Publishing House “Akademperiodyka”

National Academy of Sciences of Ukraine

Books Scientific monographs Ukrainian scientific book in a foreign language

Synthesis of Two-Dimensional Non-Equidistant Antenna Arrays Using Special Matrices

Authors:

Yiyang LUO, Cooperative Researcher of the Laboratory for Monitoring and Spectroscopy of O.Ya. Usikov Institute for Radiophysics and Electronics of the National Academy of Sciences of Ukraine, Cooperative Scientist of School of Radiophysics, Biomedical Electronics and Computer Systems, V. N. Karazin Kharkiv National University, Ph.D. degree in Applied Physics and Nanomaterial
ORCID ID: https://orcid.org/0000-0002-3376-5814
Google scholar: https://scholar.google.com/citations?hl=uk&user=-uQphsYAAAAJ&view_op=list_works&sortby=pubdate
ResearchGate: https://www.researchgate.net/profile/Y-Luo-5

 

 

 

 

Vladyslav Ivanovych LUTSENKO, Head of the Laboratory for Monitoring and Spectroscopy of O.Ya. Usikov Institute for Radiophysics and Electronics of the National Academy of Sciences of Ukraine, Doctor of Physical and Mathematical Sciences, Professor
ORCID ID: https://orcid.org/0000-0003-3753-7074
Google scholar: https://scholar.google.com/citations?user=wOYiiGsAAAAJ&hl=ru
ResearchGate: https://www.researchgate.net/profile/V-Lutsenko

 

 

 

 

 

Serhiy Mykolaiovych SHULGA, Dean of School of Radiophysics, Biomedical Electronics and Computer Systems, V. N. Karazin Kharkiv National University, Doctor of Physical and Mathematical Sciences, Senior Researcher, Professor
ORCID ID: http://orcid.org/0000-0002-9392-9366
Google scholar: https://scholar.google.com/citations?user=hl0fcPsAAAAJ&hl=uk&oi=sra
ResearchGate: https://www.researchgate.net/profile/Sergey-Shulga

 

 

 

 

Reviewers:
Yu.F. LOHVINOV, Acting Director of the O. Ya. Usikov Institute for Radiophysics and Electronics of the NAS of Ukraine, Doctor of Physical and Mathematical Sciences, Senior Staff Scientist, Corresponding Member of the NAS of Ukraine
V.V. ZAKHARENKO, Director of the Institute of Radio Astronomy of the NAS of Ukraine, Doctor of Physical and Mathematical Sciences, Senior Staff Scientist, Senior Researcher, Corresponding Member of the NAS of Ukraine
M.M. HOROBETS, Head of the Department of Applied Electrodynamics, Faculty of Radiophysics, Biomedical Electronics and Computer Systems of V.N. Karazin Kharkiv National University, Doctor of Physical and Mathematical Sciences, Professor

Year: 2025
Pages: 128
ISBN: 978-966-360-554-8
Publication Language: English
Publisher: PH “Akademperiodyka”
Place Published: Kyiv

This monograph presents innovative methods for constructing two-dimensional non-equidistant antenna arrays (AAs), particularly designed for radio telescopes operating in the 8–80 MHz range. The work introduces direct and straightforward techniques, emphasizing configurations based on Latin squares and their triangular matrices. These methods ensure full spatial frequency coverage with high rarefaction and minimal lateral radiation. Key contributions include the first use of a Latin square matrix in AA construction, the pioneering combination of circular difference sets and Latin square matrices for planar sparse arrays, and the integration of Latin square and lower triangular matrices in planar sparse array design. The proposed matrix method is more efficient and direct compared to traditional iterative and deletion-based optimization approaches.

This book is intended for scientists and specialists involved in developing remote sensing methods and technologies using radiation from existing ground and space radio engineering systems. It is also valuable for students and educators in radiophysics, offering a comprehensive approach to AA design that could advance both academic study and practical applications in radio astronomy.

Full Text: Synthesis of Two-Dimensional Non-Equidistant Antenna_

REFERENCES:

