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nm
+
n
ρ
c
=
-------------
(1.90)
where is the number of pulses containing both signal and noise, while is
the number of pulses containing noise only. Radars detect targets in azimuth,
range, and Doppler. When target returns are displayed in one coordinate, such
as range, noise sources from azimuth cells adjacent to the actual target return
converge in the target vicinity and cause a drop in the SNR. This is illustrated
in Fig. 1.24.
n
m
cell 1
c
ell
2
cell 4
range
cell 5
Figure 1.24. Illustration of collapsing loss. Noise sources in cells 1, 2, 4, and 5
converge to increase the noise level in cell 3.
1.8.5. Processing Losses
a. Detector Approximation:
The output voltage signal of a radar receiver that utilizes a linear detector is
v
I
2
()
v
2
v
()
=
+
()
(1.91)
where are the in-phase and quadrature components. For a radar using a
square law detector, we have
(
v
I
,
v
Q
)
v
2
()
v
I
2
()
v
2
.
=
+
()
Since in real hardware the operations of squares and square roots are time
consuming, many algorithms have been developed for detector approximation.
This approximation results in a loss of the signal power, typically 0.5 to 1 dB.
b. Constant False Alarm Rate (CFAR) Loss
:
In many cases the radar detection threshold is constantly adjusted as a func-
tion of the receiver noise level in order to maintain a constant false alarm rate.
For this purpose, Constant False Alarm Rate (CFAR) processors are utilized in
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