1. Remcom Inc. 315 S. Allen St., Suite 416  State College, PA 16801  USA Tel: 1-814-861-1299  Fax: 1-814-861-1308  sales@remcom.com  www.remcom.com © 2011 Remcom Inc. All rights reserved. FDTD Propagation Models

2. Urban Canyon FDTD Model (UCFDTD) A propagation model for urban high rise environments that does not use ray-based methods Uses the finite difference time domain (FDTD) method to solve Maxwell’s equation directly Assumes tall buildings and low antenna heights, as well as flat ground In principle, it includes all possible reflection, transmission, and diffraction effects within the limitation of the tall building assumptions Can be used to model wideband systems and propagation of transient pulses

3. Illustration of UCFDTD

4. Urban Canyon FDTD Algorithm The building footprints are projected onto a rectangular grid consisting of evenly spaced points in the xy plane Time is divided into evenly spaced steps At each time step, electromagnetic fields at each grid point is determined by solving Maxwell’s equation using a finite difference method A finite duration pulse is excited at the transmitter, and the electric fields as a function of time are recorded at the receivers Ground reflection effects are added analytically

5. UCFDTD Example: Computed Path Loss at 300 MHz, Vertical Pol.

6. UCFDTD Example: Electric Field Movie

8. UCFDTD Example: Path Loss with and without Ground Reflection Without Ground Reflection With Ground Reflection

9. Summary of Urban Canyon FDTD Easier to set up and run Maximum reflections: N/A Maximum transmissions: N/A Maximum diffractions: N/A Environments: Urban high rise Waveforms: Narrowband or Wideband Terrain: Flat Indoor: N/A Objects: N/A Range: Usually less than 2 km, depends on frequency and computer memory Included in the standard Wireless InSite distribution

10. Summary of Urban Canyon FDTD (2) Antenna heights: Lower than most buildings Antenna types: Isotropic only FDTD: Standard Yee algorithm with correction factors due to ground reflection and 3-D spreading of the wave. Output available: Electric field vs. time (point receivers only), power delay profile vs. time (point receivers only), path loss, excess path loss, received power Minimum frequency: N/A Maximum frequency: Depends on computer memory. The higher the frequency, the greater the amount of memory and computation time needed

11. MWFDTD Model for Propagation Over Terrain Illustration of the basic idea behind the MWFDTD (Moving Window FDTD) method

12. MWFDTD Irregular Terrain Simulations MWFDTD is a propagation model that applies full wave 2-D Finite Difference Time Domain (FDTD) method for lossy dielectric media New GPU FDTD acceleration provides substantial performance improvement –Requires a CUDA-capable GPU Uses pulsed excitation of the transmitting antenna Obtain narrowband results by application of Fourier Transform Apply FDTD mesh only to portion of propagation path which contains significant pulse energy Move FDTD mesh along the propagation path with the pulse-Moving Window FDTD (MWFDTD) Change terrain in mesh at leading/trailing edges as the mesh window moves

13. Summary of MWFDTD Easier to set up and run Maximum reflections: N/A Maximum transmissions: N/A Maximum diffractions: N/A Environments: Irregular terrain with optional urban and foliage features Terrain: All Foliage: All, at frequencies < 1 GHz Indoor: N/A Objects: N/A Included in the standard Wireless InSite distribution

14. Summary of MWFDTD (2) Range: Depends on computer memory, frequency, and run time, usually less than 100 km Antenna heights: All Antenna types: All FDTD algorithm: 2 nd order and higher order algorithms with correction factors due to 3-D spreading of the wave. Output available: Electric field vs. time (point receivers only), power delay profile vs. time (point receivers only), path loss, excess path loss, received power Minimum frequency: N/A Maximum frequency: Depends on computer memory

15. Summary of MWFDTD (3) Atmospheric effects –Standard atmospheric refraction –Ducting Attenuation due to rain Does not take into account absorption by the atmosphere

16. MWFDTD Example: Surface Wave over a Mixed Path Path Loss