efficient near-field beamforming: a review on practical channel models. Energies, 2025, vol. 18, no. 11, art. no. 2966.
- 14. Buttazzoni G. et al. Gaussian approach for the synthesis of periodic and aperiodic antenna arrays: method review and design guidelines. Sensors, 2021, vol. 21, no. 7, art. no. 2343.
- 15. Yang S.J., Kim Y.D. An accurate near-field focusing of array antenna based on near-field active element pattern and infinitesimal dipole modeling. IEEE Access, 2021, vol. 9, pp. 143771–143781.
- 16. Palmeri R. et al. Fault diagnosis of realistic arrays from a reduced number of phaseless near-field measurements. IEEE Transactions on Antennas and Propagation, 2023, vol. 71, no. 9, pp. 7206–7219.
- 17. Kumar A., Ansari A.Q., Kanaujia B.K., Kishor J., Matekovits L. A review on different techniques of mutual coupling reduction between elements of any MIMO antenna. Part 2: Metamaterials and many more. Radio Science, 2021, vol. 56, no. 3, pp. 1–22.
- 18. Mandal S., Ghosh C.K. Mutual coupling reduction in a patch antenna array based on planar frequency selective surface structure. Radio Science, 2022, vol. 57, art. no. e2021RS007392.
Last issue
Editorial office address
Executive Secretary of the Editor’s Office
Editor’s Office: 40 Lenina Prospect, Tomsk, 634050, Russia
Phone / Fax: + 7 (3822) 701-582
Executive Secretary of the Editor’s Office
Editor’s Office: 40 Lenina Prospect, Tomsk, 634050, Russia
Phone / Fax: + 7 (3822) 51-21-21 / 51-43-02
Subscription for updates
