APPLICATION OF THE FINITE-DIFFERENCE FREQUENCY-DOMAIN (FDFD) METHOD ON RADIOWAVE PROPAGATION IN URBAN ENVIRONMENTS
Keywords:Finite-Difference Frequency-Domain (FDFD), Radiowave propagation, urban environments
In this work a Finite-Difference Frequency-Domain (FDFD) propagation method for complex urban environments is proposed. The formulation starts from the discretization of the Helmholtz equation for the magnetic field instead of the usual separate one order derivative Ampere's and Faraday's laws. The Stretched Coordinate Perfectly Matched Layer (SCPML) is used as an absorbing boundary condition. These procedures produce less field components to estimate and achieve high wave absorption at the computation domain boundaries. The main goal is the rigorous prediction of VHF/SHF signals in real urban scenarios through the evaluation of several propagation mechanisms: direct rays, diffraction, reflection and refraction effects. The method is validated through an analytic problem and preliminary results are generated by two case studies: a cellular system measurement campaign and an idealized urban scenario.
Propagation, vol. 55, No.6, pp.1591-1598, 2007.
 J. T. Hviid, J. B. Andersen, J. Toftgard, J. Bojer, "Terrain-based propagation model for rural area-an integral equation approach", IEEE
Transactions on Antennas and Propagation, vol. 43, No. 1, pp.41-46, 1995.
 L. Sevgi, F. Akleman, "A novel finite-difference time-domain wave propagator", IEEE Trans. on Antennas and Propagation,vol. 48,
No. 3, pp. 839-841, 2000.
 F. Agelet, A. Formella, J. Rabanos, F. Fontan, “Efficient Ray-tracing Acceleration Techniques for Radio Propagation Modeling”,
IEEE Transactions on Vehicular Technology, vol.49 , No.6 , pp.2089-2104, 2000.
 O. Ozgun, G. Apaydin, G. M Kuzuoglu and L. Sevgi, “Two-way fourier split step algorithm over variable terrain with narrow and
wide angle propagators”, 2010 IEEE Ant. and Propag. Society International Symposium (APSURSI), Toronto, Canada, 2010.
 C. Batista and C. Rego, “An integral equation model for radiowave propagation over inhomogeneous smoothly irregular terrain”,
Microwave and Optical Tech. Letters, vol.54, pp.26-31, 2012.
 K. Wang, Y. Long, “Propagation modeling over irregular terrain by the improved two-way parabolic equation method”, IEEE
Transactions on Antennas and Propagation, vol.60, No.9, pp.4467-4471, 2012.
 C. Batista and C. Rego, “A high-order unconditionally stable FDTD-based propagation method”, IEEE Antennas and Wireless
Propagation Letters, vol.12, pp.809-812, 2013.
 C. Batista, C. Rego, M. Nunes and F. Neves, “Improved high-order FDTD parallel propagator for realistic urban scenarios and
atmospheric conditions”, IEEE Antennas and Wireless Propagation Letters, vol.15, pp.1779-1782, 2016.
 F. T. Pachon-Garcia, "Modeling ground-wave propagation at mf band in hilly environments through fdtd method and interaction with
gis", AEU - International Journal of Electronics and Communications, vol. 70, No. 8, pp. 981-989, 2016.
 G. Apaydin, C. Lu, L. Sevgi and W. Chew, “A Groundwave Propagation Model Using a Fast Far-Field Approximation”, IEEE
Antennas and Wireless Propagation Letters, vol.16, pp.1369-1372, 2017.
 Y. Yang, Y. Long, "Modeling EM pulse propagation in the troposphere based on the TDPE method", IEEE Antennas and Wireless
Propagation Letters, vol. 12, pp.190-193, 2013.
 W. Shin, 3D, Finite-difference frequency-domain method for plasmonics and nanophotonics, Ph. D. thesis, Stanford University, CA,
 C. M. Rappaport, Q. dong, E. Bishop and M. Kilmer, “Finite difference frequency domain (FDFD) modeling of two dimensional TE
wave propagation and scattering”, 2004 URSI International Symposium on Electromagnetic Theory, Pisa, Italy, May, 2004.
 Y. Zhao, K. Wu and K. Cheng, “A compact 2-D full-wave finite difference frequency-domain method for general guided wave
structures”, IEEE Transactions on Microwave Theory and Techniques, vol.50, No.7, pp.1844-1848, 2002.
 O. M. Ramahi, V. Subramanian and B. Archambeault, “A simple finitedifference frequency-domain (FDFD) algorithm for analysis of
switching noise in printed circuit boards and packages”, IEEE Transactions on Advanced Packaging, vol.26, No.2, pp.191-198, 2003.
 V. Simoncini and D. Szyld, “Recent computational developments in Krylov subspace methods for linear systems”, Numerical Linear
Algebra with Applications, vol.14, No.1, pp.1-59, 2007.
 W. C. Chew and W. H. Weedon, “A 3-D perfectly matched medium from modified Maxwell’s equations with stretched coordinates”,
Microwave and Optical Tech. Letters, vol.7, No.13, pp.599-604, 1994.
 J.-P. Berenger, Perfectly Matched Layer (PML) for Computational Electromagnetics, Morgan & Claypool Publishers, 2007.
 C. A. Balanis, Advanced Engineering Electromagnetics, 1ed, John Wiley and Sons Wiley, 1989.
 K. S. Yee, “Numerical solution of initial boundary value problems involving maxwell’s equation in isotropic media”, IEEE Trans.
onAntennas and Propag. , vol. ap.14, No. 3, pp.302-307, 1966.
 E. A. Marengo, C . M. Rappaport and E. L. Miller, “Optimum PML ABC Conductivity Profile in FDFD”, IEEE Trans. on Magnetics,
vol.35, No.3, pp.1506-1509, 1999.
 O. Schenk and K. Grtner, “Solving unsymmetric sparse systems of linear equations with PARDISO”, Future Generation Computer
Systems, vol.20, No.3, pp.475-487, 2004.
 Y. Wu, M. Lin and I. Wassell,, “Path loss estimation in 3D environments using a modified 2D Finite-Difference Time-Domain
technique”, IEEE 7th International Conference on Computation in Electromagnetics (CEM 2008), Brighton, UK, pp.98-99, 2008.
 H. L. Bertoni, Radio Propagation for Modern Wireless Systems. Englewood Cliffs, NJ, USA, Prentice-Hall, 2000.
 C. Batista, C. Rego, M. Evangelista, G. Ramos, Application of analytical propagation models on point-to-point and point-to-area RF
signal prediction, 9th European Conf. on Ant. and Propag. (EUCAP 2015), Lisbon, Portugal, April, 2015.
 W. Y. Yang, W. Cao, T.-S. Chung, and J. Morris, Applied Numerical Methods Using MATLAB. New York, NY, USA: Wiley, 2005.