Aplot of this distribution is given in Fig. 3.12 for various values of
K factor.
K ` s2 0
K `
K 10*log c A2
2s2 d (dB)
A2/2
(0 A), (0 r) p(r)
r
s2
# e
(r2 A2)
2s
2 # IoarA
s2b
From Fig. 3.12 we see as the power of the line of sight increases the envelope variations become
less and less. The number of deep fades encountered reduces thus reducing the instantaneous errors
and improving the overall average Bit Error Rate (BER) performance.
3.3.2 Statistical Properties
The mean of the Rician distributed random variable is given as
(3.22)
The CDF of the Rician signal is the probability the received signal envelope is below a specific value,
say R.
(3.23)
If we define a normalized signal level as
(3.24)
Then the CDF is written as
(3.25)
where Q(a, b) is the Marcum Q function defined below
(3.26) Q(a, b) 3
`
b
x # e
(x2 a2)
2 # Io(ax) dx
P(r R) 1 Q(22K,22(K 1)r2)
r
R 2A2 2s2
P(r R) 3
R
0
p(r) dr
E5r6 s?„p
2
# c(1 K)IoaK
2 b KI1aK
2 bd # ek/2
WIRELESS MULTIPATH CHANNEL 127
Rician Probability Density Function
0
0.5
1
1.5
2
2.5
3 2 1 0 4
Amplitude
PDF
K = 0
K = 5
K = 30
FIGURE 3.12 Rician distribution plot.
Earlier the LCR for Rayleigh fading was presented, next we present the LCR for Rician fading.
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