Compressing Electromagnetic Field by Rational Interpolation of the Spherical Wave Expansion Coefficients

Authors

  • Haobo Yuan School of Electronic Engineering Xidian University, Xi’an, Shaanxi, China
  • Pu Yang School of Electronic Engineering Xidian University, Xi’an, Shaanxi, China
  • Nannan Wang School of Electronic Engineering Xidian University, Xi’an, Shaanxi, China
  • Yi Ren School of Electronic Engineering Xidian University, Xi’an, Shaanxi, China
  • Shasha Li Beijing Institute of Space Long March Vehicle Beijing, China

DOI:

https://doi.org/10.13052/2024.ACES.J.400405

Keywords:

Antenna, data compression, rational interpolation, spherical harmonic transform

Abstract

It is of great significance to obtain the electromagnetic field radiated by an antenna or scattered by an object over a frequency band. But this data often occupies so large a memory that cannot be applied readily. This paper proposes to compress the field based on the spherical harmonic transformation (SHT) and rational interpolation. First, the tangential electric field over a sphere surrounding the antenna is obtained by simulation or measurement. Then, this field is converted into the spherical harmonic coefficients, which are sparse discrete spectra. Finally, these coefficients are interpolated over the whole frequency band with only a few sampling points. Numerical examples show that the proposed algorithm can compress the data of the near field of a rectangular waveguide antenna by about 17278 times, and those of the far field scattered from an UAV by about 103 times.

Downloads

Download data is not yet available.

Author Biographies

Haobo Yuan, School of Electronic Engineering Xidian University, Xi’an, Shaanxi, China

Haobo Yuan was born in Tianmen, Hubei, China, in 1980. He received the B.S., M.S., and Ph.D. degrees in electromagnetic fields and microwave technology from Xidian University, Xi’an, China, in 2003, 2006, and 2009, respectively. Since 2006, he has been with the School of Electronic Engineering, Xidian University, where he is an Associate Professor. He was a post-doctoral researcher at the Ohio State University in 2019. His current research interests include computational electromagnetics, antenna measurements, and electromagnetic compatibility.

Pu Yang, School of Electronic Engineering Xidian University, Xi’an, Shaanxi, China

Pu Yang was born in An’qing, Anhui, China, in 2000. He received the B.S. degree in electronic information engineering from Changchun University of Science and Technology, Changchun, China, in 2018. He is currently pursuing the M.S. degree with Xidian University. His research interests are numerical techniques in computational electromagnetics.

Nannan Wang, School of Electronic Engineering Xidian University, Xi’an, Shaanxi, China

Nannan Wang received the B.S. degree in electronic information engineering from Nanjing University of Information Science and Technology, Nanjing, China, in 2023. She is currently pursuing the M.Eng. degree with Xidian University. Her research interest is antenna measurement techniques.

Yi Ren, School of Electronic Engineering Xidian University, Xi’an, Shaanxi, China

Yi Ren (Senior Member, IEEE) was born in Anhui, China, in 1982. He received the B.S. degree from Anhui University, Hefei, China, in 2004, and the Ph.D. degree from the University of Electronic Science and Technology of China (UESTC), Chengdu, China, in 2009. In 2009, he joined Chongqing Jinmei Inc., Chongqing, China, as an Electromagnetic Compatibility Engineer. In 2011, he joined the Chongqing University of Posts and Telecommunications (CQUPT), Chongqing, where he was lately promoted as Full Professor. From 2014 to 2015, he was a Post-Doctoral Research Scholar with Duke University, Durham, NC, USA. Since August 2020, he has been a Professor with Xidian University, Xi’an, China. His research interests include computational electromagnetics and electromagnetic compatibility.

Shasha Li, Beijing Institute of Space Long March Vehicle Beijing, China

Shasha Li received the B.S. degree in electronic engineering from Northwestern Polytechnical University, Xi’an, China, in 2006. She received the Ph.D. degree in signal and information processing from Institute of Acoustics, Chinese Academy of Sciences (IACAS), Beijing, China, in 2012. Currently, she is an Engineer with Beijing Institute of Space Long March Vehicle, Beijing, China. Her current research interests include adaptive signal processing and array signal processing.

References

N. Y. Tseng and W. D. Burnside, “A very efficient RCS data compression and reconstruction technique, volume 4,” NASA, Washington, D.C., Tech. Rep. NAS 1.26:191378-Vol-4, Nov. 1992.

L. C. T. Chang, I. J. Gupta, W. D. Burnside, and C. L. T. Chang, “A data compression technique for scattered fields from complex targets,” IEEE Trans. Antennas Propagat., vol. 45, no. 8, pp. 1245-1251, Aug. 1997.

I. J. Gupta and W. D. Burnside, “Electromagnetic scattered field evaluation and data compression using imaging techniques,” NASA, Washington, D.C., Tech. Rep. NAS 1.26:207337, Sep. 1996.

T. K. Sarkar and O. Pereira, “Using the matrix pencil method to estimate the parameters of a sum of complex exponentials,” IEEE Trans. Antennas Propagat., vol. 37, no. 1, pp. 48-55, Feb. 1995.

J. Tsao and B. D. Steinberg, “Reduction of sidelobe and speckle artifacts in microwave imaging: The CLEAN technique,” IEEE Trans. Antennas Propagat., vol. 36, no. 4, pp. 543-556, Apr. 1988.

R. Bhalla and H. Ling, “Three-dimensional scattering center extraction using the shooting and bouncing ray technique,” IEEE Trans. Antennas Propagat., vol. 44, no. 11, pp. 1445-1453, Nov. 1996.

C. Wu, H. Zhao, and J. Hu, “Near field sampling compression based on matrix CUR decomposition,” in APS/URSI, Singapore, pp. 1455-1456, 2021.

