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2025-12-16
Auto-Calibration of Near-Field Microwave Measurements for Complex Permittivity Estimation
By
Progress In Electromagnetics Research M, Vol. 136, 46-56, 2025
Abstract
This paper presents a numerical study of a novel method for auto-calibration of scatteringparameter measurements in a near-field microwave sensor system. The here proposed method is applied to estimation of the average complex permittivity in a measurement domain from the scattering parameters, corrupted by gain uncertainties in the measurement instruments. Simultaneously with the average complex permittivity, the gain uncertainties are also estimated. The characteristic property of the proposed method is that no simplified mathematical model of the measurement domain is assumed, and instead a set of a-priori calibrated measurements is used. Numerical studies demonstrate the performance of the method in noiseless and noisy settings with and without nuisance stochastic perturbations in the measurement domain. An approach to compensate for the stochastic perturbations in the measurement domain permittivity is proposed, and it demonstrates an improved performance of the method in numerical examinations.
Citation
Andrei Ludvig-Osipov, Simon Stenmark, Thomas Rylander, and Tomas McKelvey, "Auto-Calibration of Near-Field Microwave Measurements for Complex Permittivity Estimation," Progress In Electromagnetics Research M, Vol. 136, 46-56, 2025.
doi:10.2528/PIERM25090302
References

1. Teppati, Valeria, Andrea Ferrero, and Mohamed Sayed, Modern RF and Microwave Measurement Techniques, Cambridge University Press, 2013.

2. Fraden, Jacob, Handbook of Modern Sensors: Physics, Designs, and Applications, Springer, 2004.

3. Hislop, Greg, Christophe Craeye, and David González Ovejero, "Antenna calibration for near-field material characterization," IEEE Transactions on Antennas and Propagation, Vol. 64, No. 4, 1364-1372, Apr. 2016.
doi:10.1109/tap.2016.2526087

4. Liu, Yongze, Xiaojian Xu, and Guangyao Xu, "MIMO radar calibration and imagery for near-field scattering diagnosis," IEEE Transactions on Aerospace and Electronic Systems, Vol. 54, No. 1, 442-452, Feb. 2018.
doi:10.1109/taes.2017.2760758

5. Zhao, Wei, Chunyue Cheng, Chao Yang, Jiankang Xiao, Yibang Wang, and Ye Huo, "Influence of non‐ideal line‐reflect‐match calibration standards on vector network analyzer S‐parameter measurements," IET Science, Measurement & Technology, Vol. 17, No. 6, 257-268, 2023.
doi:10.1049/smt2.12150

6. Lipor, John and Laura Balzano, "Robust blind calibration via total least squares," 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 4244-4248, Florence, Italy, 2014.
doi:10.1109/ICASSP.2014.6854402

7. Bilen, Çağdaş, Gilles Puy, Rémi Gribonval, and Laurent Daudet, "Convex optimization approaches for blind sensor calibration using sparsity," IEEE Transactions on Signal Processing, Vol. 62, No. 18, 4847-4856, 2014.
doi:10.1109/tsp.2014.2342651

8. Wei, Zhenyu, Wei Wang, Fuwang Dong, and Ping Liu, "Self-calibration algorithm with gain-phase errors array for robust DOA estimation," Progress In Electromagnetics Research M, Vol. 99, 1-12, 2021.
doi:10.2528/pierm20090701

9. Yuan, Bo, Zheng Jiang, Jianlin Zhang, Yuanyue Guo, and Dongjin Wang, "Sparse self-calibration for microwave staring correlated imaging with random phase errors," Progress In Electromagnetics Research C, Vol. 105, 253-269, 2020.
doi:10.2528/pierc20070104

10. Ayestaran, Rafael, Jesus A. Lopez-Fernandez, and Fernando Las Heras Andres, "Self-calibration for fault or obstacle correction in continually rotating array antennas," Progress In Electromagnetics Research, Vol. 111, 365-380, 2011.
doi:10.2528/pier10102803

11. Blakey, R. T., A. Mason, A. Al-Shamma'a, C. E. Rolph, and G. Bond, "Dielectric characterisation of lipid droplet suspensions using the small perturbation technique," Advancement in Sensing Technology: New Developments and Practical Applications, 81-91, Springer-Verlag, Heidelberg, Germany, 2013.