  1. Rocca, P., Oliveri, G., Mailloux, R.J., Massa, A. (2016). Uncon ventional phased array architectures and design metho dologies. A Review, Proc. of the IEEE. Vol. 104, No. 3. p. 544-560. https://doi.org/10.1109/JPROC.2015.2512389
  2. Ishimaru, A. (1962). Theory of unequally-spaced arrays. IRE Transactions on Antennas and Propagation. Vol. 10. No. 6. p. 691-702. https://doi.org/10.1109/TAP.1962.1137952
  3. Jain, R., Mani, G.S. (2012). Solving “antenna array thinning problem” using genetic algorithm. Applied Computational Intelligence and Soft Computing. Vol. 2012. Article ID 946398. 14 p. https://doi.org/10.1155/2012/946398
  4. Haupt, R.L. (1994). Thinned arrays using genetic algorithms. IEEE Transactions on Antennas and Propagation. Vol. 42. No. 7. p. 993-999. https://doi.org/10.1109/8.299602
  5. Mahanti, G.K., Pathak, N., Mahanti, P.K. (2007). Synthesis of thinned linear antenna arrays with fixed sidelobe level using real-coded genetic algorithm. Progress in Electromagnetics Research. Vol. 75. p. 319-328. http://dx.doi.org/10.2528/PIER07061304
  6. Zhang, L., Jiao, Y.C., Chen, B., Li, H. (2012). Orthogonal genetic algorithm for planar thinned array designs. International Journal of Antennas and Propagation. Vol. 2012. Article ID 319037. 7 p. https://doi.org/10.1155/2012/319037
  7. Goudos, S.K., Sahalos, J.N. (2016). Design of large thinned arrays using different biogeography-based optimization migration models. International Journal of Antennas and Propagation. Vol. 2016. Article ID 5359298. 11 p. https://doi.org/10.1155/2016/5359298
  8. Oliveri, G., Manica, L., Massa, A. (2010). ADS-based guidelines for thinned planar arrays. IEEE Transactions on Antennas and Propagation. Vol. 58. No. 6. p. 1935-1948. https://doi.org/10.1109/TAP.2010.2046858
  9. Jiang, Q., Chen, J.X., Liu, D. (2015). Binary inheritance learning particle swarm optimisation and its application in thinned antenna array synthesis with the minimum sidelobe level. IET Microwaves, Antennas & Propagation. Vol. 9. No. 13. p. 1386-1391. https://doi.org/10.1049/iet-map.2015.0071
  10. Quevedo-Teruel, O., Rajo-Iglesias, E. (2006). Ant colony optimization in thinned array synthesis with minimum sidelobe level. IEEE Antennas and Wireless Propagation Letters. Vol. 5. p. 349-352. https://doi.org/10.1109/LAWP.2006.880693
  11. Keizer, W.P.M.N. (2008). Linear array thinning using iterative FFT techniques. IEEE Transactions on Antennas and Propagation. Vol. 56. No. 8. p. 2757-2760. https://doi.org/10.1109/TAP.2008.927580
  12. Keizer, W.P.M.N. (2009). Large planar array thinning using iterative FFT techniques. IEEE Transactions on Antennas and Propagation. Vol. 57. No. 10. p. 3359-3362. https://doi.org/10.1109/TAP.2009.2029382
  13. Wang, X.K., Jiao, Y.C., Tan, Y.Y. (2012). Gradual thinning synthesis for linear array based on iterative Fourier techniques. Progress in Electromagnetics Research. Vol. 123. p. 299-320. http://dx.doi.org/10.2528/PIER11100903
  14. Wang, X.K., Wang, G.B. (2018). A Hybrid Method Based on the Iterative Fourier Transform andthe Differential Evolution for Pattern Synthesis of SparseLinear Arrays. International Journal of Antennas and Propagation. Vol. 2018. Article ID 6309192. p. 1-7. https://doi.org/10.1155/2018/6309192
  15. Patent USA. No 4071848. Thinned aperiodic antenna arrays with improved peak side lobe level control / D.C. Leeper. 31/01/1978. https://patentimages.storage.googleapis.com/30/73/fa/25b9b72c3d3e8a/US4071848.pdf
  16. Leeper, D.G. (1999). Isophoric arrays-massively thinned phased arrays with well-controlled sidelobes. IEEE Transactions on Antennas and Propagation. Vol. 47, No. 12. p. 1825-1835. https://doi.org/10.1109/8.817659
  17. Sodin, L.G. (2005). Some problems of the theory of phased antenna arrays, topical for radio astronomy. Radiophysics and Radio Astronomy. Vol. 10 (Special Release). p. 128-142. http://dspace.nbuv.gov.ua/bitstream/handle/123456789/103841/08-Sodin.pdf?sequence=1
  18. Kopilovich, L.E., Sodin, L.G. (2001). Multielement System Design in Astronomy and Radio Science. Dordrecht : Springer Netherlands, 183 p. https://doi.org/10.1007/978-94-015-9751-7
  19. Kopilovich, L.E., Sodin, L.G. (1989). Linear non-equidistant array antennas based on difference sets. Radio Engineering and Electronics. Vol. 34. No. 10. p. 2059-2066. https://doi.org/10.1007/978-94-015-9751-7_6
  20. Kopilovich, L.E., Sodin, L.G. (1994). Synthesis of non-equidistant array antennas based on the theory of difference sets. Radio Engineering and Electronics. Vol. 39. No. 3. p. 380-389.
  21. Kopilovich, L.E., Sodin, L.G. (1992). Sectionalized nonequidistant linear array antennas based on difference sets. Radio Engineering and Electronics. Vol. 37. No. 12. p. 2155-2160.
  22. Kravchenko, V.F., Lutsenko, V.I., Lutsenko, I.V., et al. (2017). Non-equidistant two-dimensional antenna arrays based on “magic” squares. Journal of Measurement Science and Instrumentation. Vol. 8. No. 3. p. 244-253. https://doi.org/10.3969/j.issn.1674-8042.2017.03.006
  23. Kravchenko, V.F., Lutsenko, V.I., Luo, Y,. et al. (2019). Non-equidistant two-dimensional antenna arrays based on Latin squares. Journal of Measurement Science and Instrumentation. Vol. 10. No. 1. p. 38-48. https://doi.org/10.3969/j.issn.1674-8042.2019.01.006
  24. Luo, Y., Guo, Q., Lutsenko, V.I., Zheng, Y. (2019). Non-equidistant Two-Dimensional Antenna Arrays Based on the Structure of Latin Squares Taking Cyclic Difference Sets as Elements. European Microwave Conference in Central Europe, EuMCE-2019: Conf. Proc. (Prague, Czech Republic, 13-15 May 2019). Prague, p. 421-424. https://ieeexplore.ieee.org/document/8874813/references#references
