Page 67 - Integrated Wireless Propagation Models

I n t r o d u c t i o n t o M o d e l i n g M o b i l e S i g n a l s i n W i r e l e s s C o m m u n i c a t i o n s 45

the mobile unit cause the short-term fading while the mobile is moving. How large is the
area in which the effective scatterers are surrounding the mobile unit? The radius r of a
group of active local scatterers cannot be measured. However, we can obtain it indirectly
by comparing the measured data to a theoretical model described by Lee:47

r = (R x B W)/ 2 (1.10.3.4.1)
where R is the propagation distance from the transmitter to the receiver and BW is the
beam width of the incoming signal.
The experimental data from 850 MHz is trying to match the theoretical curve of cross
correlation for two base station antennas spacing between 0 and 50 A. and R = 3 mi with
1
various BW from 0.35° to . 2°. The close match is at an angular sector of 0.5°. The radius
of effective local scatterers can be roughly estimated from Eq. (1.10.3.4.1) and turns out
to be around 70 wavelengths at 850 MHz. Then we may conclude that the radius r of
effective scatterers is around 50 to 100 /..,variously from different operational frequencies.
1.10.3.5 Near-In Propagation Distance49
When the base station antenna is mounted close to the ground in an unobstructed con­
dition, the signal propagates in free space and can maintain its exponent loss of two to
only a certain distance before experiencing a higher exponent loss due to the effect of
the ground. This range is called near-in propagation distance, d, ' The derivation of d, is
f
1
from Eq. (1.9.1.3.6). Let the location of the phase difference 11<\> between the direct wave
and ground-reflected wave be 1t :
(1.10.3.5.1)

At this location, the wave strength can still remain strong, as shown in Eq. (1.9.1.3.2).
From Eq. (1.10.3.5.1), we come up the near-in propagation distance d,/
4h �
d, = � (1.10.3.5.2)
f
Equation (1.10.3.5.2) will be a criterion used in the prediction model of the rnicrocell
(Chap. 4). Another defined distance called close-in propagation distance will be a crite­
rion used in the in-building cell (Chap. 5).

I
1 . 10.4 Predicting the n terference Signals
The prediction tool has to predict not only the local means of the mobile signal but also the
interference signals that would affect the mobile signal. Once the mobile signal and the
interference signals are predicted, the carrier-to-interference ratio, C/I, can be calculated.

1.10.4.1 Co-Channel lnterference
Based on the frequency reuse scheme deployed in the cellular system, the frequency
reuse factor K is usually 3, 4, 7, or 12. For an example, K = 7 means a cluster of seven cells
that will share the total allocated bandwidth of the cellular signals. The distance of two
co-channel cells can be found from Eq. (1.7.1.1). In any value of K, there are different tiers
of interfering cells. At the first tier, the number of interfering cells is Z1 = 6; at the second
tier, Z 2 = 12; and at the third tier, Z3 = 18. The total number of interfering cells, Z, is
Z = LZ for n = 1 to N (1.10.4 1 .1)
.
11
Usually, we consider only the interfering cells at the first tier.