Page 188 - Integrated Wireless Propagation Models

166 C h a p t e r T h r e e

2. In a Positive-Slope Condition (Fig. 3.2.4.4[b])
The power P,1 at distance r is the same as Eq. (3.2.4.3.1). At a positive-slope
1
condition, there is a gain that needs to be calculated. First is to measure from
the peak of the knoll to the valley of the knoll, h , and then to measure the
p-p
height from the peak of the knoll to the crossing of the positive slope at the
distance r ' \· The gain G,ffB is
l
1
GeffB at point B = 20 log (:' ) (3.2.4.3.3)
p-p
There are two cases (r; = r1 + r ):
2
Case : If 10 log (*T + G,ffB < 10 log(*T
1

P,; = P,, + 10 log (* r + G + L (knife-edge diffraction loss) (3.2.4.3.4)
ef!B

Case 2: If 10 log (* r + G ef!B � 10 log (* r

P , = P + 10 log (!{_)-y + L (knife-edge diffraction loss) (32.4.3,5)
rl rl r1

3.2.4.3.2 Double-Knoll Case (see Fig. 3.2.4.5)
1. In a Negative-Slope Condition (Fig. 32-4-S[a])
The power P at distance r is the same as Eq. (3.2.4.3.1). The path loss from the
1
r ,
first peak to the second peak of the knoll would be assumed the free space loss.
Then the received power at point A, where r � = r1 + r + r 3 = r� + r 3 , is
'
2
P,; P , + 10 log (*T + 10 log (�r + L (double knife-edge diffraction loss) (3.2.4.3.6)
,
=
2, In a Positive-Slope Condition (see Fig, 32-4-S[b])
We are following the same derivation as shown in the single-knoll case. In this
double-knoll case, there is a gain c: which can expressed as
ffB
h;
c; ffB = 20 log ( , J (32,4.3,7)
h
(p-p)2
h
where J and h have been shown in Fig. 32.45(b).
,, ( ) 2
p-p
There are two cases:
case 1: If 10 log (�T + c, < 10 log (�T
ffB