Let us consider using the sample mean estimate of the BER; then we have the following estimate,
given ei is the error at the ith observation.
(8.18) P^
0
1
N
# aN
i1
ei
1 22p 3
da
da
et2/2 dt 1 a
y
10k e1
d2
a
2
# c1
?„4
d2
a
1df N # 10k
P^
0 10k
P(y p y) 1 a
P^
0
n
N
P^
0(v)
1
N
# aN
i1
h0(vi)
P0 E5h0(v)6
h0(v) e1, v vth
0, v vth
P0 3
`
`
h0(v) # f0(v) dv
462 CHAPTER EIGHT
with the error signal expressed as
(8.19)
The mean is E{?†P
0} P0, which states the estimator is unbiased. We can also write down the variance
of the estimator as [3]
(8.20)
which can also be alternatively represented as
(8.21)
Here we have assumed the errors are independent.
A system simulation using the MC method for BER estimation is given in Fig. 8.5.
s2(P^
0)
1
N
# 3
`
vth
f0(v) # [1 P0] dv
s2(P^
0)
P0(1 P0)
N
ei e1, if error is present
0, otherwise
COMPUTER SIMULATION ESTIMATION TECHNIQUES 463
1.E??“03
1.E??“02
1.E??“01
1 10 100 1000
Observed Bit Length Multiplier (k ?— 102)
BER
90% 90%
99% 99%
FIGURE 8.4 Confidence interval guideline for error estimation.
Bits in Transmitter
Multipath
Channel
+
Noise and
Interference
Receiver
Error
Counter Delay
bk
bk
?†
?†P
FIGURE 8.
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