  25. Colbourn, C.J., Dinitz, J.H. (Eds.). (2006). Handbook of Combinatorial Designs. Chapman and Hall /CRC, 1016 p. https://doi.org/10.1201/9781420010541
  26. Axler, S. (2014). Linear Algebra Done Right. Cham: Springer International Publishing, 340 p. https://doi.org/10.1007/978-3-319-11080-6
  27. Konovalenko, A.A., Yerin, S.M., Bubnov, I.M., et al. (2016). Astrophysical studies using small-sized low-frequency new-generation radio telescopes. Radiophysics and Radio Astronomy. Vol. 21. No.2. p. 83-131. https://doi.org/10.15407/rpra21.02.083
  28. Konovalenko, A.A. (2017). Progress in low-frequency radio astronomy and I.S. Shklovskii’s contribution to its development. Astron. Rep. Vol. 61. p. 317-323. https://doi.org/10.1134/S1063772917040102
  29. Baumert, L.D. (1971). Cyclic Difference Sets (Lecture Notes in Mathematics, 182). Berlin: Springer-Verlag, 172 p. https://doi.org/10.1007/BFb0061260
  30. Bernstein, D.S. (2009). Matrix Mathematics: Theory, Facts, and Formulas (2nd ed.). Princeton: Princeton University Press, 1184 p. https://doi.org/10.1515/9781400833344
  31. Horn, R.A., Johnson, C.R. (2013). Matrix Analysis (2nd ed.). Cambridge: Cambridge University Press, 643 p.
  32. Shifrin, Ya.S. (1971). Issues of the statistical theory of antennas. M.: Rad. radio, 383 p.
  33. Kopilovych, L.E. (2012). Redundant changes of antennas on the two-dimensional aperture of the interferometer, which provide full coverage of the central regions in the plane of spatial frequencies. Radiophysics and Radioastronomy. Vol. 17. No. 2. p. 1176-182.
  34. Colbourn, C.J., Dinitz, J.H. (Eds.). (2007). Handbook of Combinatorial Designs (2nd ed.). Boca Raton: Chapman & Hall/CRC, 1016 p. https://doi.org/10.1201/9781420010541
  35. Bjorner, A.A, Stanley, R.P. (2010). Combinatorial Miscellany. Geneva: L’Enseignement Mathematique, 164 p.
  36. Denes, J., Keedwell, A.D. (1974). Latin Squares and their Applications. New York-London: Academic Press, 547 p.
  37. Fujimotom, K. (2001). Mobile Antenna Systems Handbook (3rd ed.). Norwood: Artech House, 680 p.
  38. Lorente, D., Limbach, M., Gabler, B. (2019). L-Band Antenna Array for Next Generation DLR Airborne SAR Sensor. 12th German Microwave Conference (GeMiC-2019): Conf. Proc. (Stuttgart, Germany, 25-27 March 2019). Stuttgart, p. 182-185. https://doi.org/10.23919/GEMIC.2019.8698151
  39. Arnauti, El-G., Saalmann, O., Brenner, A.R. (2017). Ultra-high resolution airborne experiments with a new Ka-band SAR sensor. European Radar Conference (EURAD-2017): Conf. Proc. (Nuremberg, Germany, 11-13 October 2017). Germany, p. 409-412. https://doi.org/10.23919/EURAD.2017.8249234
  40. Kraus, T., Krieger, G., Bachmann, M., et al. (2021). Formation Considerations for Distributed Satellite SAR Systems. 13th European Conference on Synthetic Aperture Radar. (EUSAR-2021): Conf. Proc. (Germany, 29 March-01 April 2021, online). Germany, p. 1-6. https://ieeexplore.ieee.org/document/9472632
  41. Fang, T., Deng, Y., Liang, D., et al. (2020). Multichannel Sliding Spotlight SAR Imaging: First Result of GF-3 Satellite. IEEE Transactions on Geoscience and Remote Sensing. Vol. 60. p. 1925-1928. https://doi.org/10.1109/TGRS. 2021.3068208 https://doi.org/10.1109/IGARSS39084.2020.9323296
  42. Li, Q., Feng, L., Zheng, S., et al. (2022). Research on Sliding spotlight imaging algorithm. 3rd China International SAR Symposium. (CISS-2022): Conf. Proc. (Shanghai, China, 02-04 November 2022). Shanghai, p. 1-5. https://doi.org/10.1109/CISS57580.2022.9971246
  43. Kendra, J.R., Bloy, G.J., Hughes, J. (2021). Rotary-Motion-Extended Array Synthesis (R-MXAS): Simultaneous Sparsity and Sensitivity in a Synthetic Aperture Imaging Radiometer. IEEE International Geoscience and Remote Sensing Symposium. (IGARSS-2021): Conf. Proc. (Brussels, Belgium, 11-16 July 2021). Brussels, p. 7696-7699. https://doi.org/10.1109/IGARSS47720.2021.9554144
  44. Chen, S. (2017). An Efficient Method for Investigating and Optimizing Near Field Characteristics of Planar Antenna Arrays. Wireless Personal Communications: An International Journal. Vol. 95 (2). p. 223-232. https://doi.org/10.1007/s11277-016-3888-2
  45. Bogosanovic, M., Williamsoni, A.G. (2005). Antenna Array with Beam Focused in Near Field Zone. Electronics Letters. Vol. 39. p. 704-705. https://doi.org/10.1049/el:20030479
  46. Wang, X., Zhong, Y., Wang, Y. (2015). An Improved Antenna Array Pattern Synthesis Method Using Fast Fourier Transform. International Journal of Antennas and Propagation. Vol. 2015 (Special Issue). Article ID 316962. p. 1-9.                          https://doi.org/10.1155/2015/316962
  47. Wang, D., Shen, Z., Su, X., et al. (2021). Gm-Compensated 46-101 GHz Broadband Power Amplifier for High-Resolution FMCW Radars. IEEE International Symposium on Circuits and Systems (ISCAS-2021): Conf. Poc. (Daegu, South Korea, 22-28 May 2021). Daegu, p. 1-5. https://doi.org/10.1109/ISCAS51556.2021.9401773
  48. Morrison, R.L., Phelps, E.B. (2019). Radio Astronomy Techniques for Multistatic Radar Imaging and Localization of Space Objects. 2019 International Applied Computational Electromagnetics Society Symposium (ACES-2019): Conf. Proc. (Miami, FL, USA, 14-19 April 2019). Miami, p. 1-2. https://ieeexplore.ieee.org/document/8713030
