In this section we will evaluate the probability of error of
both correlator type receivers and matched filter receivers. We
will only present the analysis for transmission of binary
symbols. In the process we will demonstrate that both of these
receivers have identical bit-error probabilities.
Antipodal Signals
r
t
=
s
m
t+
N
t
r
t
s
m
t
N
t
for
0≤t≤T
0
t
T
with
m=1
m
1
and
m=2
m
2
and
s
1
t=-
s
2
t
s
1
t
s
2
t
An analysis of the performance of correlation receivers with
antipodal binary signals can be found
here. A similar analysis for matched
filter receivers can be found
here.
Orthogonal Signals
r
t
=
s
m
t+
N
t
r
t
s
m
t
N
t
for
0≤t≤T
0
t
T
with
m=1
m
1
and
m=2
m
2
and
<
s
1
,
s
2
>=0
s
1
s
2
0
An analysis of the performance of correlation receivers with
orthogonal binary signals can be found
here. A similar analysis for matched
filter receivers can be found
here.
It can be shown in general that correlation and matched filter
receivers perform with the same symbol error probability if the
detection criteria is the same for both receivers.