Cryptography Reference
In-Depth Information
Figure 2.16 - Coherent receiver for 4-PSK modulation.
An exact expression of
Peb
can however be given by observing simply that
the coherent receiver for a 4-PSK modulation is made up of two components
identical to that of a 2-PSK receiver. The bit error probability
Peb
for a 4-PSK
modulation is thus the same as for a modulation 2-PSK, that is:
2
erfc
E
b
Peb
=
1
(2.75)
N
0
The symbol error probability
Pes
is equal to:
Peb
)
2
Pes
=1
−
(1
−
For high signal to noise ratios, the error probability
Peb
is much lower than
unity and thus, for 4-PSK modulation:
E
b
N
0
Pes
=2
Peb
if
>>
1
(2.76)
Figure 2.17 shows the error probability
Pes
as a function of the relation
E
b
/N
0
for different values of the parameter
M
1
.
Amplitude modulation on two quadrature carriers - M-QAM
For M-QAM modulation, the
s
j
(
t
)
signals provided by the modulator are of the
form:
s
j
(
t
)=
A
jc
h
(
t
)cos(2
πf
0
t
+
ϕ
0
)
−
A
js
h
(
t
)sin(2
πf
0
t
+
ϕ
0
)
(2.77)
Two situations can arise depending whether the length
m
of the groups of data
at the input of the modulator is even or not. When
M
=2
m
with even
m
,
1
For
M
=2
, it is the exact relation 2.74 that is used since
Pes
=
Peb
,for
M>
2
,
Pes
is
provided by Equation (2.71).
