mohatta2015.pdf

THE MATH 13
1
0.8
g
0.6
0.4
0.2
- -/ \ -
: I I :
0
-0.2
-0.4
_
-,
- 4 - 3 - 2 - 1 0 1 2 3 4
normalized time (t/T)
_
Figure 1.12 Effect of dispersion due to two, 0.75T-spaced, equal amplitude patlis on
raised (»sine with 0.22 rolloff.
Another aspect of the channel is noise, which can be modeled as an additive
term to the received signal. Characterization of the noise is discussed in the next
subsection.
Putting these two aspects together, the received signal can be modeled as
L-l
r{t) N Σ Stx(t - r Ù + n(t), (1.22)
where L is the number of taps or (resolvable) paths, ge is the medium response or
path coefficient for the fth path, and re is the path delay for the ¿th path. Note
that we use |= to emphasize that this is a model. This means we think of n(i) as a
stochastic process rather than a particular realization of the noise.
By substituting (1.19) into (1.22), we obtain the following model for the received
signal:
oo
r{t) \= v^ËT J2 h(t - mT)s{m) + n(t), (1.23)
m= —oo
where
L-l
h(t) = Y,9iP{t-n) (1.24)