12. Korostynska, O., A. Mason, and A. Al-Shamma'a, "Microwave sensors for the non-invasive monitoring of industrial and medical applications," Sensor Review, Vol. 34, No. 2, 182-191, Mar. 2014.
doi:10.1108/sr-11-2012-725

13. Stenmark, Simon, Thomas Rylander, and Tomas McKelvey, "Neural networks for the estimation of low-order statistical moments of a stochastic dielectric," 2021 IEEE International Instrumentation and Measurement Technology Conference (I2MTC), 1-6, Glasgow, United Kingdom, May 2021.
doi:10.1109/i2mtc50364.2021.9459996

14. Andria, G., F. Attivissimo, A. Di Nisio, A. Trotta, S. M. Camporeale, and P. Pappalardi, "Design of a microwave sensor for measurement of water in fuel contamination," Measurement, Vol. 136, 74-81, Mar. 2019.
doi:10.1016/j.measurement.2018.12.076

15. Chen, L. F., C. K. Ong, C. P. Neo, V. V. Varadan, and V. K. Varadan, Microwave Electronics: Measurement and Materials Characterization, John Wiley & Sons, 2004.

16. Buckmaster, H. A., "Precision microwave complex permittivity measurements of high loss liquids," Journal of Electromagnetic Waves and Applications, Vol. 4, No. 7, 645-659, 1990.
doi:10.1163/156939390x00104

17. Hasar, U. C. and O. Simsek, "A calibration-independent microwave method for position-insensitive and nonsingular dielectric measurements of solid materials," Journal of Physics D: Applied Physics, Vol. 42, No. 7, 075403, Mar. 2009.
doi:10.1088/0022-3727/42/7/075403

18. Wan, C., B. Nauwelaers, W. De Raedt, and M. Van Rossum, "Two new measurement methods for explicit determination of complex permittivity," IEEE Transactions on Microwave Theory and Techniques, Vol. 46, No. 11, 1614-1619, Nov. 1998.
doi:10.1109/22.734537

19. Lanzi, Leandro, Marcello Carlà, Cecilia M. C. Gambi, and Leonardo Lanzi, "Differential and double-differential dielectric spectroscopy to measure complex permittivity in transmission lines," Review of Scientific Instruments, Vol. 73, No. 8, 3085-3088, 2002.
doi:10.1063/1.1494870

20. Hasar, U. C. and J. J. Barroso, "Electrical characterization of 3-D periodic microwire media using calibration-independent techniques," Journal of Electromagnetic Waves and Applications, Vol. 25, No. 14-15, 2110-2119, 2011.
doi:10.1163/156939311798072072

21. Xing, Lei, Jiajia Zhu, Qian Xu, Yongjiu Zhao, Chaoyun Song, and Yi Huang, "Generalised probe method to measure the liquid complex permittivity," IET Microwaves, Antennas & Propagation, Vol. 14, No. 8, 707-711, 2020.
doi:10.1049/iet-map.2019.1009

22. Nohlert, Johan, Thomas Rylander, and Tomas McKelvey, "Microwave measurement system for detection of dielectric objects in powders," IEEE Transactions on Microwave Theory and Techniques, Vol. 64, No. 11, 3851-3863, 2016.
doi:10.1109/tmtt.2016.2613047

23. Winges, Johan, Livia Cerullo, Thomas Rylander, Tomas McKelvey, and Mats Viberg, "Compressed sensing for the detection and positioning of dielectric objects inside metal enclosures by means of microwave measurements," IEEE Transactions on Microwave Theory and Techniques, Vol. 66, No. 1, 462-476, 2018.
doi:10.1109/tmtt.2017.2708109

24. Aster, Richard C., Brian Borchers, and Clifford H. Thurber, Parameter Estimation and Inverse Problems, 2nd Ed., Academic Press, Waltham, MA, 2013.

