Page 184 - Radar Technology Encyclopedia

FALSE ALARM FANTASTRON 174

that vary the detection threshold as a function of the sensed through a narrowband IF filter, the noise envelope has a Ray-
environment. See false-alarm probability; CONSTANT leigh distribution, and in this case we can write
FALSE-ALARM RATE (CFAR). PCH 2
– æ V T ö
Ref.: IEEE (1993), p. 480; DiFranco (1968), p. 270. P fa = exp ----------- ÷
ç
è 2y 0 ø
constant false-alarm rate (see CFAR).
where y is the mean square value of the noise voltage in a
0
False-alarm control refers to any technique applied to the narrowband (compared to midfrequency) IF filter.
output of a radar detector or detection scheme that attempts to In Fig. F1, T is the time between crossing of the thresh-
k
maintain a constant false-alarm rate under varying environ- old V by the noise envelope, when the slope of crossing
T
mental conditions. (See CFAR). A fixed detection threshold, noise voltage is positive, and t , t , t are the times during
k k+1 k+n
if set sufficiently high, will result in a uniform false-alarm
rate, but at the cost of reduced sensitivity to true target
returns. Such use of a fixed threshold is generally unaccept-
able, and three different forms of false-alarm control have
been devised in an attempt to solve the problem:
(1) Adaptive thresholding.
(2) Nonparametric detectors.
(3) Clutter maps.
The adaptive thresholding and nonparametric detector
Figure F1 Envelope of receiver output showing false alarms
approaches both make the assumption that the samples in the due to noise (from Skolnik, 1980, Fig. 2.4, p. 25, reprinted by
reference cells, or the range cells surrounding the test cell, are permission of McGraw-Hill).
independent, both in space and time, and have the same statis-
tical distribution. The detectors then compare the return from which the noise voltage lies above the threshold. The average
the test cell with the statistical average from the reference time interval between crossings of the threshold by noise
cells and make a detection decision if the test cell return is alone is the false alarm time T where
fa
sufficiently larger. N
1
Clutter maps are most effective in fixed-frequency, t = lim ---- å T
ground-based radars in a stationary land clutter environment. fa N ® ¥ N k
k = 1
A clutter map is made by storing an average background clut-
ter level for each range-azimuth cell, and a target detection is The false-alarm probability may also be defined as the ratio
declared in a particular cell if the return exceeds the average of the duration of time the noise voltage envelope is actually
for that cell by a preestablished amount. The threshold is above the threshold, to the total time it could have been above
determined based on the average return in that cell over previ- the threshold. The average duration of a noise pulse is
ous scans (e.g., 5 to 10 scans). An advantage of clutter maps approximately equal to the reciprocal of the bandwidth B, so
is that they give the radar a useful interclutter visibility capa- that
bility; they can see targets that lie between large clutter t áñ 1
k av
P = ---------------- = ---------
returns. (See CFAR.) PCH fa á T ñ t B
k av fa
Ref.: Skolnik (1990), pp. 8.12–8.21.
The false-alarm time can be seen also to equivalent to
The false-alarm number is the reciprocal of the false-alarm 2
probability 1/P where P is the probability that the interfer- t fa = 1 æ V T ö
ç
fa
---exp ---------- ÷
fa
ence voltage envelope will exceed some threshold voltage V . B è 2y 0 ø
T
(See false-alarm probability.) PCH
PCH
Ref.: Skolnik (1980), p. 24.
Ref.: Skolnik (1980), pp. 23–25.
False-alarm probability. If a threshold device is used to
make a decision as to the presence or absence of a signal in a false-alarm time (see false-alarm probability).
background of noise, the performance of this device can be FANTASTRON. A fantastron is a single-stage relaxation
expressed in terms of two probabilities: the probability of vacuum-tube oscillator of linearly dropping voltage operating
detection P and the probability of false alarm P . The in the free-running or delay-line mode. A fantastron processes
fa
d
threshold can be considered the value of a receiver output sawtooth and rectangular voltage pulses, the duration of
voltage V , that when exceeded, indicates a detection. Due to which can be regulated within broad limits by changing the
T
the presence of thermal noise in the receiver, there is always a control voltage.
nonzero probability that the threshold will be exceeded, even Fantastrons were used in older types of radars to obtain
in the absence of a target signal. The probability that the precise adjustable pulse delays, to determine the time interval
threshold value V is exceeded when no signal is present is between pulses, and to generate sawtooth voltage. IAM
T
the false-alarm probability. For Gaussian noise passed Ref.: Popov (1980), p. 454.