I.A. Barannikov1, Yu.G. Pasternak2, V.A. Pendyurin3, S.M. Fedorov4

1,2,4 Voronezh State Technical University (Voronezh, Russia)

3 JSC NPP "Automated Communication Systems" (Voronezh, Russia)

1 8thbar@gmail.com, 2 pasternakyg@mail.ru, 3 pva777777@yandex.ru, 4 fedorov_sm@mail.ru

Problem statement. The multipath nature of the propagation of radio waves in urban areas, or in areas with a highly heterogeneous landscape, significantly degrades the quality of communication, despite a sufficient level of field strength created by radio transmitting means, as well as sufficient sensitivity of radio receivers. It is also necessary to note the problem of providing stable and high-speed communication with distant low-flying objects, which is caused by the interference of the direct wave and waves reflected from the underlying surface, which have almost the same amplitudes and are formed al-most in antiphase. A promising direction for solving the problem of providing reliable and high-speed communication that is resistant to interference fading of received signals is the development of methods for approximating the field structure and synthesizing radiation patterns that are optimal for the current electromagnetic environment.

Goal. Conducting a review of existing methods for field approximation and synthesis of radiation patterns, highlighting their strengths and weaknesses to create the possibility of choosing the optimal method and identifying directions for further development.

Results. Existing algorithms for approximating the electromagnetic field and synthesizing the radiation pattern of antenna arrays are considered. Examples of the application of these algorithms in practice are presented, the basic principles of their operation are described.

Practical significance. The considered methods make it possible to deal with problems that arise in radio electronic systems, such as interference distortion due to the multipath nature of signal propagation, distortion of the field structure due to nearby scatterers, as well as the problem of forming a radiation pattern with an optimal shape.

Barannikov I.A., Pasternak Yu.G., Pendyurin V.A., Fedorov S.M. Overview of algorithms for approximation of the electromagnetic field and synthesis of antenna array radiation patterns. Electromagnetic waves and electronic systems. 2024. V. 29. № 1. P. 56−74. DOI: https://doi.org/10.18127/j15604128-202401-05 (in Russian)

