radioelectronicsИзвестия высших учебных заведений России. РадиоэлектроникаJournal of the Russian Universities. Radioelectronics1993-89852658-4794Saint Petersburg Electrotechnical University10.32603/1993-8985-2025-28-3-106-115radioelectronics-1020Research ArticleРАДИОЛОКАЦИЯ И РАДИОНАВИГАЦИЯRADAR AND NAVIGATIONAutocorrelation Method for Phased Antenna Array Calibration Based on Far-Field Measurement SystemAutocorrelation Method for Phased Antenna Array Calibration Based on Far-Field Measurement Systemhttps://orcid.org/0000-0002-9222-2502NguyenXuan LuongNguyenXuan Luong

Xuan Luong Nguyen, Systems Engineer of the Research Institute of Radio Navigation Systems, Researcher of Air Defense – Air Force Technical Institute. PhD student of the Department of Radio Physics of VNU University of Science.

The author of 3 scientific publications. Area of expertise: ultra-high frequency radio engineering; systems engineering of multifunctional systems.

334, Nguyen Trai, Hanoi 100000

https://orcid.org/0000-0001-6626-893XNhanNguyen TrongNhanNguyen Trong

Nguyen Trong Nhan, Cand. Sci. (Eng.) (2023), Researcher of Air Defense

The author of more than 30 scientific publications. Area of expertise: radio engineering and telecommunications.

166, Hoang Van Thai, Hanoi 11400

https://orcid.org/0009-0000-5213-7349ThanhTran VanThanhTran Van

Tran Van Thanh, Researcher of Air Defense

The author of 2 scientific publications. Area of expertise: radio engineering and telecommunications.

166, Hoang Van Thai, Hanoi 11400

NguyenPhung BaoNguyenPhung Bao

Phung Bao Nguyen, Cand. Sci. (Eng.) (1996), Lecturer of the Department of Electronic Technology of Institute of System Integration

The author of 30 scientific publications. Area of expertise: radar information processing; radio-electronic and radar technology; systems engineering.

236, Hoang Quoc Viet, Hanoi 11917

VNU University of ScienceВьетнамVNU University of ScienceViet NamAir Defense-Air Force Technical InstituteВьетнамAir Force Technical InstituteViet NamLe Quy Don Technical UniversityВьетнамLe Quy Don Technical UniversityViet Nam202505072025283106115Copyright © Nguyen X.L., Nhan N.T., Thanh T.V., Nguyen P.B., 20252025Nguyen X.L., Nhan N.T., Thanh T.V., Nguyen P.B.Nguyen X.L., Nhan N.T., Thanh T.V., Nguyen P.B.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://re.eltech.ru/jour/article/view/1020

Introduction. An autocorrelation method can be used for calibration of phased antenna arrays (PAA) in the presence of interference. In scenarios where the PAA size is substantial, the initial elements of post-calibration are designated as a reference element for subsequent comparison with the following antenna elements. However, this method becomes time-consuming when the PAA size increases, also affecting the adaptive calibration proposed in this work. In practical applications, the calibration of PAA may be affected by various factors, such as intentional interference, passive interference, weather conditions, equipment aging, etc. Therefore, the impact of different interference levels on the calibration accuracy of PAA should be investigated. In addition, using a calibration antenna instead of a reference antenna may decrease the calibration accuracy of the received signal.Aim. To design and investigate a method for calibrating a PAA with high accuracy and low complexity based on an autocorrelation algorithm.Materials and methods. The efficiency of the developed algorithm was estimated using MATLAB/Simulink-based simulation and experimental validation.Results. To verify the feasibility of the proposed method for a large-scale antenna array, a 2 × 8 phased array antenna is implemented at 3 GHz. The proposed autocorrelation method for PAA exhibited superior performance over the conventional autocorrelation method. In comparison with the conventional autocorrelation technique, the developed method enhances the peak value of the combined beam in the E-plane by 3.2 and 3.7 dB, respectively. Furthermore, the beams at a distance between two antennas equal 0.625λ were tilted by 1.5 and 8° for the proposed and conventional autocorrelation methods, respectively.Conclusion. The validation through actual measurement data confirmed that the proposed autocorrelation method is more accurate than conventional methods in determining amplitude and phase offsets. The paper points out that the proposed autocorrelation calibration method performs well in large-scale on-site and factory-level calibration, being also effective in scenarios under the presence of external interference. 

