Page 154 - Integrated Wireless Propagation Models

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

-- Line-of-sight wave
......... Water reflected wave
-
. - - Land reflected wave
FIGURE 3.1.6.1 Effect of water-reflected waves.

as illustrated in Fig. 3.1.6.1. In this case, the Lee model compensates for the effect of the
water-reflected wave by adjusting the path loss at the mobile upward to approach the
free space curve.

3.1.6. 1 Over-the-Water Conditions15
When the mobile is traveling on the other side of the water from the base station antenna
as shown in Fig. 3.1.6.1, three waves arrive at the mobile. Since there are no human­
made structures over the water, the reflected wave over the water is still considered a
speculative reflected wave, although the reflection point of the wave is at a distant loca­
tion away from the mobile. The received signal strength from three waves can be
expressed by extending from two waves, shown in Eq. (1.9.1.3.1), as
(3 1 . 6.1.1)
.
where a and a are the reflection coefficients of water and land, respectively, and 11<\> 1
1
2
and 11<\> are the phase differences between a direct path and a reflected path from water
2
and from land, respectively.
In a mobile environment, a 1 and a are equal to -1 because the energy of the signal
2
is totally reflected with a phase reversed. Then Eq. (3 1 . 6.1.1) becomes
.
2
.
P, = P0 (1/ (4 nd/f.. )) 1 1 - (cos 11<\> 1 + cos 11<\> ) - j (sin 11<\> 1 + sin 11<\> ) 1 2 (3 1 . 6.1.2)
2
2
= P0 (1/ ( 4 nd//..)) 2 • L,
where L is the loss factor and
r
L, = 1 1 - (cos 11<\> + cos 11<\> ) -j (sin 11<\> 1 + sin 11<\> ) 1 2
1
2
2
1
= [1 - (cos 11<\> 1 + cos 11<\> ) F + [sin 11<\> 1 + sin 11<\> F (3. . 6.1.3)
2
2
since
2
1
cos 11<\> = 1 - 2 sin (.:1</2) (3. . 6.1.4)
.
Substituting Eq. (3 1 . 6.1.4 ) into Eq. (3.1.6.1.3) and simplifying the equation yields
2
L, = 1 - [- 2 + 2 - 2 sin ((.:1< 1 .:1< ) / 2)]
-
2
2
= 1 - 2 sin ((.:1<1 - .:1<J/2)
"" 1 (3. . 6.1.5)
1