Above we see there is a decrease in power by 6 dB for each doubling of distance.
We can actually rewrite the free space path loss equation to equal the following (making use of
):
(3.57)
where c speed of light (meters per second).
PRx PTx # GTx # GRx # c c
4pdf d2
lf c
PRx PTx # GTx # GRx # c l
4pd d2
150 CHAPTER THREE
Modulator
#N
BPF Demodulator
Modulator
#N+1
ejwN+1t
ejwNt
ejwN+2t
Modulator
#N+2
mN+2(t)
mN+1(t)
mN(t)
n(t)
FIGURE 3.44 Simplified ACI simulation model.
Now we can see there is a decrease in power by 6 dB when either the distance or the carrier frequency
is doubled. Since we are typically interested in the effects of the power exponent, we can write
down the normalized free space path loss as follows:
(3.58)
Assuming we wish to represent this free space path loss as a positive value then the above equation
can be inversed and expressed below in dB form, where distance is measured in km and the carrier
frequency is expressed in MHz.
(3.59)
As discussed above this path loss model assumes the channel has no obstructions between the
transmitter and receiver; in reality there are obstructions and the resulting receiver power will be less.
In other words, path loss predicted by this model is overly optimistic.
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