  49. Carter, W.H. (1999). On Refocusing a Radio Telescope to Image Sources in the Near Field of the Antenna Array. IEEE Transactions on Antennas and Propagation. Vol. 37 (3). p. 314-319. https://doi.org/10.1109/8.18727
  50. Chen, S.-P. (2014). Improved Near Field Focusing of Antenna Arrays with Novel Weighting Coefficients. 2014 IEEE 6th International Symposium on Wireless Vehicular Communications (WiVeC 2014): Conf. Proc. (Vancouver, BC, Canada, 14-15 September 2014). Vancouver, p. 1-4. https://doi.org/10.1109/WIVEC.2014.6953228
  51. Schungel, M., Dietrich, S., Ginthor, D., et al. (2020). Analysis of Time Synchronization for Converged Wired and Wireless Networks. 2020 25th IEEE International Conference on Emerging Technologies and Factory Automation (ETFA): Conf. Proc. (Vienna, Austria, 08-11 September 2020). Vienna, p. 198-205. https://doi.org/10.1109/ETFA46521.2020. 9212068 https://doi.org/10.1109/ETFA46521.2020
  52. Ebadi, S., Gatti, R. V., Marcaccioli, L., et al. (2009). Near Field Focusing in Large Reflector Array Antennas Using 1-bit Digital Phase Shifters. 2009 European Microwave Conference (EuMC-2009): Conf. Proc. (Rome, Italy, 29 September-01 October 2009). Rome, p. 1029-1032. https://doi.org/10.23919/EUMC.2009.5296377
  53. Mailloux, R.J. (2005). Phased Array Antenna Handbook (2nd ed.). Norwood: Artech House Inc., 515 p.
  54. Goldstein, R.M., Zebker, H.A. (1987). Interferometric radar measurement of ocean sur face currents. Nature. Vol. 328, No. 6132. p. 707-709. https://doi.org/10.1038/328707a0
  55. Piquenard, A. (1974). Radio Wave Propagation. New York: Wiley, 343 p. https://doi.org/10.1007/978-1-349-01394-4
  56. Mazda, F. (1993). Telecommunications Engineer’s Reference Book (1st ed.). Oxford: Butterworth-Heinemann, 1142 p. https://doi.org/10.1016/C2013-0-06529-2 https://doi.org/10.1016/B978-0-7506-1162-6.50017-4
  57. Collin, R.E. (1969). Antenna Theory, Part 1 (R.E. Collin, F.J. Zucker Eds.). New York: McGraw-Hill Book Company, 676 p. ISBN 10: 0070117993
  58. Fang, D.G. (2010). Antenna Theory and Microstrip Antennas. Boca Raton: CRC Press, 311 p. https://doi.org/10.1201/b10302
  59. Balanis, C.A. (1997). Antenna Theory Analysis and Design. Hoboken: John Wiley, 1095 p.
  60. Hartley, R.V.L. (1923). Relations of carrier and side-bands in radio transmission. Proceedings of the Institute of Radio Engineers. Vol. 2, No. 2. p. 90-112. https://doi.org/10.1109/JRPROC.1923.219862
  61. Shu, F., Qin, Y., Liu, T., et al. (2018). Low-Complexity and High-Resolution DOA Estimation for Hybrid Analog and Digital Massive MIMO Receive Array. IEEE Transactions on Communications. Vol. 66, No. 6. p. 2487-2501 https://doi.org/10.1109/TCOMM.2018.2805803
  62. Couch, Leon W. (2001). Digital and analog communication systems (7th ed.). Englewood Cliffs: Prentice-Hall Inc., 758 p.
  63. Hui, W., Chen, Z., Zheng, S. (2017). Preliminary Research of Low-RCS Moving Target Detection Based on Ka-Band Video SAR. IEEE Geoscience and Remote Sensing Letters. Vol. 14, No. 6. p. 1-5. https://doi.org/10.1109/LGRS.2017.2679755 
  1. Tommasini, R., Lowenthal, F., Balmer, J., et al. (1998). Iterative method for phase-amplitude retrieval and its application to the problem of beam-shaping and apodization. Opt. Commun. Vol. 153, No. 4-6. p. 339-346. https://doi.org/10.1016/S0030-4018(98)00246-6
  2. Hao, Z.-C., He, M., Hong, W. (2016). Design of a millimeter-wave high angle selectivity shaped-beam conformal array antenna using hybrid genetic/space mapping method. IEEE Antennas Wireless Propag. Lett. Vol. 15. p. 1208-1212. https://doi.org/10.1109/LAWP.2015.2501403
  3. Josefsson, L. (2006). Conformal Array Antenna Theory and Design. Hoboken: Wiley-IEEE Press, 488 p. https://doi.org/10.1002/047178012X
  4. Bhattacharyya, A.K. (2006). Phased Array Antennas: Floquet Analysis, Synthesis, BFNs and Active Array Systems. Hoboken: Wiley-Interscience, 528 p. https://doi.org/10.1002/0471769126
  5. Chatterjee, D. (2006). Numerical Modeling of Conformal Phased Arrays on Tactical Systems. 2006 IEEE Military Communications conference (MILCOM-2006): Conf.Proc. (Washington, USA, 23-25 October 2006) Washington, p. 1-7. https://doi.org/10.1109/MILCOM.2006.302359
  6. Li, H., Jiang, Y., Ding, Y., et al. (2018). Low-sidelobe pattern synthesis for sparse conformal arrays based on PSO-SOCP Optimization. IEEE Access. Vol. 6. p. 77429-77439. https://doi.org/10.1109/ACCESS.2018.2883042
  7. Lee, S.W. (1982). A Review of GTD Calculation of Mutual Admittance of Slot Conformal Array. Electromagnetics. Vol. 2, No. 2. p. 85-127. https://doi.org/10.1080/02726348208915159
  8. Erturk, V.B., Bakir, O., Rojas, R.G., et al. (2006). Scan Blindness Phenomenon in Conformal Finite Phased Arrays of Printed Dipoles. IEEE Trans. Antennas and Propagat. Vol. 54, No. 6. p. 1699-1708. https://doi.org/10.1109/TAP.2006.875482
  9. Shapira, J., Felsen, L.B., Hessel, A. (1974). Ray Analysis of Conformal Antenna Arrays. IEEE Trans. Antennas. Propagat. Vol. 22, No. 1. p. 49-63. https://doi.org/10.1109/TAP.1974.1140710
  10. Macon, C.A., Trott, K.D., Kempel, L.C. (2003). A Practical Approach to Modeling Doubly Curved Conformal Microstrip Antennas. Progress in Electromagnetics Research (PIER). Vol. 40. p. 295-314. http://dx.doi.org/10.2528/PIER02122903
  11. Balanis, C.A. (2016). Antenna theory: analysis and design (3rd ed.). New Jersey: John Wiley & Sons, 1072 p.
  12. Jakes, W.C. (1974). Microwave mobile communications (1st ed.). New Jersey: John Wiley & Sons, 645 p.