25. Engen, G. F. and C. A. Hoer, "Thru-reflect-line: An improved technique for calibrating the dual six-port automatic network analyzer," IEEE Transactions on Microwave Theory and Techniques, Vol. 27, No. 12, 987-993, 1979.
doi:10.1109/tmtt.1979.1129778

26. Agilent Technologies "Applying error correction to network analyzer measurements," Agilent AN 1287-3, 2002.

27. Nicolson, A. M. and G. F. Ross, "Measurement of the intrinsic properties of materials by time-domain techniques," IEEE Transactions on Instrumentation and Measurement, Vol. 19, No. 4, 377-382, Nov. 1970.
doi:10.1109/tim.1970.4313932

28. Weir, W. B., "Automatic measurement of complex dielectric constant and permeability at microwave frequencies," Proceedings of the IEEE, Vol. 62, No. 1, 33-36, 1974.
doi:10.1109/proc.1974.9382

29. Valagiannopoulos, C. A., "A novel methodology for estimating the permittivity of a specimen rod at low radio frequencies," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 5-6, 631-640, 2010.
doi:10.1163/156939310791036331

30. Kress, Rainer and William Rundell, "Inverse scattering for shape and impedance revisited," Journal of Integral Equations and Applications, Vol. 30, No. 2, 293-311, 2018.
doi:10.1216/JIE-2018-30-2-293

31. Balanis, Constantine A., Antenna Theory: Analysis and Design, John Wiley & Sons, 2016.

32. Jaglan, Naveen, Binod Kanaujia, Samir Dev Gupta, and Shweta Srivastava, "Triple band notched UWB antenna design using electromagnetic band gap structures," Progress In Electromagnetics Research C, Vol. 66, 139-147, 2016.
doi:10.2528/pierc16052304

33. Koziel, Slawomir and Leifur Leifsson, Surrogate-Based Modeling and Optimization, Springer, 2013.

34. Jin, Jing, Chao Zhang, Feng Feng, Weicong Na, Jianguo Ma, and Qi-Jun Zhang, "Deep neural network technique for high-dimensional microwave modeling and applications to parameter extraction of microwave filters," IEEE Transactions on Microwave Theory and Techniques, Vol. 67, No. 10, 4140-4155, Oct. 2019.
doi:10.1109/tmtt.2019.2932738

35. Sahu, Kaustab C., Slawomir Koziel, and Anna Pietrenko-Dabrowska, "Surrogate modeling of passive microwave circuits using recurrent neural networks and domain confinement," Scientific Reports, Vol. 15, No. 1, 13322, Apr. 2025.
doi:10.1038/s41598-025-91643-3

36. Chávez-Hurtado, José Luis and José Ernesto Rayas-Sánchez, "Polynomial-based surrogate modeling of RF and microwave circuits in frequency domain exploiting the multinomial theorem," IEEE Transactions on Microwave Theory and Techniques, Vol. 64, No. 12, 4371-4381, Dec. 2016.
doi:10.1109/tmtt.2016.2623902

37. Ardizzone, Lynton, Jakob Kruse, Sebastian Wirkert, Daniel Rahner, Eric W. Pellegrini, Ralf S. Klessen, Lena Maier-Hein, Carsten Rother, and Ullrich Köthe, "Analyzing inverse problems with invertible neural networks," ArXiv Preprint ArXiv:1808.04730, Feb. 2019.
doi:10.48550/arXiv.1808.04730

38. Radev, Stefan T., Ulf K. Mertens, Andreas Voss, Lynton Ardizzone, and Ullrich Köthe, "BayesFlow: Learning complex stochastic models with invertible neural networks," IEEE Transactions on Neural Networks and Learning Systems, Vol. 33, No. 4, 1452-1466, 2022.
doi:10.1109/tnnls.2020.3042395

39. Valagiannopoulos, Constantinos, "On measuring the permittivity tensor of an anisotropic material from the transmission coefficients," Progress In Electromagnetics Research B, Vol. 9, 105-116, 2008.
doi:10.2528/pierb08072005

40. Nilsson, F., U. W. Gedde, and M. S. Hedenqvist, "Modelling the relative permittivity of anisotropic insulating composites," Composites Science and Technology, Vol. 71, No. 2, 216-221, 2011.
doi:10.1016/j.compscitech.2010.11.016