Page 353 - Integrated Wireless Propagation Models

I n - B u i l d i n g ( P i c o c e l l ) P r e d i c t i o n M o d e l s 331

The 3D ray-tracing tool is used for evaluation in urban wave propagation, and its
major advantage is the wideband analysis of the channel. The frequency dependence,
such as the time delay spread, and the time variance, such as the Doppler spread of the
channel, can be determined.

5.6.2 FDTD
5.6.2. 1 What Is FDTD?
FDTD was developed based on the Maxwell's equations to handle a complicated com­
munication environment in which transmitting and receiving antennas are often installed
close to structures with complex material properties. Such problems can be solved not by
asymptotic solutions but by the numerical solution of Maxwell's equations, called the
FDTD method. The FDTD method simultaneously provides a complete solution for all
the points on the map that can give signal-coverage information throughout a given area
2
very accurately. In a simple outdoor environment, a 2D FDTD is generally applied. 9.37
5.6.2.2 General Procedure of the FDTD Algorithm

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5.6.2. . 1 Starting from Maxwell's Equations FDTD was developed based on the
Maxwell's equations to cover all the propagation phenomena, such as reflections,
diffractions, refractions, and transmission.
Maxwell's equations in the time domain are

- a fr
V' x E = -fl at (5.6.2.2.1)
- - a £

V' x H = CJE + E at (5.6.2.2.2)
Modify two equations for FDTD:
Eq. (5.6.2.2.1) becomes

a Fr 1 - 1 -
- = - V x E - - crH (5.6.2.2.3)
at fl fl
Eq. (5.6.2.2.2) becomes

a £ 1 - 1 -
- = - V x H - - cr E (5.6.2.2.4)
dt E E
The vector differential equations can be converted into three coupled scalar equations:
For E-field:
() E x ( - () H Y - crE ) (5.6.2.2.5)
.!_ {)Hz
=
at E ay az x
()E y .!_({)Hx - () Hz - crE )
dt = E dZ dX Y (5.6.2.2.6)

() E z ( dH Y () Hx - crE ) (5.6.2.2.7)
.!_
=
dt E dX - ()y z