The above
multipath propagation scenario is modeled by a three-ray model that has the following PDP with
, denoting the average power of the kth ray (see Fig. 3.15). P(tk) a2k
130 CHAPTER THREE
t1 t2 t3
t
P(t)
P(t1)
??†t1 ??†t2
P(t3)
P(t2)
FIGURE 3.15 A power delay profile example.
The times of arrival and their associated powers are modeled as random variables. The significant
multipaths arriving at times, 1, 2, and, 3 are sometimes called echoes. The corresponding FSF channel
model can be drawn as shown in Fig. 3.16.
Z??“??†t1
R1(t)
R2(t)
R3(t)
Channel Input Channel Output
Z??“??†t2
FIGURE 3.16 Three-ray frequency selective fading channel model.
Where three independent and identically distributed random variables, R1, R2, and, R3 are used to
model the Rayleigh fading process of each respective echo. It is common practice to assume the rays
arriving at distinct times are independent of each other.
In order to assist in the derivation of mathematically closed form expressions, some mathematical
representations of delay spread profiles are given as follows:[13]
Exponential (3.35)
Double spike (3.36)
Gaussian (3.37)
The procedure used to capture this information is to transmit a pulse at some location in the area
of interest and then travel through this area of interest capturing the transmitted pulse plus the echoes
P(t)
1
tRMS22p
# e
t
2
2t
2
RMS
P(t) '(t) '(t K # tRMS)
P(t)
A
tRMS
# e
Bt
tRMS
that arrive.
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