  13. Panduro, M.A., Covarrubias, D.H., Brizuela, C.A., et al. (1992). A multi-objective approach in the linear antenna array design. AEU-Int J Electron Commun. 2005. Vol. 59. No. 4. p. 205-212 https://doi.org/10.1016/j.aeue.2004.11.017
  14. Haykin, S., Reilly, J. P., Kezys, V. (1992). Some aspects of array signal processing. IEE Proceedings F – Radar and Signal Processing. Vol. 139, No. 1. p. 1-26. https://doi.org/10.1049/ip-f-2.1992.0001
  15. Munk, B.A. (2003). Finite Antenna Arrays and FSS. NY, USA: IEEE-Wiley Press, 357 p. https://doi.org/10.1002/0471457531
  16. Bhattacharya, A.K. (2006). Phased Array Antennas: Floquet Analysis, Synthesis, BFNs and Active Array Synthesis. NY, USA: Wiley-Interscience, 528 p. https://doi.org/10.1002/0471769126
  17. Lo, Y.T., Lee, S.W. (1998). Antenna Handbook: Theory, Applications and Design. NY, USA: Van Nostrand Reinhold Co., 1131 p. https://doi.org/10.1007/978-1-4615-6459-1
  1. Erturk, V.B., Rojas, R.G. (2003). Efficient Analysis of Input Impedance and Mutual Coupling of Microstrip Antennas on Large Cylinders. IEEE Trans. Antennas and Propagat. Vol. 51. No. 4. p. 739-749. https://doi.org/10.1109/TAP.2003.811060
  2. Chapman, S.J., Lawry, J.M.H., Ockendon, J.R., et al. (1999). On The Theory of Complex Rays. SIAM Review. Vol. 41. No. 3. p. 417-509. https://doi.org/10.1137/S0036144599352058
  3. Almagboul, M.A., Shu, F., Qian, Y., et al. (2019). Atom search optimization algorithm based hybrid antenna array receive beamforming to control sidelobe level and steering the null. AEU-Int J Electron Commun. Vol. 111. Article ID 152854. 15 p. https://doi.org/10.1016/j.aeue.2019.152854
  4. Zhang, J., Mao, X., Zhang, M., et al. (2023). Synthesis of thinned planar arrays based on precoded subarray structures. IEEE Antennas and Wireless Propagation Letters. Vol. 22. No. 1. p. 44-8. https://doi.org/10.1109/LAWP.2022.3201382
  5. Kibaroglu, K., Sayginer, M., Rebeiz, G.M. (2018). A scalable 64-element 28 ghz phased- array transceiver with 50 dbm eirp and 8-12 gbps 5g link at 300 meters without any calibration. 2018 IEEE/MTT-S International Microwave Symposium – IMS (IMS-2018): Conf. Proc. (Philadelphia, PA, USA, 10-15 June 2018). Philadelphia, p. 496-8. https://doi.org/10.1109/MWSYM.2018.8439404 https://doi.org/10.1109/RFIC.2018.8428989
  6. Maher, T., Cheng, D. (1963). Random removal of radiators from large linear arrays. IEEE Trans Antennas and Propagation. Vol. 11. No. 2. p. 106-112. https://doi.org/10.1109/TAP.1963.1138000
  7. Lo, Y. (1964). A mathematical theory of antenna arrays with randomly spaced elements. IEEE Trans Antennas and Propagation. Vol. 12, No. 3. p. 257-268. https://doi.org/10.1109/TAP.1964.1138220
  8. Urvinder, S., Munish, R. (2014). Design of thinned concentric circular antenna arrays using firefly algorithm. IET Microw. Antennas. Propag. Vol. 8. No. 12. p. 894-900. https://doi.org/10.1049/iet-map.2013.0695
  9. Aksoy, E., Afacan, E. (2009). Planar antenna pattern nulling using differential evolution algorithm. AEU-Int J Electron. Commun. Vol. 63. No. 2. p. 116-122. https://doi.org/10.1016/j.aeue.2007.11.006
  10. Ghosh, P., Das, S. (2011). Synthesis of thinned planar concentric circular antenna arrays – A differential evolutionary approach. Prog. Electromagn. Res. B. Vol. 29. p. 63-82. http://dx.doi.org/10.2528/PIERB11020204
  11. Vankayalapati, S., Pappula, L., Ghosh, D. (2023). Element thinning using discrete cat swarm optimization for 5G/6G applications. Prog. Electromagn. Res. B. Vol. 101. p. 119-135. https://doi.org/10.2528/PIERB23051702
  12. Pradhan, P.M., Panda, G. (2012). Connectivity constrained wireless sensor deployment using multiobjective evolutionary algorithms and fuzzy decision making. Ad. Hoc. Networks. Vol. 10. No. 6. p. 1134-1145. https://doi.org/10.1016/j.adhoc.2012.03.001
  13. Zhang, J., Mao, X., Zhang, M., et al. (2023). Synthesis of thinned planar arrays based on precoded subarray structures. IEEE Antennas Wirel. Propag. Lett. Vol. 22. No. 1. p. 44-48. https://doi.org/10.1109/LAWP.2022.3201382
  14. Durmus, A. (2020). The optimal synthesis of thinned concentric circular antenna arrays using slime mold algorithm. Electromagnetics. Vol. 40. No. 8. p. 541-553. https://doi.org/10.1080/02726343.2020.1838044
  15. Monzingo, R.A., Haupt, R., Miller, T. (2011). Introduction to Adaptive Arrays (2nd ed.). Raleigh: SciTechPublishing, Inc., 559 p. https://doi.org/10.1049/SBEW046E
  1. Trees, H.L.V. (2004). Optimum Array Processing: Part IV of Detection, Estimation, and Modulation Theory. Virginia: John Wiley & Sons, 1471 p.
  2. Naidu, P.S. (2009). Sensor Array Signal Processing (2nd ed.). London: CRC Press, 558 p. https://doi.org/10.1201/9781439883136
  3. Massa, A., Rocca, P., Oliveri, G. (2015). Compressive Sensing in Electromagnetics – A Review. IEEE Antennas and Propagation Magazine. Vol. 57. No. 1. p. 224-38. https://doi.org/10.1109/MAP.2015.2397092
  4. Berry, M.V. (1989). Uniform Asymptotic Smoothing of Stokes’ Discontinuities. Proc. R. Soc. Lond. A. Vol. 422. p. 7-21. https://doi.org/10.1098/rspa.1989.0018
  5. Thors, B., Rojas, R.G. (2003). Uniform Asymptotic Solution for the Radiation from a Magnetic Current Source on a Large Dielectric Coated Circular Cylinder: Non-Paraxial Region. Radio Science. Vol. 38. No. 5. 12 p. https://doi.org/10.1029/2002RS002782
  6. Togkoz, C., Pathak, P.H., Marhefka, R.J. (2005). An Asymptotic Solution for the Surface Magnetic Field Within the Paraxial Region of a Circular Cylinder with a Impedance Boundary Condition. IEEE Trans. Antennas Propagat. Vol. 53. No. 4. p. 1435-1443. https://doi.org/10.1109/TAP.2005. 844461
