In order to analyze the Doppler spectrum of three-dimensional (3-D) moving targets above a time-evolving sea surface, a hybrid method with acceleration techniques is proposed to simulate the electromagnetic (EM) scattering from the composite moving model. This hybrid iterative method combines Kirchhoff approximation (KA) and the multilevel fast multipole algorithm (MLFMA) to solve the EM backscattering from the rough sea surface and the targets, respectively, then mutual EM coupling effects between them are taken into account through an iterative process. To overcome the vast computational cost in the iterative process, acceleration approaches which can greatly reduce the calculation time are applied. Coupling area on the sea surface is truncated according to geometrical optic principle. Then a fast far-field approximation (FAFFA) is applied to speed up the mutual interactions between the targets and the sea surface. A successive iteration method is proposed to reduce the convergence steps for the MLFMA process. The accuracy and efficiency of this hybrid method with accelerations are demonstrated. Doppler spectra of backscattering signals obtained from such numerical EM simulations are compared for different incident angles, target velocities and surface models. The broadening effects of the Doppler spectra due to the mutual EM coupling interactions are studied.
2. Wang, , Y., Y.-M. Zhang, and L.-X. Guo, "Microwave doppler spectra of sea echoes at high incidence angles: Influences of large-scale waves," Progress In Electromagnetics Research B,, Vol. 48, 99-113, 2013.
3. Valagiannopoulos, C. and N. Uzunoglu, "Simplified model for EM inverse scattering by longitudinal subterranean inhomogeneities exploiting the dawn/dusk ionospheric ridge," IET Microwaves, Antennas & Propagation,, Vol. 5, 1319-1327, 2011.
4. Sun, , R.-Q., M. Zhang, C. Wang, and Y. Chen, "Study of electromagnetic scattering from ship wakes on PEC sea surfaces by the small-slope approximation theory," Progress In Electromagnetics Research, Vol. 129, 387-404, 2012..
5. Valagiannopoulos, , C. A., "On jamming unfriendly submarine communication by radiating across an island in the vicinity of the opponent's coastline," Electromagnetics, Vol. 32, 438-449, 2012.
6. Valagiannopoulos, , C. A., "On developing alternating voltage around a rotating circular ring under plane wave excitation in the presence of an eccentrically positioned metallic core," Progress In Electromagnetics Research M, Vol. 12, 193-204, 2010.
7. Bi, S. and X. Y. Ren, "Maneuvering target doppler-bearing tracking with signal time delay using interacting multiple model algorithms," Progress In Electromagnetics Research, Vol. 87, 15-41, 2008.
8. Valagiannopoulos, , C. A., "Study of an electrically anisotropic cylinder excited magnetically by a straight strip line," Progress In Electromagnetics Research, Vol. 73, 297-325, 2007.
9. Chen, H., , M. Zhang, and H.-C. Yin, "Facet-based treatment on microwave bistatic scattering of three-dimensional sea surface with electrically large ship," Progress In Electromagnetics Research, Vol. 123, 385-405, 2012.
10. Wu, , Z.-S., J.-J. Zhang, and L. Zhao, "Composite electromagnetic scattering from the plate target above a one-dimensional sea surface: Taking the diffraction into account," Progress In Electromagnetics Research, Vol. 92, 317-331, 2009.
11. Liu, , Z. , L. Carin, and , "Effcient evaluation of the half-space Green's function for fast-multipole scattering models," Microwave and Optical Technology Letters, Vol. 29, 388-392, 2001.
12. Geng, N., , A. Sullivan, and L. Carin, "Fast multipole method for scattering from an arbitrary PEC target above or buried in a lossy half space," IEEE Transactions on Antennas and Propagation, Vol. 49, 740-748, 2001.
13. Johnson, , J. T., "A numerical study of scattering from an object above a rough surface," IEEE Transactions on Antennas and Propagation, Vol. 50, 1361-1367, 2002.
14. Zhang, Y., , Y. Yang, H. Braunisch, and J. Kong, "Electromagnetic wave interaction of conducting object with rough surface by hybrid SPM/MOM technique," Progress In Electromagnetics Research, Vol. 22, 315-335, 1999.
15. Yang, W., , Z. Zhao, C. Qi, and Z. Nie, "Electromagnetic modeling of breaking waves at low grazing angles with adaptive higher order hierarchical legendre basis functions," IEEE Transactions on Geoscience and Remote Sensing, Vol. 49, , 346-352, 2011.
16. Beckmann, P. , A. Spizzichino, and , "The Scattering of Electromag netic Waves from Rough Surfaces," Artech House, Inc., Vol. 1, 511, 1987.
17. Tsang, , L., , J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves, Theories and Applications,, Vol. 27, Wiley-Interscience, 2004.
18. Chew, W. C., T. J. Cui, and J. M. Song, "A FAFFA-MLFMA algorithm for electromagnetic scattering," IEEE Transactions on Antennas and Propagation, Vol. 50, 1641-1649, 2002.
19. Chaitin-Chatelin, F. and S. Gratton, "Convergence in finite pre-cision of successive iteration methods under high nonnormality," BIT Numerical Mathematics, Vol. 36, 455-469, 1996.
20. Toporkov, , J. V. , G. S. Brown, and , "Numerical simulations of scattering from time-varying, randomly rough surfaces," IEEE Transactions on Geoscience and Remote Sensing, Vol. 38, 1616-1625, 2000.
21. Nie, D., , M. Zhang, X. Geng, and P. Zhou, "Investigation on doppler spectral characteristics of electromagnetic backscattered echoes from dynamic nonlinear surfaces of finite-depth sea," Progress In Electromagnetics Research, Vol. 130, 169-186, 2012.
22. Li, X. , X. Xu, and , "Scattering and doppler spectral analysis for two-dimensional linear and nonlinear sea surfaces," IEEE Transactions on Geoscience and Remote Sensing,, Vol. 49, 603-611, 2011.
23. Coifman, , R., , V. Rokhlin, and S. Wandzura, "The fast multipole method for the wave equation: A pedestrian prescription," IEEE Antennas and Propagation Magazine, Vol. 35, 7-12, 1993.