Cryptography Reference
In-Depth Information
B
c
of the channel. We can also transmit these data by using the same carrier but
at a time separated by a quantity at least equal to the coherence time
t
c
of the
channel. This way of proceeding amounts to performing frequency interleaving
combined with time interleaving.
Implementing multicarrier transmissions
Considering an M-QAM modulation on each carrier, the OFDM signal has
the expression:
+
∞
N
n
=0
{
−
1
s
(
t
)=
A
c
n,i
h
(
t
−
iT
)exp(
j
2
πf
n
t
)
}
(2.181)
i
=
−∞
where
c
n,i
=
a
n,i
+
jb
n,i
is a complex modulation symbol,
h
(
t
)
a unit ampli-
tude rectangular pulse shape of width
T
,and
N
is the number of carriers with
frequency
f
n
.
Considering time interval
[
iT,
(
i
+1)
T
[
, the signal
s
(
t
)
is equal to:
N−
1
n
=0
{
s
(
t
)=
A
c
n,i
exp(
j
2
πf
n
t
)
}∀
t
∈
[
iT,
(
i
+1)
T
[
(2.182)
The implementation of an OFDM signal requires
N
M-QAM modulators with
carrier frequency
f
n
to be realized. We can show that these
N
modulators can
be realized from an inverse discrete Fourier transform, which allows a reasonable
complexity of implementation.
Considering
N
orthogonal carriers, the frequencies
f
n
must be separated by
at least
1
/T
.
n
T
f
n
=
n
=0
,
1
,
···
,
(
N
−
1)
(2.183)
The power spectral density
γ
OFDM
(
f
)
of an OFDM signal in baseband is pro-
portional to:
sin
π
(
f
2
N−
1
−
n/T
)
T
γ
OFDM
(
f
)
∝
(2.184)
π
(
f
−
n/T
)
T
n
=0
which gives a flat spectrum in the frequency band
B
=(
N
1)
/T
.
The signal
s
(
t
)
can be sampled at frequency
f
e
on condition that
f
e
satisfies
the Nyquist criterion, that is:
−
2(
N
−
1)
f
e
≥
(2.185)
T
We can cho ose
f
e
=2
N/T
, and thus signal
s
(
t
)
sampled at time
lT
e
with
T
e
=1
/f
e
is equal to:
c
n,i
exp
j
2
π
nl
2
N
N
n
=0
−
1
s
l
=
s
(
lT
e
)=
A
l
=0
,
1
,
···
,
(2
N
−
1)
(2.186)