  7. Togkoz, C., Marhefka, R.J. (2006). A UTD Based Asymptotic Solution for the Surface Magnetic Field on a Source Excited Circular Cylinder with an Impedance Boundary Condition. IEEE Trans. Antennas Propagat. Vol. 54. No. 6. p. 1750-1757. https://doi.org/10.1109/TAP.2006.875490
  8. Elliot, R.S. (2003). Antenna Theory and Design (rev. ed.). NY, USA: IEEE-Wiley Press (Classic Reissue), 625 p. https://doi.org/10.1109/9780470544174
  9. Ridwan, M., Abdo, M., Jorswieck, E. (2011). Design of non-uniform antenna arrays using genetic algorithm. 13th International Conference on Advanced Communication Technology (ICACT2011): Conf. Proc. (Gangwon, South Korea, 13-16 February 2011). Gangwon, p. 422-427. https://ieeexplore.ieee.org/xpl/conhome/5740523/proceeding
  10. Sim on, R.S., Aragon-Zavala, A. (2007). Antennas and Propagation for Wireless Communication Systems (2nd ed.). London: John Wiley & Sons., 546 p.
  11. Marr, J.M., Snell, R.L., Kurtz, S.E. (2016). Fundamentals of radio astronomy: Observational methods. Boca Raton: CRC Press Publ., 350 p. https://doi.org/10.1201/b20506
  12. Condon, J.J., Ransom S.M. (2016). Essential Radio Astronomy. Princeton: Princeton University Press Publ., 376 p. https://doi.org/10.1515/9781400881161
  13. Mogyla, A.A., Mytsenko, I.M., Voytovich, O.A., et al. (2019). Building a passiveactive radio-meteorological measuring system based on dual-frequency radar. Telecommunications and Radio Engineering. Vol. 78. No. 15. p. 1355-1367. https://doi.org/10.1615/TelecomRadEng.v78.i15.50
  14. Coleman, C.J., Watson, R.A., Yardley, H. (2008). A practical bistatic passive radar system for use with DAB and DRM illuminators. 2008 IEEE Radar Conference: Conf. Proc. (Rome, Italy, 26-30 May 2008). Rome, p. 1-6. https://doi.org/10.1109/RADAR.2008.4721007
  15. Brzozowski, M., Pakowski, M., Jakielaszek, Z., et al. (2021). Challenges of preparation and realization of combined field tests of passive and active radar sensors on an example APART-GAS 2019 trials. 2021 IEEE 8th International Workshop on Met rology for AeroSpace (MetroAeroSpace): Conf. Proc. (Naples, Italy, 23-25 June 2021). Naples, p. 188-192. https://doi.org/10.1109/MetroAeroSpace51421. 2021. 9511746
  16. Franken, D., Liegl, A. (2022). Integration of Multi-Band Passive and Multi-Functional Active Radar Data. IEEE Radar Conference. (RadarConf22): Conf. Proc. (New York City, NY, USA, 21-25 March 2022). NY, p. 1-6. https://doi.org/10.1109/RadarConf2248738.2022.9764215
  17. Pavlikov, V., Volosyuk, V., Zhyla, S., et al. (2021). Active-Passive Radar for Radar Imaging from Aerospace Carriers. IEEE 19th International Conference on Smart Technologies (EUROCON): Conf. Proc. (Lviv, Ukraine, 06-08 July 2021). Lviv, p. 18-24. https://doi.org/10.1109/EUROCON52738.2021.9535619
  18. Andriychuk, M. (2021). Asymptotic regularisationof the solution to theproblemof electromagneticfield scattering froma set of small impedanceparticles. IET Microw. Antennas Propag. Vol. 15. No. 10. p. 1330-1346. https://doi.org/10.1049/mia2.12171
  19. Bird, T.S. (1985). Accurate Asymptotic Solution for the Surface Field Due to Apertures in a Conducting Cylinder. IEEE Trans. Antennas and Propagat. Vol. 33. p. 1108-1117. https://doi.org/10.1109/TAP.1985.1143497
  20. Bahrami, H., Porter, E., Santorelli, A., et al. (2015). Flexible sixteen antenna array for microwave brest cancer detection. IEEE Transactions on Biomedical Engineering. Vol. 62. No. 10. p. 2516-2525. https://doi.org/10.1109/TBME.2015.2434956
  21. Volosyuk, V., Zhyla, S., Pavlikov ,V., et al. (2021). Mathematical description of imaging processes in ultra-wideband active aperture synthesis systems using stochastic sounding signals. Radioelectronic and Computer Systems. No. 4. p. 166-182. https://doi.org/10.32620/reks.2021.4.14
  22. Patwari, A., Gudheti, R.R. (2020). Novel MRA-Based Sparse MIMO and SIMO Antenna Arrays for Automotive Radar Applications. Progress In Electromagnetics Research B. Vol. 86. p. 103-119. https://doi.org/10.2528/PIERB19121602
  23. Schooneveld, V.C. (1987). Image Formation from Coherence Functions in Astronomy. Berlin: Springer Publ., 340 p. https://doi.org/10.1007/978-94-009-9449-2
  24. Carozzi, T.D., Woan, G. (2021). A generalized measurement equation and van Cittert-Zernike theorem for wide-field radio astronomical interferometry. Monthly Notices of the Royal Astronomical Society. Vol. 395. No. 3. p. 1558-1568. https://doi.org/10.1111/j.1365-2966.2009.14642.x
  25. Cappellen, W.A., Ardenne, A. (2017). Development of mid-frequency aperture arrays for radio astronomy. IEEE Radio and Antenna Days of the Indian Ocean (RADIO-2017): Conf. Proc. (Cape Town, South Africa, 25-28 September 2017). Cape Town, p. 1-2. https://doi.org/10.23919/RADIO.2017.8242214
  26. Hall, P.J., Benthem, P., Sutinjo, A.T. (2016). Aperture array verification system 1: Overview of a square kilometre array prototype. International Conference on Electromagnetics in Advanced Applications (ICEAA-2016): Conf. Proc. (Cairns, QLD, Australia, 19-23 September 2016). Cairns, p. 345-348. https://doi.org/10.1109/ICEAA.2016.7731394
  27. International Commission on Non-Ionizing Radiation Protection (ICNIRP). (2009). Exposure to high frequency electromagnetic fields, biological effects and health consequences (100kHz – 300GHz). Germany, 358 p. http://www.emf.ethz.ch/archive/var/ICNIRP_effekte_RFReview.pdf
  28. Stutzman, W.L., Thiele, G.A. (2012). Antenna theory and design (3rd ed.). New York: Wiley, 848 p.