1. Roy T., Gout C., Le Guyader C., Lenglart E. Wind velocity field approximation from sparse data. IEEE International Geoscience and Remote Sensing Symposium. Melbourne, Australia. 2013. P. 1606–1609. DOI 10.1109/IGARSS.2013.6723098.
2. Makaryants G.M. Fundamentals of the finite element method: Textbook. Samara: Publishing House of Samara University. 2017. 104 p. (in Russian)
3. Dyer S.A., Dyer J.S. Cubic-spline interpolation. 1. IEEE Instrumentation & Measurement Magazine. 2001. V. 4. № 1. P. 44–46. DOI 10.1109/5289.911175.
4. Ma A., Engin A.E. Orthogonal rational approximation of transfer functions for high-frequency circuits. International journal of circuit theory and application. 2023. V. 5. № 3. P. 1007–1019.
5. Wu H., Niu S., Zhang Y., Zhao X., Fu W. Fast Magnetic Field Approximation Method for Simulation of Coaxial Magnetic Gears Using AI. IEEE Journal of Emerging and Selected Topics in Industrial Electronics. 2023. V. 4. № 1. P. 400–408. DOI 10.1109/JESTIE.2022. 3185558.
6. Barkhudaryan N.V., Sazonov A.Z., Sukharevsky O.I. Calculation of near-zone electromagnetic fields scattered by complex shape airborne objects and estimation of their angular coordinates by onboard antenna systems. International Conference on Mathematical Methods in Electromagnetic Theory. Kiev, Ukraine. 2002. V. 2. P. 493–495. DOI 10.1109/MMET.2002.1106977.
7. Binti Mohd Baharin R.H., Uno T., Arima T., Omi S. Electric Field Reconstruction of Antenna inside Phantom for Non-invasive SAR Measurement. International Symposium on Antennas and Propagation. Osaka, Japan. 2020. P. 371–372. DOI 10.23919/ISAP47053. 2021.9391148.
8. Bashly P.N., Manuilov B.D. The Method of Synthesis of Diagrams of the Orientation of the Phased Antenna Lattice. Antennas. 2007. № 6(121). P. 9–14. (in Russian)
9. Petrov A.S., Chikov V.A. Linear and planar antenna arrays synthesis realization using the iterative fast Fourier transform method. Achievements of modern radioelectronics. 2021. V. 75. № 12. P. 32–41. DOI 10.18127/j20700784-202112-03. (in Russian)
10. Las Heras F., Ortiz-Valbuena C. Antenna diagnosis and pattern reconstruction using near field amplitude data and iterative source reconstruction. IEEE Antennas and Propagation Society International Symposium. 1998. V. 3. P. 1343–1346.
11. Alvarez Y., Las-Heras F., Pino M.R. Antenna characterization using the Sources Reconstruction Method. Proceedings of the Fourth European Conference on Antennas and Propagation. Barcelona, Spain. 2010. P. 1–5.
12. Li P., Li Y., Jiang L.J., Hu J. A Wide-Band Equivalent Source Reconstruction Method Exploiting the Stoer-Bulirsch Algorithm with the Adaptive Frequency Sampling. IEEE Transactions on Antennas and Propagation. 2013. V. 61. № 10. P. 5338–5343. DOI 10.1109/ TAP.2013.2274032.
13. Las-Heras F., Galocha B., Besada J.L. Equivalent source modelling and reconstruction for antenna measurement and synthesis. IEEE Antennas and Propagation Society International Symposium. Montreal, Canada. 1997. V. 1. P. 156–159. DOI 10.1109/APS.1997. 630110.
14. Mitsui Y., Hayashi Y., Arai H. Far field estimation by current distribution reconstruction from 5-sided box near field. International Symposium on Antennas and Propagation. Osaka, Japan. 2021. P. 251–252. DOI 10.23919/ISAP47053.2021.9391460.
15. Pfeifer S., Carrasco E., Crespo-Valero P., Neufeld E., Kuhn S., Samaras T., Christ A., Capstick M.H., Kuster N. Total Field Reconstruction in the Near Field Using Pseudo-Vector E-Field Measurements. IEEE Transactions on Electromagnetic Compatibility. 2019. V. 61. № 2. P. 476–486. DOI 10.1109/TEMC.2018.2837897.
16. Zaridze R., Bit-Babik G., Tavzarashvili K. Solution of inverse problems by the method of auxiliary sources (MAS). IEEE Antennas and Propagation Society International Symposium. 1998. V. 2. P. 722–725.
17. Pasternak Y.G., Fedorov S.M., Zhuravlev D.V., Ashikhmin A.V., Rembovsky Y.A. Virtual Antenna Array for Minimization of DOA Estimation Systematic Error Caused by Scattering of Incident Waves on Antenna Carrier Body. Electronics. 2020. V. 9. № 2. P. 308. DOI 10.3390/electronics9020308.
18. Pasternak Y.G., Pendyurin V.A., Popov I.V., Fedorov S.M. Extrapolated Virtual Antenna Array for Enhancement of Resolution of Uniform Linear Array. Photonics & Electromagnetics Research Symposium. Hangzhou, China. 2022. P. 1045–1052. DOI 10.1109/PIERS55526. 2022.9793306.
