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9
P
fa
=
10
Figure 2.14. Probability of detection versus SNR. Swerling IV.
.
2.7. The Radar Equation Revisited
The radar equation developed in
Chapter 1
assumed a constant target RCS
and did not account for integration loss. In this section, a more comprehensive
form of the radar equation is introduced. In this case, the radar equation is
given by
P
av
G
t
G
r
λ
2
σ
In
()
4(
3
kT
e
FB
τ
f
r
L
t
L
f
R
4
=
----------------------------------------------------------------------
(2.94)
(
SNR
)
1
where
P
av
=
P
t
τ
f
r
is the average transmitted power,
P
t
is the peak transmit-
ted power,
τ
is pulsewidth,
f
r
is PRF,
G
t
is transmitting antenna gain,
G
r
is
receiving antenna gain,
λ
is wavelength,
σ
is target cross section,
In
()
is
improvement factor,
n
P
is the number of integrated pulses,
k
is BoltzmanÓs
constant,
T
e
is effective noise temperature,
F
is the system noise figure,
B
is
receiver bandwidth,
L
t
is total system losses including integration loss,
L
f
is
loss due to target fluctuation, and
(
SNR
)
1
is the minimum single pulse SNR
required for detection.
The fluctuation loss, , can be viewed as the amount of additional SNR
required to compensate for the SNR loss due to target fluctuation, given a spe-
cific
L
f
P
D
value. This was demonstrated for a Swerling I fluctuation in Fig.
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