  29. Lutsenko, I.V., Popov, I.V., Lutsenko, I.V. (2008). Bistatic Radars with Illumination by Ionospheric Signals of High-Frequency Communication Stations. Telecommunications and Radio Engineering. Vol. 67. No. 4. p. 285-292. https://doi.org/10.1615/TelecomRadEng.v67.i4.10
  30. Lutsenko V. I., Lutsenko I. V., Popov I. V. (2008). Illumination of air environment using radiation of SW broadcasting stations. The 5th European Radar Conference: Conf. Proc. (Amsterdam, Netherlands, 30-31 October 2008). Amsterdam, p. 396-399. https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4760885
  31. Lutsenko, V.I., Lutsenko, I.V., Popov, I.V. (2015). Illumination of the Air Environment Using Radiation of HF Broadcast Stations. Radiophysics and Quantum Electronics. Vol. 58. No. 1. p. 9-18. https://doi.org/10.1007/s11141-015-9576-3
  32. Anderson, T.S., McCarthy, M.P., Holzworth, R.H. (2020). Detection of VLF attenuation in the Earth‐ionosphere waveguide caused by X‐class solar flares using a global lightning location network. Space Weather. Vol. 18. Article ID e2019SW002408. 9 p. https://doi.org/10.1029/2019SW002408
  33. Georges, T.M. (1967). Evidence for the influence of atmospheric waves on ionospheric motions. Journal of Geophysical Research. Vol. 72. No. 1. p. 422-425. https://doi.org/10.1029/JZ072i001p00422
  34. Hussar, P.E., Smith-Rowland, E.M. (2002). An Asymptotic Solution for Boundary Layer Fields Near a Convex Impedance Surface. Journal of Electromagnetic Waves and Applications. Vol. 16. No. 2. p. 185-208. https://doi.org/10.1163/156939302X00831
  35. Federal Communications Commission (FCC). (2016). FCC. Title 47: Telecommunication, Electronic Code of Federal Regulations. https://www.ecfr.gov/current/title-47
  36. Chatterjee, D. (2005). Paraxial and Source Region Behavior of a Class of Asymptotic and Rigorous (MoM) Solutions in the High-Frequency Planar Limit. IEEE Antennas and Wireless Propagation Letters. Vol. 4. p. 71-74. https://doi.org/10.1109/LAWP.2005.844140
  37. Chatterjee, D. (2005). Paraxial Region Comparison of Creeping Wave Formulations for Axial and Circumferential Magnetic Current Elements on a PEC Circular Cylinder. IEEE Antennas and Propagation Symposium Digest: Conf. Proc. (Washington, DC, 3-8 July 2005). Washington, Vol. 3B. p. 147-150. https://doi.org/10.1109/APS.2005.1552456
  38. IEEE. (2014). American National Standard Dictionary of Electromagnetic Compatibility (EMC) including Electromagnetic Environmental Effects (E3). ANSI C63.14-2014 (Revision of ANSI C63.14-2009). p. 1-76, https://doi.org/10.1109/IEEESTD.2014.6974973
  39. Volosyuk, V. & Zhyla, S. (2022). Statistical Theory of Optimal Stochastic Signals Processing in Multichannel Aerospace Imaging Radar Systems. Computation. Vol 10. Special Issue. Article ID 224. 16 p. https://doi.org/10.3390/computation10120224
  40. ITU. (1990). Feasibility of Frequency Sharing between Radio Astronomy and other Services (Report 696-2). CCIR: Doc. of the XVIIth Plenary Assembly. Dusseldorf, Annex to Vol. II. p. 568‑584.
  41. ITU. (1966). Documents of the XIth Plenary Assembly (Report 224-1). CCIR: ITU, Geneva, Vol. IV. p. 537-548.
  42. Barnbaum, C.A., Bradley R.F. (1998). A new approach to interference excision in Radio Astronomy: real-time adaptive cancellation. Astron. J. Vol. 116. p. 2598-2614. https://doi.org/10.1086/300604
  43. Ellingson, S.W., Cazemier, W. (2003). Efficient multibeam synthesis with interference nulling for large arrays. IEEE Trans. Ant. Prop. Vol. 51. No. 3. p. 503-511. https://doi.org/10.1109/TAP.2003.809840
  44. Fomalont, E.B., Windhorst, R., Kristian, J.A., et al. (1991). The micro-jansky radio source population at 5 GHz. Astron. J. Vol. 102. p. 1258-1277. https://doi.org/10.1086/115952
  45. Kraus, J.D. (1986). Radio Astronomy (2nd ed.). New York: Cygnus-Quasar Books, 719 p.
  46. Greenhill, L.J., Kondratko ,P.T., Lovell, J.E.J., et al. (2003). The Discovery of H2O Maser Emission in Seven Active Galactic Nuclei and at High Velocities in the Circinus Galaxy. Astrophys. J. (Letters). Vol. 582. No. 1. p. 11‑14. https://doi.org/10.1086/367602
  47. Thompson, A.R. (1982). The response of a radio-astronomy synthesis array to interfering signals. IEEE Trans. Ant. Prop. Vol. 30, No 3. p. 450-456. https://doi.org/10.1109/TAP.1982.1142799 
  1. Wootten, A., Thompson, A.R. (2009). The Atacama Large Millimeter/Submillimeter Array. Proceedings of the IEEE. Vol. 97. No. 8. p. 1463-1471. https://doi.org/10.1109/JPROC.2009.2020572
  2. Walter, F., Decarli, R., Carilli, C., et al. (2012). The intense starburst HDF 850.1 in a galaxy overdensity at z ≈ 5.2 in the Hubble Deep Field. Nature. Vol. 486. p. 233-238. https://doi.org/10.1038/nature11073
  3. Kallunki, J., Bezrukovs, V., Madkour, W., (2022). et al. Importance of Spectrum Management in Radio Astronomy. Latvian Journal of Physics and Technical Sciences. Vol. 59. No. S3. p. 30-38. https://doi.org/10.2478/lpts-2022-0022
  4. Burke, B.F., Graham-Smith, F. (2019). An introduction to radio astronomy (4th ed.). Cambridge: CambridgeUniversityPress, 516 p. https://doi.org/10.1017/9781316987506
  5. Ewen, H.I., Purcell, E.M. (1951). Observations of a line in the galactic radio spectrum. Nature. Vol. 168. p. 356. https://doi.org/10.1038/168356a0
  6. Wei, L., Wijnholds, S.J., Hurley, P. (2017). Robust recovery for aperture synthesis imaging. IEEE International Conference on Image Processing (ICIP-2017): Conf. Proc. (Beijing, China, 17-20 September 2017). Beijing, p. 3570-3574. https://doi.org/10.1109/ICIP.2017.8296947