H. Zhao, X. Li, Z. Chen, and J. Hu, “Skeletonization-scheme-based adaptive near field sampling for radio frequency source reconstruction,” IEEE Internet Things, vol. 6, no. 6, pp. 10219-10228, Dec. 2019.

H. Guo, Y. Liu, J. Hu, and E. Michielssen, “A butterfly-based direct integral-equation solver using hierarchical LU factorization for analyzing scattering from electrically large conducting objects,” IEEE Trans. Antennas Propagat., vol. 65, no. 9, pp. 4742-4750, Sep. 2017.

G. M. Binge and E. Micheli-Tzanakou, “Fourier compression-reconstruction technique (MRI application),” in Images of the Twenty-First Century. Proceedings of the Annual International Engineering in EMBC, Seattle, WA, pp. 524-525, 1989.

W. X. Sheng, D. G. Fang, J. Zhuang, T. J. Liu, and Z. L. Yang, “Data compression in RCS modeling by using the threshold discrete Fourier transform method,” Chinese Journal of Electronics, vol. 10, no. 4, pp. 557-559, Oct. 2001.

S. J. Li, H. Pang, P. Y. Li, Y. N. Li, and Z. X. Liu, “Image compression based on SVD algorithm,” in CISAI, Kunming, China, pp. 306-309, 2021.

V. Cheepurupalli, S. Tubbs, K. Boykin, and N. Naheed, “Comparison of SVD and FFT in image compression,” in CSCI, Las Vegas, Nevada, pp. 526-530, 2015.

M. L. Don and G. R. Arce, “Antenna radiation pattern compressive sensing,” in MILCOM, Los Angeles, CA, pp. 174-181, 2018.

P. Debroux and B. Verdin, “Compressive sensing reconstruction of wideband antenna radiation characteristics,” Progress In Electromagnetics Research C, vol. 73, pp. 1-8, 2017.

M. Don, “Compressive antenna pattern measurement: A case study in practical compressive sensing,” in 2022 IEEE AUTOTESTCON, National Harbor, MD, pp. 1-9, 2022.

W. Chen, C. Gao, Y. Cui, Y. Q. Jiang, and L. Yang, “A complex RCS calibration data interpolation method based on compressed sensing,” in PIERS - Fall, Xiamen, China, pp. 1295-1299,2019.

H. Zhang, Y. Jiang, and X. Li, “Reconstruction of antenna radiation pattern based on compressed sensing,” Journal of Shanghai Jiaotong Univ. (Sci.), vol. 25, pp. 790-794, July 2020.

A. Massa, P. Rocca, and G. Oliveri, “Compressive sensing in electromagnetics: A review,” IEEE Trans. Antennas Propagat., vol. 57, no. 1, pp. 224-238, Feb. 2015.

W. Dullaert and H. Rogier, “Novel compact model for the radiation pattern of UWB antennas using vector spherical and Slepian decomposition,” IEEE Transactions on Antennas and Propagation, vol. 58, no. 2, pp. 287-299, 2010.

B. Fuchs, L. le Coq, S. Rondineau, and M. D. Migliore, “Fast antenna far-field characterization via sparse spherical harmonic expansion,” IEEE Transactions on Antennas and Propagation, vol. 65, no. 10, pp. 5503-5510, 2017.

R. J. Allard and D. H. Werner, “The model-based parameter estimation of antenna radiation patterns using windowed interpolation and spherical harmonics,” IEEE Transactions on Antennas and Propagation, vol. 51, no. 8, pp. 1891-1906, 2003.

J. Gilewicz and Y. Kryakin, “Froissart doublets in Padé approximation in the case of polynomial noise,” Journal of Computational and Applied Mathematics, vol. 153, no. 1-2, pp. 235-242, 2003.

Z. Du, M. Kwon, D. Choi, and J. Koh, “Radiation pattern reconstruction techniques for antenna,” ICEIC, pp. 143-146, 2008.

J. E. Hansen, Spherical Near-Field Antenna Measurements. London: IET, 1988.

Q. T. le Gia, M. Li, and Y. G. Wang, “Algorithm 1018: FaVeST-fast vector spherical harmonic transforms,” ACM Transactions on Mathematical Software, vol. 47, no. 4, Dec. 2021.

Y. Q. Xiao, S. Grivet-Talocia, P. Manfredi, and R. Khazaka, “A novel framework for parametric loewner matrix interpolation,” IEEE Transactions on Components, Packaging and Manufacturing Technology, vol. 9, no. 12, pp. 2404-2417, Dec. 2019.

Y. Nakatsukasa, O. Sete, and L. N. Trefethen, “The AAA algorithm for rational approximation,” SIAM J. Sci. Comput., vol 40, no. 3, pp. A1494-A1522, 2018.

W. X. Sheng, D. G. Fang, J. Zhuang, T. Liu, and Z. L. Yang, “Comparative study on the data compression in RCS modeling,” in ISAPE, Beijing, China, pp. 573-576, 2000.

G. Giannetti and L. Klinkenbusch, “A numerical alternative for 3D addition theorems based on the bilinear form of the dyadic Green’s function and the equivalence principle,” Advances in Radio Science, vol. 22, pp. 9-15, 2024.

Downloads

Published

2025-04-30

How to Cite

[1]
H. . Yuan, P. . Yang, N. . Wang, Y. . Ren, and S. . Li, “Compressing Electromagnetic Field by Rational Interpolation of the Spherical Wave Expansion Coefficients”, ACES Journal, vol. 40, no. 04, pp. 317–325, Apr. 2025.

Issue

2025: Vol 40 Iss 4

Section

General Submission

Categories