The LCR is given by the following expression:
(3.27)
where we have defined the normalized signal level as
(3.28)
As a sanity check by forcing K0 will produce exactly the same result given earlier for the Rayleigh
fading case. In Fig. 3.13 we plot the LCR for various values of K.
r
R
RRMS
LR 22p(K 1) # fm # r # eK(K1)r2 # IoA2r2K(K 1) B
128 CHAPTER THREE
Normalized Level Crossing Rate (LCR)
1.0E??“3
1.0E??“2
1.0E??“1
1.0E+0
1.0E+1
??“40 ??“30 ??“20 ??“10 0 10
20*LOG(R) [dB]
Normalized LCR
K = 0
K = 10
FIGURE 3.13 Rician LCR comparison for various K factors.
Similarly we can provide the AFTD for the Rician-faded signal, it is given by the following
expression [10, 11].
(3.29)
Lastly, for the sake of completeness the PDF of Nakagami faded signals is presented.
(3.30)
where and m Nakagami parameter, m 1/2 and is a gamma function.
The corresponding CDF is given as follows, using the following definition: r/.
(3.31)
where the incomplete gamma function is defined below.
(3.32) (a, b) 3
b
0
x a1 # ex dx
P(r)
(m, mr2)
(m)
(m) E5r26 p(r)
2mm
(m) # m
# r2m1 # e
mr2
AFTD
1 Q(22K,22(K 1)r2) 22p(K 1) # fm # r # eK(K1)r2 # Io(2r2K(K 1))
The level crossing rates and average fade time durations can also be derived, we simply show the
results below for the Nakagami channel.
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