Cryptography Reference
In-Depth Information
=2
m
and even
m
.
Figure 2.18 - Coherent receiver for M-QAM modulation with
M
The symbol error probability
Pes
on the group of
m
binary data is therefore
equal to:
Pe
m/
2
)
2
When
m
is odd, the probability of error
Pes
on a group of
m
binary data can
be upper bound by the following expression:
Pes
=1
−
(1
−
3log
2
(
√
M
)
M
E
b
N
0
Pes
≤
2
erfc
(2.80)
−
1
The bit error probability
Peb
can be deduced from
Pes
if Gray coding is used
and for a suciently high signal to noise ratio:
Pes
log
2
(
M
)
Peb
=
(2.81)
For the values of
M
8
, the performance of M-PSK and M-QAM modulations
can easily be compared. Indeed, by making the following approximation:
sin
π
M
≥
=
π
M
if
M
≥
8
the bit error probability for an M-PSK modulation can be written:
1
log
2
(
M
)
erfc
log
2
(
M
)
π
2
E
b
N
0
E
b
N
0
Peb
=
if
>>
1
(2.82)
M
2
