Page 123 - Radar Technology Encyclopedia

detectability factor, coherent DETECTION [of radar targets] 113

which is received with full antenna gains and a matched-filter and the target missed probability:
receiver. This detectability factor can be calculated exactly, PB A )
(
0 1
=
(
using the inverse of the integral of the normal distribution: P tm = PB A ) ---------------------
0
1
(
PA )
1
1 – 1 – 1 Under conditions of target absence (A ) are the false alarm
–
=
D n () ------ Q ([ P ) Q ( P )] 0
c 2n fa d probability:
-1
where the inverse function Q is defined by PB A )
(
1 0
P = PB A ) ---------------------
(
=
(
¥ fa 1 0 PA )
2 0
1 æ v ö – 1
() ---------- exp –
QE = ò ----- vd = P , Q () E and the true nondetection probability:
P =
2p è 2 ø
(
E PB A )
0 0
(
=
P tn = PB A ) ---------------------
0
0
where P and P are probabilities of detection and false PA )
(
0
fa
d
alarm. DKB from which
Ref.: Barton (1988), p. 63. P + P = 1; P + P = 1
tn
fa
d
tm
The effective detectability factor D is the actual energy The basic values used in practical applications are detec-
x
ratio required of the central sample (pulse) at the receiver tion probability and false-alarm probability. The decision as
input, given a matching factor M a beamshape loss L , and a to target presence is made based on analysis of the received
p
miscellaneous signal-processing loss, L : radar return to determine whether the signal plus interference
x
or only interference are present. This is done by comparing
the intensity (amplitude) of the received return with a thresh-
,
(
=
D nn ,( ) D nn ) ML L
x e e e p x
old level and making the decision based on the chosen detec-
Since this factor includes all terms that depend on the proba- tion criterion. Since interference is generally a random
bility of detection, its use permits all other terms in the radar function of time, the process of radar detection is a statistical
range equation to be entered as constant parameters. DKB procedure using the mathematical approaches of probability
theory. The most used theory is developed for detection of
Ref.: Barton (1988), pp. 19–20.
weak signals in a background of white noise with a Gaussian
DETECTION [of radar targets]. In radio applications, the distribution. Many recent works have been devoted to algo-
term detection has two distinct meanings. The first meaning is rithms for radar detection in other types of interference (col-
sensing the presence of electromagnetic fields, or in radar ored noise, nonstationary clutter, etc.), but the resulting
applications sensing the presence of a radar target. This is algorithms for nonstationary, non-Gaussian interference are
termed radar detection or target detection and is covered largely empirical rather than theoretical.
immediately below. The second meaning is demodulation of Radar circuits performing the process of target detection
signals, to be covered after target detection under the heading are called radar detectors. Radar detectors fall into several
of DETECTOR. basic categories, depending on the fundamental principles
Target detection is the process of reaching a decision on underlying the detection process, as shown in Table D3.
whether a target is present in the specified volume of space.
The decision is made between two mutually exclusive condi- Table D3
tions: Types of Radar Detection
A = target is present; A = target is absent. Basis Options
0
1
These conditions are unknown at the moment the decision is
to be made. Because interference is present in the receiver, Number of hypotheses Binary or M-ary [multialternative]
tested
along with the signal, either input condition may lead to either
of two decisions: Structure of algorithms Optimum or Nonoptimum (quasiop-
B = target is present; B = target is absent. timum)
1
0
As a result there are four possible results: Principle of integration Coherent or Noncoherent
B A = true detection; B A = target missed; Threshold Automatic or Visual
1 1
0 1
B A = false alarm; B A = true nondetection. Knowledge of statistics Parametric (distribution dependent)
1 0
0 0
The sum of the probabilities of these four results is equal to or Nonparametric (distribution-free)
unity:
Typically, modern radar detection systems are binary, qua-
+
(
+
(
PB A ) PB A ) PB A ) B A ) 1=
(
+
(
1 1 0 1 1 0 0 0 sioptimum, automatic, distribution-free devices using either
or both coherent and noncoherent integration. M-out-of-n
The values describing the quality of detection perfor-
detection (binary integration) is widely used. SAL
mance under conditions of target presence (A ) are the (true)
1
detection probability: Ref.: IEEE (1993), p. 337; Helstrom (1968); Whalen (1971); Meyer (1973);
Blake (1980), Ch. 2; DiFranco (1968); Skolnik (1980), Ch. 10; Bakut
PB A ) (1984); Barton (1988), Ch. 2; Barkat (1991); Haykin (1992); Morchin
(
1 1
(
P = PB A ) ---------------------
=
d 1 1 PA ) (1993), Ch. 5; Shirman (1970), Ch. 3; Kolosov (1989).
(
1