19. Quijano J.L.A., Vecchi G. Source Reconstruction in antenna synthesis. Proceedings of the Fourth European Conference on Antennas and Propagation. Barcelona, Spain. 2010. P. 1–4.
20. Olen C.A., Compton R.T. A numerical pattern synthesis algorithm for arrays. International Symposium on Antennas and Propagation Society. Dallas, USA. 1990. V. 2. P. 828–831. DOI 10.1109/APS.1990.115236.
21. Sultan K., Abdullah H., Abdallah E., El-Hennawy H. MOM/GA-Based Virtual Array for Radar Systems. Sensors. 2020. V. 20. № 3. P. 713. DOI 10.3390/s20030713.
22. El-dawi H.A., Napoleon S.A., Hussein A.H. VAE/MPM/GA Technique for DoA Estimation Using Optimized Antenna Arrays. Wireless Personal Communications. 2017. V. 92. № 3. P.1271–1279. DOI 10.1007/s11277-016-3605-1.
23. Nai S.E., Ser W., Yu Z.L., Chen H. Beampattern Synthesis for Linear and Planar Arrays with Antenna Selection by Convex Optimization. IEEE Transactions on Antennas and Propagation. 2010. V. 58. № 12. P. 3923–3930. DOI 10.1109/TAP.2010.2078446.
24. Fuchs B., Skrivervik A., Mosig J.R. Shaped Beam Synthesis of Arrays via Sequential Convex Optimizations. IEEE Antennas and Wireless Propagation Letters. 2013. V. 12. P. 1049–1052. DOI 10.1109/LAWP.2013.2280043.
25. Zhang X., He Z., Zhang X., Peng W. High-Performance Beampattern Synthesis via Linear Fractional Semidefinite Relaxation and Quasi-Convex Optimization. IEEE Transactions on Antennas and Propagation. 2018. V. 66. № 7. P. 3421–3431. DOI 10.1109/TAP.2018. 2835310.
26. Shi Z., Feng Z. A new array pattern synthesis algorithm using the two-step least-squares method. IEEE Signal Processing Letters. 2005. V. 12. № 3. P. 250–253. DOI 10.1109/LSP.2004.842282.
27. Zhang Y., He W., Hong W., Song Z. Flat topped radiation pattern synthesis based on FIR filter concept. IEEE Asia Pacific Microwave Conference. 2017. P. 751–754. DOI 10.1109/APMC.2017.8251556.
28. Deng H., Himed B. A Virtual Antenna Beamforming (VAB) Approach for Radar Systems by Using Orthogonal Coding Waveforms. IEEE Transactions on Antennas and Propagation. 2009. V. 57. № 2. P. 425–435. DOI 10.1109/TAP.2008.2011387.
29. Zhang X., He Z., Liao B., Zhang X., Yang Y. Pattern Synthesis via Oblique Projection-Based Multipoint Array Response Control. IEEE Transactions on Antennas and Propagation. 2019. V. 67. № 7. P. 4602–4616. DOI 10.1109/TAP.2019.2911317.
30. Zhang X., He Z., Liao B., Zhang X., Peng W. Pattern Synthesis for Arbitrary Arrays via Weight Vector Orthogonal Decomposition. IEEE Transactions on Signal Processing. 2018. V. 66. № 5. P. 1286–1299. DOI 10.1109/TSP.2017.2787143.
31. Dib N. Design of linear antenna arrays with low side lobes level using symbiotic organisms search. Progress In Electromagnetics Research B. 2016. V. 68. № 1. P. 55–71. DOI 10.2528/PIERB16032504.
32. Akdagli A., Guney K. Shaped‐beam pattern synthesis of equally and unequally spaced linear antenna arrays using a modified tabu search algorithm. Microwave and Optical Technology Letters. 2003. V. 36. № 1. P.16–20. DOI 10.1002/mop.10657.
33. Al-Azza A.A., Al-Jodah A.A., Harackiewicz F.J. Spider Monkey Optimization: A Novel Technique for Antenna Optimization. IEEE Antennas and Wireless Propagation Letters. 2016. V. 15. P. 1016–1019. DOI 10.1109/LAWP.2015.2490103.
34. Subhashini K. Antenna array synthesis using a newly evolved optimization approach: Strawberry algorithm. Journal of Electrical Engineering. 2019. V. 70. № 4. P. 317–322. DOI 10.2478/jee-2019-0062.
35. Basu B., Mahanti G. Fire Fly and Artificial Bees Colony Algorithm for Synthesis of Scanned and Broadside Linear Array Antenna. Progress In Electromagnetics Research B. 2011. V. 32. P. 169–190. DOI 10.2528/PIERB11053108.
36. Shihab M., Najjar Y., Dib N., Khodier M. Design of Non-uniform Circular Antenna Arrays Using Particle Swarm Optimization. Journal of Electrical Engineering. 2008. V. 59. № 4. P. 216–220.
37. Das A., Mandal D., Ghoshal S.P., Kar R. Moth flame optimization based design of linear and circular antenna array for side lobe reduction. International Journal of Numerical Modelling: Electronic Networks. Devices and Fields. 2019. V. 32. P. e2486. DOI 10.1002/ jnm.2486.
