8.9, assuming SNR2 SNR1.
We need to consider a system with memory of length M. Let??™s define the system as follows: Y is
to be determined by M independent samples.
(8.50) Y G(x1, x2,c, xM)
SNR2
PS
s2*
SNR1
PS
s2
r
N
N*
<
3
`
vth
fN(n)dn
3
`
vth
fN(n) # w(n)dn
s2(P^
0) s2(P^
0*)
r
N
N*
<
3
?
vth
f(v) dv
3
?
vth
f(v) # w(v) dv
468 CHAPTER EIGHT
Eb/No
(dB)
BER
(Eb/No)2
BER2
BER1
(Eb/No)1
FIGURE 8.9 IS functional application.
Then the weight function becomes
(8.51)
where is an M-dimensional PDF of the noise source. Assuming independent noise samples,
we arrive at the product of the individual noise statistics.
(8.52)
The memory in the system has a negative impact on the system improvement. The reader can visit
the applicable references in the end of this chapter to see various examples, in order to provide numerical
results (see [3] and [8]). Some noteworthy observations are, as the memory increases, the
improvement of IS over MC decreases. Also the optimum value of 1 varies as the length of the
memory changes.
Let us build a simple IS system and compare the error rate estimates. The noise samples are scaled
to produce a larger variance and more frequent error events.
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