Cryptography Reference
In-Depth Information
no longer flat and some spectral components of the modulated signal can be very
attenuated. The channel introduces a distortion of the modulated signal which
results in the phenomenon of Intersymbol Interference (ISI). In the presence of
ISI, the signal at a sampling time is a function of the symbol of the modulated
signal at this time but also of the symbols prior to and after this time. ISI
appears as noise that is added to the additive white Gaussian noise and, of
course, degrades the performance of the transmission.
Coherence time
The coherence time
t
c
of a fading channel is defined by:
1
B
d
t
c
≈
(2.160)
where
B
d
is the Doppler band of the channel that is well approximated by
f
max
with:
f
max
=
Max
f
n
(2.161)
The coherence time of the channel is a measure of its evolution speed over time.
If
t
c
is much higher than the symbol period
T
of the modulated signal, the
channel is said to be slow-fading. For a frequency non-selective slow-fading
channel, attenuation
α
(
t
)
and phase
φ
(
t
)
are practically constant over one or
more symbol periods
T
.
A channel is frequency non-selective slow-fading if it satisfies the following
condition:
T
M
B
d
<
1
(2.162)
2.4.2 Transmission on non-frequency-selective slow-fading
channels
Performance on a Rayleigh channel
For this channel, the modulated signal undergoes an attenuation
α
(
t
)
and a
random dephasing
φ
(
t
)
of constant realizations over a duration higher than or
equal to
T
. Considering a coherent receiver, the error probability per binary
data, conditionally to a realization
α
of the attenuation
α
(
t
)
,isequalto:
α
2
E
b
N
0
Peb
(
α
)=
1
2-PSK or 4-PSK modulation
2
erfc
(2.163)
α
2
E
b
2
N
0
Peb
(
α
)=
1
2-FSK modulation
2
erfc
(2.164)
