Page 143 - Integrated Wireless Propagation Models

M a c r o c e l l P r e d i c t i o n M o d e l s - P a r t 2 : P o i n t - t o - P o i n t M o d e l s 121

3.1.4.2 Terrain Averaging
When a terrain-averaging program is turned on, the Lee model uses a simple running
average by averaging the elevations from three points, the current local point, the pre­
ceding point, and the succeeding point to find a new elevation at the current local point.
For example, when the averaging scope is set to 5 points, the new elevation for any
given point on the radial is obtained by averaging the current elevation with the 2 pre­
vious points and 2 succeeding points along the radial.
For those points where only fewer than 3 or 5 points can be averaged (such as the
last point on a radial), the extrapolate elevations are used for those points.
3 . 1 . 4.3 Effective Earth Curvature12·13
When the distance is greater than 10 miles, we may consider the effect of earth curva­
ture. Terrain elevation values can be adjusted with an offset value to compensate for the
horizon effect caused by the earth's curvature. This offset represents a reduction in
elevation at the point of the mobile, which increases with distance from the base station.
When the earth curvature offset is used, a parameter known as the K factor can be
specified to represent the earth's radius. This parameter is used to adjust the earth cur­
vature offset to compensate for the slight curvature of the signal path.
The earth curvature offset can be turned on or off based on a specified value for the
K factor, as described below.

3.1.4.3.1 Earth Curvature Offset The earth curvature offset value is the difference between
a straight line drawn from the site elevation point to a point along the radial as compared
with the curve of the earth through these same points, as illustrated in Fig. 3.1.4.3.1.
A formula for the earth curvature offset can be derived as follows:

1 . Consider a mobile elevation point is at a distance (D) in meters from the site
elevation and assume the earth's radius (R) to be 6,370,997 m.
2. The angular distance from the site to a point is given by

. D
ang e = (3 1 . 4.3.1)
.
1 a rc sm
R
3. The dip below the horizon is given by
.
dip = (1.0 - cos( angle)) x R (3 1 .4.3.2)
3.1.4.3.2 K Factor When the earth curvature option in the prediction model is turned
on, a parameter known as the K factor can be specified to adjust the calculated earth
curvature offset. The K factor represents a proportion of the actual radius of the earth.
1
The Lee model uses a default value of . 33:
2
Offset = 2D /3K (3.1.4.3.5)
Any value of K factor larger than 1 assumes that the radius of the earth is larger than
the actual one, thus resulting in a smaller earth curvature offset. Because the signal path
is somewhat curved rather than straight, the signal horizon is lower than would be
represented by drawing a straight line from the transmitter to the mobile. Thus, the
earth curvature offset should be less than that calculated by using the actual radius of
the earth, and use of K factor values larger than 1 is recommended.