Introduction. An autocorrelation method can be used for calibration of phased antenna arrays (PAA) in the presence of interference. In scenarios where the PAA size is substantial, the initial elements of post-calibration are designated as a reference element for subsequent comparison with the following antenna elements. However, this method becomes time-consuming when the PAA size increases, also affecting the adaptive calibration proposed in this work. In practical applications, the calibration of PAA may be affected by various factors, such as intentional interference, passive interference, weather conditions, equipment aging, etc. Therefore, the impact of different interference levels on the calibration accuracy of PAA should be investigated. In addition, using a calibration antenna instead of a reference antenna may decrease the calibration accuracy of the received signal.Aim. To design and investigate a method for calibrating a PAA with high accuracy and low complexity based on an autocorrelation algorithm.Materials and methods. The efficiency of the developed algorithm was estimated using MATLAB/Simulink-based simulation and experimental validation.Results. To verify the feasibility of the proposed method for a large-scale antenna array, a 2 × 8 phased array antenna is implemented at 3 GHz. The proposed autocorrelation method for PAA exhibited superior performance over the conventional autocorrelation method. In comparison with the conventional autocorrelation technique, the developed method enhances the peak value of the combined beam in the E-plane by 3.2 and 3.7 dB, respectively. Furthermore, the beams at a distance between two antennas equal 0.625λ were tilted by 1.5 and 8° for the proposed and conventional autocorrelation methods, respectively.Conclusion. The validation through actual measurement data confirmed that the proposed autocorrelation method is more accurate than conventional methods in determining amplitude and phase offsets. The paper points out that the proposed autocorrelation calibration method performs well in large-scale on-site and factory-level calibration, being also effective in scenarios under the presence of external interference. 

