Digital Signal Processing Reference
In-Depth Information
where, d(t) is the information symbol and the pulse g(t) is defined from the Eq. (
7.2
)
as
2
E
S
T
B
⎧
⎨
√
2
P
S
=
;0
≤
t
≤
T
B
g
(
t
)
=
(7.8)
⎩
0;
otherwise
and c(t) is the PN code generated, in the bit interval 0
≤
t
≤
T
B
expressed as
L
C
−
1
c
(
t
)
=
c
n
p
(
t
−
nT
C
)
(7.9)
n
=
0
Here,
L
c
=
number of chips per bit
{c
n
}
=
PN sequence
The code chip sequence is uncorrelated (white), i.e.,
E
(
c
n
c
m
)
=
0;
for
n
=
m
(7.10)
and each chip is +1 or
−
1 with probability 0.5.
and
E
c
n
∴
E
(
c
n
)
=
0,
=
1
(7.11)
When the signal is interfered by an additive signal n(t), the received signal is
r
(
t
)
=
d
(
t
)
g
(
t
)
c
(
t
) cos 2
π
f
c
t
+
n
(
t
)
(7.12)
Since the received signal is the output of a bandpass signal, n(t) must have only the
band pass components, i.e.,
n
(
t
)
=
n
c
(
t
) cos 2
π
f
c
t
−
n
s
(
t
)sin2
π
f
c
t
(7.13)
Equation (
7.13
) is the expression of bandpass random noise.
n
c
(
t
) and
n
s
(
t
)arethe
two quadrature components.
After this, the received signal is multiplied by c(t) and goes through an integrator,
as shown in Fig.
7.9
. Taking out only the received noise part from Eq. (
7.4
), sampled
at t
=
T
B
,
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