  7. Fu, P., Hu, F., Hu, H., et al. (2020). A Wavenumber Domain Imaging Algorithm for Synthetic Aperture Interferometric Radiometry in Near-Field. IEEE International Geoscience and Remote Sensing Symposium. (IGARSS-2020): Conf. Proc. (September 26-October 2 2020, Virtual Symposium). p. 6511-6514. https://doi.org/10.1109/IGARSS39084.2020.9323395
  8. Philippe, B., Reynaert, P. (2020). A Quadrature Phase Detector in 28 nm CMOS for Differential mm-Wave Sensing Applications Using Dielectric Waveguides. IEEE 44th European Solid State Circuits Conference (ESSCIRC 2018): Conf. Proc. (Dresden, Germany, 03-06 September 2018). Dresden, p. 114-117. https://doi.org/10.1109/ESSCIRC.2018.8494306
  9. Robinson, J., Rahmat-Samii, Y. (2004). Particle Swarm Optimization in Electro magnetics. IEEE Transactions on Antennas and Propagation. Vol. 52. No.2. p. 397-407. https://doi.org/10.1109/TAP.2004.823969
  10. Liu, Y., Nie, Z., Liu, Q.-H. (2008). Reducing the number of elements in a linear antenna array by the matrix pencil method. IEEE Trans. Antennas Propag. Vol. 56. No. 9. p. 2955-2962. https://doi.org/10.1109/TAP.2008.928801
  11. Bucci, O., Perna, S., Pinchera, D. (2012). Advances in the deterministic synthesis of uniform amplitude pencil beam concentric ring arrays. IEEE Trans. Antennas Propag. Vol. 60. No. 7. p. 3504-3509. https://doi.org/10.1109/TAP.2012.2196945
  12. Kay, S., Saha, S. (2002). Design of sparse linear arrays by Monte Carlo importance sampling. IEEE J. Ocean. Eng. Vol. 27. No. 4. p. 790-799. https://doi.org/10.1109/JOE.2002.804325
  13. Cui, J., Legenkiy, M., Khrychov, V. (2020). Diffraction properties of azimuthally symmetric gratings in a hollow circular dielectric waveguide. Results in Physics. Vol. 18. p. 103204-103204. https://doi.org/10.1016/j.rinp.2020.103204
  14. Legenkyi, M., Khrychov, V. (2019). Pulsed antenna based on a non-homogeneous conical line. Bulletin of Kharkiv National University named after V. N. Karazin. Series “Radio Physics and Electronics”. Issue 31. p. 59-65. https://doi.org/10.26565/2311-0872-2019-31-06
  15. Legenkiy, M., Khrychov, V. (2021). Numerical modeling of electromagnetic scattering from complex shape object with coating. Frequenz. Vol. 76. No. 1-2. p. 75-82. https://doi.org/10.1515/freq-2021-0062
  16. Akhmedov, R., Dumin, O., Katrich, V. (2018). Impulse radiation of antenna with circular aperture. Telecommunications and Radio Engineering. Vol. 77. Iss. 20. p. 1767-1784. https://doi.org/10.1615/TelecomRadEng.v77.i20.10
  17. Dumin, O., Akhmedov, R., Cherkasov, D. (2018). Pulsed radiation of an antenna with a circular aperture in the near zone. Bulletin of Kharkiv National University named after V. N. Karazin. Series “Radio Physics and Electronics”. Issue 28. p. 30-33. https://periodicals.karazin.ua/radiophysics/article/view/12591
  18. Berdnik, S.L., Katrich, V.A., Nesterenko, M.V., et al. (2020). Yagi-Uda Combined Radiating Structures of Centimeter and Millimeter Wave Band. Progress in Electromagnetics Research M. Vol. 93. p. 89-97. http://dx.doi.org/10.2528/PIERM20041506
  19. Pogarsky, S.A., Mayboroda, D.V. (2023). A broadband patch antenna based on a planar unclosed annular radiator. Radio Physics and Radio Astronomy. Vol. 28. No. 2. p. 158-165. https://doi.org/10.15407/rpra28.02.158
  20. Kaliberda, M.E., Pogarsky, S.A., Sierhieieva, A.A. (2023). Integral equations in the H-polarized wave scattering from metasurface formed by finite multilayer graphene strip grating inside grounded dielectric slab. Opt. Quant. Electron. Vol 55. Article ID 1050. 18 p. https://doi.org/10.1007/s11082-023-05288-5
  21. Mayboroda, D., Pogarsky, S. (2021). Microstrip monopole antenna with complicated topology. Lecture Notes in Networks and Systems. Vol. 152. p. 394-403. https://doi.org/10.1007/978-3-030-58359-0_22
  22. Qi, L., Kaliuzhnyi, M., Shen, Z., et al. (2023). Chirp Rates Estimation for Multiple LFM Signals by DPT-SVD. Circuits, Systems and Signal Processing. Vol. 42. No. 5. p. 2804-2827. https://doi.org/10.1007/s00034-022-02225-x
  23. Guo, Q., Kaliuzhnyi, M., Liu, J. (2022). YOLOX-SAR: High-precision Object Detection System Based on Visible and Infrared Sensors for SAR Remote Sensing. IEEE Sensors Journal. Vol 22. No. 17. p. 17243-17253. https://doi.org/10.1109/JSEN.2022.3186889
  24. Kaliuzhnyi, M. (2021). Generalizing the sampling theorem for a frequency-time domain to sample signals under the conditions of a priori uncertainty. Eastern-European Journal of Enterprise Technologies. Vol. 3. No. 9 (111). p. 6-15. https://doi.org/10.15587/1729-4061.2021.235844
  25. Volosyuk, V., Zhyla, S. (2022). Statistical Theory of Optimal Functionally Deterministic Signals Processing in Multichannel Aerospace Imaging Radar Systems. Computation. Vol. 10. Special Issue. Article ID 213. 20 p. https://doi.org/10.3390/computation10120213
  26. Volosyuk, V., Zhyla, S., Pavlikov, V. (2021). Optimal Radar Cross Section Estimation in Synthetic Aperture Radar with Planar Antenna Array. Radioelectronic and Computer Systems. Vol. 1. p. 50-59. https://doi.org/10.32620/REKS.2021.1.04

 

 

 

Related Post

Books Scientific monographs

Investment support reconfiguration and resilience formation of agri-enterprises within the bioeconomic paradigm of the new security reality: methodology, diagnostics, modelling

Books Educational edition

Operational calculus

Books Scientific monographs Ukrainian scientific book in a foreign language

Economic inequality through the lens of finance in Ukraine