phased array antennaPAAcorrelation functionfar-field measurement systemscanning timeinterference sourcephased array antennaPAAcorrelation functionfar-field measurement systemscanning timeinterference sourceReferencesHe G., Gao X., Zhang R., Sun L., Zhou H. Phased Array Antenna Basics. Multibeam Phased Array Antennas as Satellite Constellation Ground Station. Modern Antenna. Singapore, Springer, 2024, pp. 9–37. doi: 10.1007/978-981-99-7910-3_2He G., Gao X., Zhang R., Sun L., Zhou H. Phased Array Antenna Basics. Multibeam Phased Array Antennas as Satellite Constellation Ground Station. Modern Antenna. Singapore, Springer, 2024, pp. 9–37. doi: 10.1007/978-981-99-7910-3_2Díaz J. D., Salazar-Cerreno J. L., Ortiz J. A., Aboserwal N. A., Lebrón R. M., Fulton C. A Cross-Stacked Radiating Antenna with Enhanced Scanning Performance for Digital Beamforming Multifunction Phased-Array Radars. IEEE Transactions on Antennas and Propagation. 2018, vol. 66, iss. 10, pp. 5258–5267. doi: 10.1109/TAP.2018.2862252Díaz J. D., Salazar-Cerreno J. L., Ortiz J. A., Aboserwal N. A., Lebrón R. M., Fulton C. A CrossStacked Radiating Antenna with Enhanced Scanning Performance for Digital Beamforming Multifunction Phased-Array Radars. IEEE Transactions on Antennas and Propagation. 2018, vol. 66, iss. 10, pp. 5258–5267. doi: 10.1109/TAP.2018.2862252Fenn A. J., Hurst P. T. Phased Array Antenna Theory. Ultrawideband Phased Array Antenna Technology for Sensing and Communications Systems. Cambridge, MIT Press, 2015, pp. 91–133.Fenn A. J., Hurst P. T. Phased Array Antenna Theory. Ultrawideband Phased Array Antenna Technology for Sensing and Communications Systems. Cambridge, MIT Press, 2015, pp. 91–133.Sorace R. Phased array calibration. Proc. IEEE Intern. Conf. on Phased Array Systems and Technology (Cat. no. 00TH8510), Dana Point, USA, 21–25 May 2000. IEEE, 2000, pp. 533–536. doi: 10.1109/PAST.2000.859013Sorace R. Phased array calibration. Proc. IEEE Intern. Conf. on Phased Array Systems and Technology (Cat. no. 00TH8510), Dana Point, USA, 21–25 May 2000. IEEE, 2000, pp. 533–536. doi: 10.1109/PAST.2000.859013Tang S., Wang Z., Pan C., Su R., Fan W., Gao S. A Fast and Efficient Calibration Method for Phased Array Antennas Using Fourier-Structured Excitation Matrix. IEEE Transactions on Antennas and Propagation. 2023, vol. 71, no. 3, pp. 2290–2299. doi: 10.1109/TAP.2023.3234814Tang S., Wang Z., Pan C., Su R., Fan W., Gao S. A Fast and Efficient Calibration Method for Phased Array Antennas Using Fourier-Structured Excitation Matrix. IEEE Transactions on Antennas and Propagation. 2023, vol. 71, no. 3, pp. 2290–2299. doi: 10.1109/TAP.2023.3234814Fulton C., Chappell W. Calibration techniques for digital phased arrays. IEEE Intern. Conf. on Microwaves, Communications, Antennas and Electronics Systems, Tel Aviv, Israel, 09–11 Nov. 2009. IEEE, 2009, pp. 1–10. doi: 10.1109/COMCAS.2009.5385979Fulton C., Chappell W. Calibration techniques for digital phased arrays. IEEE Intern. Conf. on Microwaves, Communications, Antennas and Electronics Systems, Tel Aviv, Israel, 09–11 Nov. 2009. IEEE, 2009, pp. 1–10. doi: 10.1109/COMCAS.2009.5385979Lier E., Zemlyansky M., Purdy D., Farina D. Phased array calibration and characterization based on orthogonal coding: Theory and experimental validation. IEEE Intern. Symp. on Phased Array Systems and Technology, Waltham, USA, 12–15 Oct. 2010. IEEE, 2010, pp. 271–278. doi: 10.1109/ARRAY.2010.5613357Lier E., Zemlyansky M., Purdy D., Farina D. Phased array calibration and characterization based on orthogonal coding: Theory and experimental validation. IEEE Intern. Symp. on Phased Array Systems and Technology, Waltham, USA, 12–15 Oct. 2010. IEEE, 2010, pp. 271–278. doi: 10.1109/ARRAY.2010.5613357Xiao Y., Fan Y., Cheng Y. J. Phased Array Antenna With Self-Calibration Network and Improved Scanning Performance. IEEE Antennas and Wireless Propagation Let. 2023, vol. 22, no. 6, pp. 1226–1230. doi: 10.1109/LAWP.2023.3237211Xiao Y., Fan Y., Cheng Y. J. Phased Array Antenna With Self-Calibration Network and Improved Scanning Performance. IEEE Antennas and Wireless Propagation Let. 2023, vol. 22, no. 6, pp. 1226–1230. doi: 10.1109/LAWP.2023.3237211Lee D.-H., Seo J.-W., Lee M.-S., Chung D., Lee D., Bang J.