This paper presents a complete ray-tracing based model which takes into account scattering from rough surfaces in indoor environments. The proposed model relies on a combination between computer graphics and radar techniques. The paths between the transmitter and the receiver are found thanks to a Bi-Directional Path-Tracing algorithm, and the scattering field after each interaction between the electromagnetic wave and the environment is computed according to the Kirchhoff Approximation. This propagation model is implemented as a plug-in in an existing full 3-D ray-tracing software. Thus, we compare the results of classical ray-tracing with those of our model to study the influence of the scattering phenomenon on the wave propagation in typical indoor environments.
1. Breto, R. and A. Monorchio, "Time-domain hybrid methods to solve complex electromagnetic problems," EMC Congress, 2003.
2. Maystre, D., "Electromagnetic scattering by a set of objects: an integral method based on scattering operator," Progress In Electromagnetics Research, Vol. 57, 55-84, 2006. doi:10.2528/PIER05040901
3. Al Sharkawy, M. H., V. Demir, and A. Z. Elsherbeni, "The iterative multi-region algorithm using a hybrid finite difference frequency domain and method of moment techniques," Progress In Electromagnetics Research, Vol. 57, 19-32, 2006. doi:10.2528/PIER05071001
4. Wang, S., X. Guan, D.Wang, X. Ma, and Y. Su, "Electromagnetic scattering by mixed conducting/dielectric objects using higherorder MoM," Progress In Electromagnetics Research, Vol. 66, 51-63, 2006. doi:10.2528/PIER06092101
5. Mouysset, V., P. A. Mazet, and P. Borderies, "Efficient treatment of 3d time-domain electromagnetic scattering scenes by disjointing sub-domains and with consistent approximations," Progress In Electromagnetics Research, Vol. 71, 41-57, 2007. doi:10.2528/PIER07013005
6. Deschamps, G. A., Ray techniques in electromagnetics, Proc. IEEE, Vol. 60, No. 9, 1022-1035, 1972.
7. Balanis, C. A., Advanced Engineering Electromagnetics, John Wiley and Sons, 1989.
8. Keller, J. B., "Geometrical theory of diffraction," J. Opt. Soc. Am., Vol. 52, No. 2, 116-130, 1962.
9. Kouyoumjian, R. G. and P. H. Pathak, A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface, Proc. IEEE, Vol. 62, No. 11, 1448-1461, 1974.
10. Beckmann, P. and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces, Pergamon, 1963.
11. Ament, W. S., Toward a theory of reflection by a rough surface, Proc. IEEE, Vol. 41, No. 1, 142-146, 1953.
12. Boithias, L., Radio Wave Propagation, McGraw-Hill, 1987.
13. Anderson, H. R., A second generation 3-D ray-tracing model using rough surface scattering, VTC '1996 Proceedings, Vol. 1, No. 5, 46-50, 1996.
14. Ng, K. H., E. K. Tameh, and A. R. Nix, A new hybrid geometrical optics and radiance based scattering model for raytracing applications, ICC '2005 Proceedings, Vol. 4, No. 5, 2168-2172, 2005.
15. Oren, M. and S. K. Nayar, "Generalization of the Lambertian model and implications for machine vision," International Journal of Computer Vision, Vol. 14, No. 3, 227-251, 1995. doi:10.1007/BF01679684
16. Didascalou, D., M. Dottling, N. Geng, and W. Wiesbeck, "An approach to include stochastic rough surface scattering into deterministic ray-optical wave propagation modeling," IEEE Trans. Antennas Propagat., Vol. 51, No. 7, 1508-1515, 2003. doi:10.1109/TAP.2003.813600
17. Lafortune, E. P. and Y. D. Willems, Bi-directional path tracing, SIGGRAPH '1993 Proceedings, No. 12, 145-153, 1993.
18. Ogilvy, J. A., Theory of Wave Scattering from Random Rough Surfaces, Institute of Physics Publishing, 1991.
19. Ulaby, F. T., R. K. Moore, and A. K. Fung, Microwave Remote Sensing: Active and Passive, Vol. II: Radar Remote Sensing and Surface Scattering and Emission Theory, Vol. II: Radar Remote Sensing and Surface Scattering and Emission Theory, Artech House, 1986.
20. Edgeworth, F. Y., On the Representation of Statistical Frequency by a Series, JRSS, 1907.
21. Longuet-Higgins, M. S., "The effect of non-linearities on statistical distributions in the theory of sea waves," J. Fluid Mech., Vol. 17, 459-480, 1963. doi:10.1017/S0022112063001452
22. Cocheril, Y., R. Vauzelle, and L. Aveneau, 3-D channel simulations including scattering from non-Gaussian rough surfaces, VTC '2006 Proceedings, No. 9, 1-5, 2006.
23. Chakravarti, I. M., R. G. Laha, and J. Roy, Handbook of Methods of Applied Statistics, Vol. 1, Vol. 1, John Wiley and Sons, 1967.
24. Appel, A., "Some techniques for shading machine renderings of solids," in AFIPS 1968 Spring Joint Computer Conf., Vol. 32, 37-45, 1968.
25. Kajiya, J. T., "The rendering equation," Computer Graphics, Vol. 20, No. 4, 143-150, 1986. doi:10.1145/15886.15902
26. Goral, C. M., K. E. Torrance, D. P. Greenberg, and B. Battaile, Modelling the interaction of light between diffuse surfaces, SIGGRAPH '84 Proceedings, Vol. 18, No. 7, 212-222, 1984.
27. Whitted, T., "An improved illumination model for shaded display," Communications of the ACM, Vol. 23, No. 6, 343-349, 1980. doi:10.1145/358876.358882
28. Jensen, H. W. and N. J. Christensen, "Photon maps in bi-directional Monte-Carlo Ray-Tracing of complex objects," Computers and Graphics, Vol. 19, No. 2, 215-224, 1995. doi:10.1016/0097-8493(94)00145-O
29. Hammersley, J. M. and D. C. Handscomb, Monte-Carlo Methods, Chapman and Hall, 1964.
30. Cocheril, Y., S. Reynaud, and R. Vauzelle, Comparison between two original methods including scattering in 3D channel simulations, ECWT '2006 Proceedings, No. 9, 2006.
31. Lafortune, E. P., "Mathematical models and Monte-Carlo algorithms for physically based rendering," Ph.D. Dissertation, 1996.
32. Pousset, Y., R. Vauzelle, L. Aveneau, and M. Meriaux, "Characterization of the mobile channel by a 3-D UTD propagation model," PSIP '2001, No. 1, 3, 2001.