Graphics Programs Reference
In-Depth Information
y
m
()
s
()
n
m
=
+
()
(2.35)
where
s
()
is the radar return of interest and
n
m
()
is white uncorrelated addi-
tive noise signal. Coherent integration of
n
P
pulses yields
n
P
∑
n
P
∑
n
P
∑
1
n
P
1
n
P
1
n
P
z
()
=
-----
y
m
()
=
-----
[
s
()
n
m
+
()
]
=
s
()
+
-----
n
m
()
(2.36)
m
=
1
m
=
1
m
=
1
The total noise power in
z
()
is equal to the variance. More precisely,
n
P
∑
n
P
∑
∗
1
n
P
1
n
P
2
-----
n
m
-----
n
l
ψ
nz
=
E
()
()
(2.37)
m
=
1
l
=
1
where
E
[]
is the expected value operator. It follows that
n
P
∑
n
P
∑
1
n
2
1
n
2
1
n
P
2
ψ
n
2
δ
ml
2
-----
()
n
l
∗
()
-----
-----
ψ
ny
ψ
nz
=
En
m
[
]
=
=
(2.38)
ml
,
=
1
ml
,
=
1
2
where
ψ
ny
is the single pulse noise power and
δ
ml
is equal to zero for
ml
≠
and unity for . Observation of Eqs. (2.36) and (2.38) shows that the
desired signal power after coherent integration is unchanged, while the noise
power is reduced by the factor
ml
=
1
⁄
n
P
. Thus, the SNR after coherent integration
is improved by
n
P
.
Denote the single pulse SNR required to produce a given probability of
detection as
(
SNR
)
1
. Also, denote
(
SNR
)
n
P
as the SNR required to produce
the same probability of detection when
n
P
pulses are integrated. It follows that
1
n
P
(
SNR
)
n
P
=
-----
(
SNR
)
1
(2.39)
The requirements of knowing the exact phase of each transmitted pulse as well
as maintaining coherency during propagation is very costly and challenging to
achieve. Thus, radar systems would not utilize coherent integration during
search mode, since target micro-dynamics may not be available.
2.4.2. Non-Coherent Integration
Non-coherent integration is often implemented after the envelope detector,
also known as the quadratic detector. A block diagram of radar receiver utiliz-
ing a square law detector and non-coherent integration is illustrated in
Fig. 2.5.
In practice, the square law detector is normally used as an approximation to the
optimum receiver.
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