volume | PIER Journals

Abstract

This study presents a method for generating multiple electromagnetic field minima in specified spatial regions. The relationship between the complex amplitudes of signals at receiving points and those of radiated signals is described using an S-parameter matrix. It is shown that the determination of the complex amplitudes of the radiated signals can be reduced to solving an underdetermined system of linear algebraic equations, which may be unstable because such a system can admit either infinitely many solutions or no solution. To address this issue, an optimization problem is formulated based on minimizing the squared error between the required and obtained electric field distributions. Its solution leads to a new system of linear algebraic equations, to which Tikhonov regularization is applied to ensure the stability and uniqueness of the solution. The proposed approach is validated by mathematical modeling for three electric field configurations, with the complex amplitudes of the radiated signals determined for each configuration. The modeling results confirm the correctness of the theoretical conclusions.

1. Voudoukis, Nikolaos, "Performance analysis, characteristics, and simulation of digital QAM," European Journal of Electrical Engineering and Computer Science, Vol. 1, No. 1, 2017.
doi:10.24018/ejece.2017.1.1.3 Google Scholar

2. Svensson, Arne, "An introduction to adaptive QAM modulation schemes for known and predicted channels," Proceedings of the IEEE, Vol. 95, No. 12, 2322-2336, 2007.
doi:10.1109/jproc.2007.904442 Google Scholar

3. Hansen, R., "Focal region characteristics of focused array antennas," IEEE Transactions on Antennas and Propagation, Vol. 33, No. 12, 1328-1337, 1985.
doi:10.1109/tap.1985.1143539 Google Scholar

4. Iuzvik, Denis and Maksim Stepanov, "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, Vol. 38, No. 18, 2106-2123, 2024.
doi:10.1080/09205071.2024.2425708 Google Scholar

5. Iuzvik, Denis and Maksim Stepanov, "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, Vol. 38, No. 4, 411-427, 2024.
doi:10.1080/09205071.2024.2315063 Google Scholar

6. Schelkunoff, S. A., "A mathematical theory of linear arrays," The Bell System Technical Journal, Vol. 22, No. 1, 80-107, 1943.
doi:10.1002/j.1538-7305.1943.tb01306.x Google Scholar

7. Hansen, Robert C., Phased Array Antennas, John Wiley & Sons, 2009.
doi:10.1002/0471224219

8. Capon, J., "High-resolution frequency-wavenumber spectrum analysis," Proceedings of the IEEE, Vol. 57, No. 8, 1408-1418, 1969.
doi:10.1109/proc.1969.7278 Google Scholar

9. Frost, O. L., "An algorithm for linearly constrained adaptive array processing," Proceedings of the IEEE, Vol. 60, No. 8, 926-935, 1972.
doi:10.1109/proc.1972.8817 Google Scholar

10. Carlson, B. D. and D. Willner, "Antenna pattern synthesis using weighted least squares," IEE Proceedings H (Microwaves, Antennas and Propagation), Vol. 139, No. 1, 11-16, 1992.
doi:10.1049/ip-h-2.1992.0003

11. Lebret, H. and S. Boyd, "Antenna array pattern synthesis via convex optimization," IEEE Transactions on Signal Processing, Vol. 45, No. 3, 526-532, 1997.
doi:10.1109/78.558465 Google Scholar

12. Pino, Marcos R., Rafael G. Ayestarán, Paolo Nepa, and Giuliano Manara, "An overview on synthesis techniques for near-field focused antennas," Recent Wireless Power Transfer Technologies, 2019.
doi:10.5772/intechopen.89600 Google Scholar

13. Ni, Haoran, Mahnoor Anjum, Deepak Mishra, and Aruna Seneviratne, "Energy-efficient near-field beamforming: A review on practical channel models," Energies, Vol. 18, No. 11, 2966, 2025.
doi:10.3390/en18112966 Google Scholar

14. Nepa, Paolo and Alice Buffi, "Near-field-focused microwave antennas: Near-field shaping and implementation," IEEE Antennas and Propagation Magazine, Vol. 59, No. 3, 42-53, 2017.
doi:10.1109/map.2017.2686118 Google Scholar

15. Chou, Hsi-Tseng, Nan-Nan Wang, Hsi-Hsir Chou, and Jing-Hui Qiu, "An effective synthesis of planar array antennas for producing near-field contoured patterns," IEEE Transactions on Antennas and Propagation, Vol. 59, No. 9, 3224-3233, 2011.
doi:10.1109/tap.2011.2161554 Google Scholar

16. Buttazzoni, Giulia, Fulvio Babich, Stefano Pastore, Francesca Vatta, and Massimiliano Comisso, "Gaussian approach for the synthesis of periodic and aperiodic antenna arrays: Method review and design guidelines," Sensors, Vol. 21, No. 7, 2343, 2021.
doi:10.3390/s21072343 Google Scholar

17. Yang, Sung Jun and Young Dam Kim, "An accurate near-field focusing of array antenna based on near-field active element pattern and infinitesimal dipole modeling," IEEE Access, Vol. 9, 143771-143781, 2021.
doi:10.1109/access.2021.3120697 Google Scholar

18. Palmeri, Roberta, Giada Maria Battaglia, Andrea Francesco Morabito, Sandra Costanzo, Francesca Venneri, and Tommaso Isernia, "Fault diagnosis of realistic arrays from a reduced number of phaseless near-field measurements," IEEE Transactions on Antennas and Propagation, Vol. 71, No. 9, 7206-7219, 2023.
doi:10.1109/tap.2023.3293004 Google Scholar

19. Iuzvik, D. and M. Stepanov, "Focusing of the electromagnetic field in several given areas of space," Progress In Electromagnetics Research M, Vol. 113, 11-22, 2022.
doi:10.2528/pierm22070704 Google Scholar

20. Skolnik, M. I., Radar Handbook, 3rd Ed., McGraw-Hill, New York, NY, USA, 2012.

21. Strang, Gilbert, Linear Algebra and Its Applications, 4th Ed., 2006.

22. Gantmakher, F. R., The Theory of Matrices, LitRes, Moscow, Russia, 2016 (in Russian).

23. Ben-Israel, Adi and Thomas N. E. Greville, Generalized Inverses: Theory and Applications, Springer, 2003.

24. Tikhonov, A. N. and V. Y. Arsenin, Solutions of Ill-posed Problems, 1977.

25. Brandwood, D. H., "A complex gradient operator and its application in adaptive array theory," IEE Proceedings F (Communications, Radar and Signal Processing), Vol. 130, No. 1, 11-16, 1983.
doi:10.1049/ip-f-1.1983.0003

Dr. Denis Iuzvik

Professor Maksim Stepanov