-H., Satriyotomo B., Pyo S. An S-Band-Receiving Phased-Array Antenna with a Phase-Deviation-Minimized Calibration Method for LEO Satellite Ground Station Applications. Electronics. 2022, vol. 11, iss. 23, art. no. 3847. doi: 10.3390/electronics11233847Lee D. -H., Seo J. -W., Lee M. -S., Chung D., Lee D., Bang J. -H., Satriyotomo B., Pyo S. An SBand-Receiving Phased-Array Antenna with a PhaseDeviation-Minimized Calibration Method for LEO Satellite Ground Station Applications. Electronics. 2022, vol. 11, iss. 23, art. no. 3847. doi: 10.3390/electronics11233847Liu H., Guan T., Fu C., Zhang S., Xu X., Xu Z., Qing A., Lin X. Improving Scanning Performance of Patch Phased Array Antenna by Using a Modified SIW Cavity and Sequential Rotation Technique. Electronics. 2024, vol. 13, iss. 9, art. no. 1776. doi: 10.3390/electronics13091776Liu H., Guan T., Fu C., Zhang S., Xu X., Xu Z., Qing A., Lin X. Improving Scanning Performance of Patch Phased Array Antenna by Using a Modified SIW Cavity and Sequential Rotation Technique. Electronics. 2024, vol. 13, iss. 9, art. no. 1776. doi: 10.3390/electronics13091776Li R., Zhang J., Li C., Li Y., Tian B., Wu C. An Accurate Mid-Field Calibration Technique for Large Phased Array Antenna. 6th Asia-Pacific Conf. on Antennas and Propagation (APCAP), Xi'an, China, 16–19 Oct. 2017. IEEE, 2017, pp. 1–3. doi: 10.1109/APCAP.2017.8420685Li R., Zhang J., Li C., Li Y., Tian B., Wu C. An Accurate Mid-Field Calibration Technique for Large Phased Array Antenna. 6th Asia-Pacific Conf. on Antennas and Propagation (APCAP), Xi'an, China, 16–19 Oct. 2017. IEEE, 2017, pp. 1–3. doi: 10.1109/APCAP.2017.8420685Zhou R., Hu Z., Zhao Q., Chen G., Tao J. Absolute Field Calibration of Receiver Antenna Phase Center Models for GPS/BDS-3 Signals. J. Geodesy. 2023, vol. 97, art. no. 83. doi: 10.1007/s00190-023-01773-7Zhou R., Hu Z., Zhao Q., Chen G., Tao J. Absolute Field Calibration of Receiver Antenna Phase Center Models for GPS/BDS-3 Signals. J. Geodesy. 2023, vol. 97, art. no. 83. doi: 10.1007/s00190-023-01773-7Pöhlmann R., Zhang S., Staudinger E., Dammann A., Hoeher P. A. Simultaneous Localization and Antenna Calibration. 16th Europ. Conf. on Antennas and Propagation (EuCAP), Madrid, Spain, 27 March– 01 Apr. 2022. IEEE, 2022, pp. 1–5. doi: 10.23919/EuCAP53622.2022.9769393Pöhlmann R., Zhang S., Staudinger E., Dammann A., Hoeher P. A. Simultaneous Localization and Antenna Calibration. 16th Europ. Conf. on Antennas and Propagation (EuCAP), Madrid, Spain, 27 March– 01 Apr. 2022. IEEE, 2022, pp. 1–5. doi: 10.23919/EuCAP53622.2022.9769393Horváth K. A., Ill G., Milánkovich Á. Calibration Method of Antenna Delays for UWB-Based Localization Systems. IEEE 17th Intern. Conf. on Ubiquitous Wireless Broadband (ICUWB), Salamanca, Spain, 12–15 Sept. 2017. IEEE, 2017, pp. 1–5. doi: 10.1109/ICUWB.2017.8250969Horváth K. A., Ill G., Milánkovich Á. Calibration Method of Antenna Delays for UWB-Based Localization Systems. IEEE 17th Intern. Conf. on Ubiquitous Wireless Broadband (ICUWB), Salamanca, Spain, 12–15 Sept. 2017. IEEE, 2017, pp. 1–5. doi: 10.1109/ICUWB.2017.8250969Lee Y.-S., Yoon T., Kim M., Lee S., Jung B., Oh J. A Design and Characterization Method of a Scalable Large Transmitting Array for Wireless Power Transfer. IEEE Transactions on Microwave Theory and Techniques, 2024, pp. 1–13. doi: 10.1109/TMTT.2024.3487911Lee Y.-S., Yoon T., Kim M., Lee S., Jung B., Oh J. A Design and Characterization Method of a Scalable Large Transmitting Array for Wireless Power Transfer. IEEE Transactions on Microwave Theory and Techniques, 2024, pp. 1–13. doi: 10.1109/TMTT.2024.3487911Linder M., Meinecke B., Halici E., Schwarz D., Waldschmidt C. Highly Efficient Calibration of Antenna Arrays by Active Targets in the Near-Field. IEEE Open J. of Antennas and Propagation. 2023, vol. 4, pp. 326–338. doi: 10.1109/OJAP.2023.3253942Linder M., Meinecke B., Halici E., Schwarz D., Waldschmidt C. Highly Efficient Calibration of Antenna Arrays by Active Targets in the Near-Field. IEEE Open J. of Antennas and Propagation. 