The first approach is
typically chosen in order to reduce the computer simulation
run time. However, it was our intention to inform the
system designer of the available choices [12??“15].
Let??™s consider the system in Fig. 8.6, where the goal
is to derive the IS weight that is a function of the noise
random variable.
Let??™s define the following error estimator, with
:
(8.31)
Employing the IS biasing technique discussed above, we arrive at
(8.32)
(8.33) P0 3
`
`
h0[g(x)] # w(x) # f *
X (x) dx
P0 3
`
`
h0[g(x)] # fX(x)
f *
X (x)
# f *
X (x) dx
P0 3
`
`
h0(v) # f0(v)dv 3
`
`
h0[g(x)] # fX(x)dx
vi g(xi)
s2(P^
0)
s2(P^
0*)
1
N
# 3
`
vth
f0(v) # [1 P0 ] dv
1
N*
# 3
`
vth
f0(v) # [w(v) P0 ]dv
s2(P^
0*)
1
N*
# 3
`
vth
f0(v) # [w(v) P0] dv
E5P^
0*6 P0
P^
o*
P ^
o*
1
N*
# aN
*
i1
h0(vi) # w(vi)
COMPUTER SIMULATION ESTIMATION TECHNIQUES 465
n(t)
s(t)
x(t)
+ v g(x)
FIGURE 8.6 Simple error estimation receiver.
which is equivalent to
(8.34)
Using the sample mean estimator, the ensemble average can be replaced with the following
equation:
(8.35)
This involves biasing the PDF; we prefer to bias the noise PDF. Since s(t) and n(t) are
assumed to be independent, this is possible.
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