Cryptography Reference
In-Depth Information
Figure 2.17 - Error probability
Pes
as a function of the relation
E
b
/N
0
for different
values of
M
of an M-PSK modulation.
the group of data can be separated into two sub-groups of length
m/
2
,each
sub-group being associated respectively with amplitudes
A
jc
and
A
js
,with:
−
√
M
)
Aj
=1
,
2
,
,
√
M
A
jc
=(2
j
−
1
···
(2.78)
−
√
M
)
Aj
=1
,
2
,
,
√
M
A
js
=(2
j
−
1
···
In this case, the M-QAM modulation is equivalent to two
√
M
-ASK modulations
having quadrature carriers. The coherent receiver for an M-QAM modulation is
made up of two components called phase and quadrature, and each component,
similar to a receiver for modulation
√
M
-ASK, performs the estimation of a
group of
m/
2
binary data. The receiver is shown in Figure 2.18.
The error probability on a group of
m/
2
binary data is equal to the error
probability of an ASK
√
M
modulation, that is:
Pe
m/
2
=
√
M
−
3log
2
(
√
M
)
M
−
1
E
b
N
0
√
M
erfc
(2.79)
−
1