2023, vol. 4, pp. 326–338. doi: 10.1109/OJAP.2023.3253942Jones D. L., Bagri D. S., Miyatake H. C., Tehrani B. J., Gatti M. S., Cooper H. W. Calibration of Antennas During Construction or Expansion of Radio Arrays. IEEE Aerospace Conf., Big Sky, USA, 01– 08 March 2008. IEEE, 2008, pp. 1–8. doi: 10.1109/AERO.2008.4526308Jones D. L., Bagri D. S., Miyatake H. C., Tehrani B. J., Gatti M. S., Cooper H. W. Calibration of Antennas During Construction or Expansion of Radio Arrays. IEEE Aerospace Conf., Big Sky, USA, 01– 08 March 2008. IEEE, 2008, pp. 1–8. doi: 10.1109/AERO.2008.4526308Wang B., Yan Li, Tian B. Rotating-Element Electric-Field Vector (REV) Calibration Method Based on Power Measurement for Phased Array Antenna. Intern. Applied Computational Electromagnetics Society Symp. (ACES), Suzhou, China, 01–04 Aug. 2017. IEEE, 2017, pp. 1–2.Wang B., Yan Li, Tian B. Rotating-Element Electric-Field Vector (REV) Calibration Method Based on Power Measurement for Phased Array Antenna. Intern. Applied Computational Electromagnetics Society Symp. (ACES), Suzhou, China, 01–04 Aug. 2017. IEEE, 2017, pp. 1–2.Zhang Y., Gao, Liu J. Single Reference Element Rotating-Element Electric-Field Vector Method for Phased Array Antenna Calibration. Systems Engineering and Electronics. 2024, vol. 46, iss. 5, pp. 1525–1534.Zhang Y., Gao, Liu J. Single Reference Element Rotating-Element Electric-Field Vector Method for Phased Array Antenna Calibration. Systems Engineering and Electronics. 2024, vol. 46, iss. 5, pp. 1525–1534.Yoon H.-J., Min B.-W. Improved Rotating-Element Electric-Field Vector Method for Fast Far-Field Phased Array Calibration. IEEE Transactions on Antennas and Propagation. 2021, vol. 69, no. 11, pp. 8021–8026. doi: 10.1109/TAP.2021.3083796Yoon H.-J., Min B.-W. Improved Rotating-Element Electric-Field Vector Method for Fast Far-Field Phased Array Calibration. IEEE Transactions on Antennas and Propagation. 2021, vol. 69, no. 11, pp. 8021–8026. doi: 10.1109/TAP.2021.3083796Liu M., Feng Z. Combined Rotating-element Electric-field Vector (CREV) Method for nearfield Calibration of Phased Array Antenna. Intern. Conf. on Microwave and Millimeter Wave Technology, Guilin, China, 18–21 Apr. 2007. IEEE, 2007, pp. 1–4. doi: 10.1109/ICMMT.2007.381281Liu M., Feng Z. Combined Rotating-element Electric-field Vector (CREV) Method for nearfield Calibration of Phased Array Antenna. Intern. Conf. on Microwave and Millimeter Wave Technology, Guilin, China, 18–21 Apr. 2007. IEEE, 2007, pp. 1–4. doi: 10.1109/ICMMT.2007.381281Su Y., Song Z., Zhang S., Gong S. Determination of Excitation Amplitude and Phase for Wide-Band Phased Array Antenna Based on Spherical Wave Expansion and Mode Filtering. Electronics. 2022, vol. 11, iss. 21, art. no. 3479. doi: 10.3390/electronics11213479Su Y., Song Z., Zhang S., Gong S. Determination of Excitation Amplitude and Phase for Wide-Band Phased Array Antenna Based on Spherical Wave Expansion and Mode Filtering. Electronics. 2022, vol. 11, iss. 21, art. no. 3479. doi: 10.3390/electronics11213479Wang J. P., Tsai Y.-L., Chen W.-J., Chen J.-H., Hwang R.-B. A Fast Phased Array System Calibration Method by Fully Utilising In-Built Beamformers. IEEE Conf. on Antenna Measurements and Applications (CAMA), Guangzhou, China, 14–17 Dec. 2022. IEEE, 2022, pp. 1–2. doi: 10.1109/CAMA56352.2022.10002539Wang J. P., Tsai Y.-L., Chen W.-J., Chen J.-H., Hwang R.-B. A Fast Phased Array System Calibration Method by Fully Utilising In-Built Beamformers. IEEE Conf. on Antenna Measurements and Applications (CAMA), Guangzhou, China, 14–17 Dec. 2022. IEEE, 2022, pp. 1–2. doi: 10.1109/CAMA56352.2022.10002539Pan C., Ba X., Tang Y., Zhang F., Zhang Y., Wang Z., Fan W. Phased Array Antenna Calibration Method Experimental Validation and Comparison. Electronics. 2023, vol. 12, iss. 3, art. no. 489. doi: 10.3390/electronics12030489Pan C., Ba X., Tang Y., Zhang F., Zhang Y., Wang Z., Fan W. Phased Array Antenna Calibration Method Experimental Validation and Comparison. Electronics. 2023, vol. 12, iss. 3, art. no. 489. doi: 10.3390/electronics12030489Nguyen X. L., Nhan N. T., Dang Thi T. T., Thanh T. V., Nguyen P. B., Trien N. D. Phased Array Antenna Calibration Based on Autocorrelation Algorithm. Sensors. 2024, vol. 24, iss. 23, art. no. 7496. doi: 10.3390/s24237496Nguyen X. L., Nhan N. T., Dang Thi T. T., Thanh T. V., Nguyen P. B., Trien N. D. Phased Array Antenna Calibration Based on Autocorrelation Algorithm. Sensors. 2024, vol. 24, iss. 23, art. no. 7496. doi: 10.3390/s24237496

The authors declare that there are no conflicts of interest present.