Page 263 - Radar Technology Encyclopedia

253 loss, field degradation loss, fluctuation

subjective estimation of the quality of maintenance personnel, Filter straddling loss results from the use of a fixed doppler
or by flight testing. DKB filter bank to process signals from targets having arbitrary
doppler shifts, some of which fall in regions having response
Filter matching loss results from departure of the actual
lower than the maximum. It is defined as the increase in sig-
receiver filter from the matched filter for the transmitted
nal energy required to achieve given probability of detection
waveform, on a single-pulse basis. It is defined as the ratio of
for target doppler shifts uniformly distributed over the filter
receiver output signal-to-noise ratio to that available from a
bank response, compared with a target centered in a doppler
filter matched to the individual pulse. For simple rectangular
filter. The loss is minimized by use of closely spaced filters,
pulses (having no phase modulation), the loss for different
such as those formed in an FFT filter bank when low-sidelobe
types of filter is shown in Fig. L25. For linear-FM pulse com-
weighting is used, or use of zero-padding of the FFT input (a
pression signals, the loss as a function of sidelobe level, for
process that adds strings of zeroes at each end of the n-pulse
different families of weighting function, is identical to that for
data sample, decreasing the filter spacing while leaving the
doppler filters, shown in Fig. L10. DKB
filter bandwidth constant).
Ref.: Barton (1969), pp. 56, 84.
An approximation for L is
ef
1
-- - 2
æ
------- (dB)
L = 1.25P 3 Df ö
ef d è B ø
f
where D is the filter spacing, B is filter bandwidth, and P is
f
f
d
detection probability. For the FFT processor, Df/Bf = 1/t f
B , and the straddling loss will be a function of the weight-
f
ing function (Table L11) DKB
Barton (1993), p. 133.
Table L11
Bandwidth Constants for Weighted FFT
Figure L25 Filter matching loss vs. filter noise bandwidth B nh Weighting function Bandwidth constant t B
for rectangular pulse of with t with different filters (from f f
Barton, 1969, Fig. 3.17, p. 84). Uniform (rectangular) 0.886
The filter matching [loss] factor M differs slightly from the Cosine 1.19
filter matching loss in two cases:
(1) A narrowband mismatch reduces the number of Cosine-squared 1.44
opportunities for false alarm by a factor x, equal to the ratio of
Taylor 0.9 - 0.0135(G + 15)
s
signal bandwidth to filter bandwidth. This permits the thresh-
old to be lowered (false-alarm probability increased from P f Dolph-Chebyshev 0.8 - 0.0135(G + 10)
s
to xP ) while still maintaining the required false-alarm time.
f
The filter matching factor is then equal to the filter matching G is sidelobe level in dB relative to mainlobe.
s
loss multiplied by the ratio (< 1) of detectability factors for
Fluctuation loss results when targets have other than steady
the two false-alarm probabilities:
RCS and depends on the fluctuation model. It is defined as
the increase in average signal energy required to achieve a
DxP )
(
f
M = L ----------------- given detection probability, compared to that required for a
m
(
DP )
f
steady target. The loss is greater for high detection probabili-
(2) A wideband mismatch at IF if followed by a video ties, where target fading can reduce detection probability
bandwidth less than half the IF bandwidth (or an equivalent more than the increase for upwards fluctuations. The fluctua-
broad range gate) is accounted for by calculating a collapsing tion loss L (1) for cases in which a single sample from a Ray-
f
loss (Table L9) rather than taking the full loss in IF SNR. The leigh target is available is shown in Fig. L26, as a function of
value of collapsing loss L may be substituted for M, in which detection probability P for different false-alarm probabilities
c
d
case L is excluded from the miscellaneous signal-processing P . It is defined as
c
fa
loss.
D 1 ()
1
=
The difference between L and M is seldom more than a L 1 () ---------------
m
f
0
fraction of one decibel, but it is M that is used to calculate the D 1 ()
effective detectability factor used in the radar equation. In the where D (1) is the detectability factor for a steady target and
0
Blake chart, the value M is included to describe the net effect D (1) = (lnP /lnP ) - 1 is the detectability factor for the
1
d
fa
of a filter mismatch. DKB Swerling case 1 fluctuating target.
This case applies to signals resulting from multiple scat-
Ref.: Barton (1988), p. 78.
tering centers on the target whose relative phase does not
change significantly during the observation time t (giving
o