38. Fuchs B. Application of Convex Relaxation to Array Synthesis Problems. IEEE Transactions on Antennas and Propagation. 2014. V. 62. № 2. P. 634–640. DOI 10.1109/TAP.2013.2290797.
39. Fuchs B., Rondineau S. Array Pattern Synthesis with Excitation Control via Norm Minimization. IEEE Transactions on Antennas and Propagation. 2016. V. 64. № 10. P. 4228–4234. DOI 10.1109/TAP.2016.2594300.
40. Guney K., Basbug S. Seeker Optimization Algorithm for Interference Suppression of Linear Antenna Arrays by Controlling Position-Only, Phase-Only, and Amplitude-Only. International Journal of RF and Microwave Computer‐Aided Engineering. 2011. V. 21. №5. P. 505–518. DOI 10.1002/mmce.20536.
41. Guney K., Basbug S. Linear Antenna Array Synthesis Using Mean Variance Mapping Method. Electromagnetics. 2014. V. 34. № 2. P. 67–84. DOI 10.1080/02726343.2013.863665.
42. Guo Q., Liao G., Wu Y., Li J. Pattern synthesis method for arbitrary arrays based on LCMV criterion. Electronics Letters. 2003. V. 39. № 23. P. 1628–1630. DOI 10.1049/el:20031068.
43. Guney K., Onay M. Optimal synthesis of linear antenna arrays using a harmony search algorithm. Expert Systems with Applications. 2011. V. 38. № 12. P. 15455–15462. DOI 10.1016/j.eswa.2011.06.015.
44. Khodier M. Comprehensive Study of Linear Antenna Array Optimisation Using the Cuckoo Search Algorithm. IET Microwaves. Antennas & Propagation. 2019. V. 13. № 9. P. 1325–1333. DOI 10.1049/iet-map.2018.5649.
45. Morabito A.F., Massa A., Rocca P., Isernia T. An Effective Approach to the Synthesis of Phase-Only Reconfigurable Linear Arrays. IEEE Transactions on Antennas and Propagation. 2012. V. 60. № 8. P. 3622–3631. DOI 10.1109/TAP.2012.2201099.
46. Wang F., Balakrishnan V., Zhou P.Y., Chen J., Yang R., Frank C. Optimal array pattern synthesis using semidefinite programming. IEEE International Conference on Acoustics, Speech, and Signal Processing. Salt Lake City, USA. 2001. V. 5. P. 2925–2928. DOI 10.1109/ ICASSP.2001.940259.
47. Fady N., Bataineh M. Optimizing and Thinning Planar Array Using Chebyshev Distribution and Improved Particle Swarm Optimization. Jordanian Journal of Computers and Information Technology. 2016. V. 1. № 1. P. 31–40. DOI 10.5455/jjcit.71-1439047564.
48. Pappula L., Ghosh D. Linear Antenna Array Synthesis using Cat Swarm Optimization. AEU – International Journal of Electronics and Communications. 2014. V. 68. № 6. P. 540–549. DOI 10.1016/j.aeue.2013.12.012.
49. Rajo-Iglesias E., Quevedo-Teruel O. Array synthesis with diversity pattern using an Ant Colony algorithm. IEEE International Symposium on Antennas and Propagation. 2011. P. 2433–2436. DOI 10.1109/APS.2011.5997014.
50. Recioui A. Optimization of Antenna Arrays Using Different Strategies Based on Taguchi Method. Arabian Journal for Science and Engineering. 2013. V. 39. № 2. P. 935–944. DOI 10.1007/s13369-013-0644-8.
51. Shahab S.N., Zainun A.R., Noordin N.H., Mohamed I.I., Abdullah W.D. Null steering Optimization based MVDR beamformer using hybrid PSOGSA approach for antenna array system. IEEE Student Conference on Research and Development. Kuala Lumpur, Malaysia. 2016. P. 1–6. DOI 10.1109/SCORED.2016.7810078.
52. Subhashini K.R., Satapathy J. Development of an Enhanced Ant Lion Optimization Algorithm and its Application in Antenna Array Synthesis. Applied Soft Computing. 2017. V. 59. P. 153–173. DOI 10.1016/j.asoc.2017.05.007.
53. Wang X., Aboutanios E., Amin M.G. Thinned Array Beampattern Synthesis by Iterative Soft-Thresholding-Based Optimization Algorithms. IEEE Transactions on Antennas and Propagation. 2014. V. 62. № 12. P. 6102–6113. DOI 10.1109/TAP.2014.2364048.
54. Wang X., Zhou Y., Wang Y. An Improved Antenna Array Pattern Synthesis Method Using Fast Fourier Transforms. International Journal of Antennas and Propagation. 2015. V. 2015. DOI 10.1155/2015/316962.
55. Zhang F., Jia W., Yao M. Linear Aperiodic Array Synthesis Using Differential Evolution Algorithm. IEEE Antennas and Wireless Propagation Letters. 2013. V. 12. P. 797–800. DOI 10.1109/LAWP.2013.2270930.
56. Zhang X., He Z., Liao B., Zhang X., Cheng Z., Lu Y. A2RC: An Accurate Array Response Control Algorithm for Pattern Synthesis. IEEE Transactions on Signal Processing. 2017. V. 65. № 7. P. 1810–1824. DOI 10.1109/TSP.2017.2649487.