Digital Signal Processing Reference
In-Depth Information
T
B
y
n
(
T
B
)
=
c
(
t
)
n
(
t
)
g
(
t
) cos
(
2
π
f
c
t
)
dt
0
T
B
L
C
−
1
(7.14)
=
c
n
p
(
t
−
nT
c
)
n
(
t
)
g
(
t
) cos
(
2
π
f
c
t
)
dt
n
=
0
0
2
E
S
T
B
L
C
−
1
=
c
n
s
n
n
=
0
where,
(
n
+
1
)
T
c
s
n
=
n
(
t
) cos
(
2
π
f
c
t
)
dt
(7.15)
nT
c
The probability of error directly depends upon the statistical parameters of the
interfering signal. The mean of the noise is
E
y
n
(
T
B
)
=
0
(7.16)
And the variance is
E
y
n
(
L
C
−
L
C
−
1
1
2
E
S
T
B
T
B
)
=
E
(
c
n
c
m
)
E
(
s
n
s
m
)
n
=
0
m
=
0
As
E
(
c
n
c
m
)
=
δ
nm
, as the property of PN sequence suggests, therefore,
E
y
n
2
L
C
−
1
E
s
n
2
2
E
S
T
B
(
T
B
)
=
(7.17)
n
=
0
Now, considering a single tone interference, i.e.,
2
P
N
cos 2
n
(
t
)
=
π
f
c
t
(7.18)
where,
P
N
is the average noise power. Substituting Eq. (
7.18
) into Eq. (
7.15
),
√
2
P
N
2
(
n
+
1
)
T
c
(
n
+
1
)
T
c
T
c
√
P
N
√
2
2
P
N
cos
2
s
n
=
(
2
π
f
c
t
)
dt
=
dt
=
(7.19)
nT
c
nT
c
Here also, mean of noise
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