Page 134 - Radar Technology Encyclopedia

124 detection of a signal with unknown parameters detection, single-scan [burst]

At the output of the detector during time T there will be Detection of a random signal is based on an anticipated ran-
an additive mixture of the useful signal u(t,y) and interfer- dom process. The problem of detecting random processes
ence n(t): occurs in radar astronomy, radio prospecting, and passive
y(t) = u(t,y) + n(t) radar. In detecting a random process in an observation y(t), in
If the interference is white noise, the likelihood ratio for a sig- addition to white n(t) there might also be a normal useful pro-
nal with random phase has the form cess u(t) with zero mean and correlation function K (t, t + t),
u
E s 2ZT () which is uncorrelated with the noise n(t), where t is the corre-
æ
L = exp – ------J --------------- ö
1 N 0 è N ø lation time. If the process u(t) is stationary and, consequently,
0
0
K (t, t + t) = k then the decision on detection of a random pro-
u
where E is the signal energy, Z(T) is the correlation integral, cess is made when the quantity Z exceeds the threshold
s
J (×) is the modified Bessel function of zero order, and N is
0
0
the noise power spectral density. Z = ò 2 d Z 0
y t () t ³
The optimum decision rule for the problem of signal T
detection is calculation of the correlation integral Z(T) and its where Z is the threshold which depends on the selected
0
comparison with the threshold value Z : detection criterion, and T is the random process observation
0
Z
If Z(T) ³ there is a signal. time. In practical implementation, the detector repeats the
0
If Z(T) < Z there is no signal. structure of the correlation receiver with the difference being
0
The circuit of an optimum detector in this case will con- that the reference signal u (t) in it is not generated autono-
y
sist of a matched filter, which computes the correlation inte- mously but from the observed oscillation y(t), itself, which
gral Z(T), an amplitude detector, which removes the envelope passes through the linear filter.
of Z(T ), and a threshold unit. The threshold Z is selected to During reception of a radio thermal signal the power den-
0
achieve the desired low false-alarm probability. sities of the detected and interfering signals are unknown,
The correlation integral Z(T ) can also be represented in therefore one usually uses the contrast method of detection,
the form of quadrature components Z (T ) and Z (T ): which consists of comparing output signals with one another
1
2
2 2 for two different measured components (two positions of the
+
ZT () = Z T () Z T ()
2
1
antenna radiation pattern). In this case the decision on detec-
where tion is assumed based on comparison with the threshold,
T
which will depend on the anticipated temperature contrast,
Ay t () [
f t
Z T () = ò cos wt () ()] td difference DQ = Q - Q , where Q and Q are the output sig-
+
1 0 1 2 1 2
nals of the thermal receiver (radiometer) for the analyzed
0
components. (See also detection of a signal with known
T
parameters and detection of a signal with unknown
Ay t () [
Z T () = ò sin 0 wt () ()] td
+
f t
2
parameters.) AIL
0
Ref.: Kazarinov (1990), pp. 56–60, 432–436.
An optimum circuit of a detector in this case should
Single-channel detection occurs in a single-channel radar
include two channels (I and Q), a summing circuit and a
when the signal detection and processing is done sequentially
threshold unit. The presence of two channels is due to lack of
for each resolution cell. It requires more time to detect the tar-
knowledge of the initial phase of the signal. Such a detector is
get in comparison with multichannel detection, but with the
called a correlation detector (see coherent detection).
advantage of simplicity and cost reduction, as the number of
A signal with random amplitude and initial phases can be
hardware components is considerably less in this case. AIL
written in the form
Ref.: Sosulin (1992), p. 25.
U(t,y,b) = bA(t) cos [w t + f(t) + y]
0
where band y are random quantities. Usually it is assumed Single-pulse [hit, sample] detection is based on processing a
that the value of b has a Rayleigh distribution, and y has a single pulse or receiver output. In most radars many pulses
uniform distribution over 2p. The likelihood ratio for this sig- are available, and these are best combined by integration
nal is written in the form before being applied to the detection threshold. If this integra-
2
N 0 Z T () tion is performed coherently (using a filter matched to the
L = ------------------exp ------------------------------
2 E + N N E + N ) pulse train), the output can be considered a single-sample pro-
(
s 0 0 s 0
cess. Such processes are also used in some phased-array
Insofar as Z (T ) ³ 0, the likelihood ratio L is a mono- radars that dwell for only a single pulse repetition interval
2
2
tonic function of its argument and the circuit of an optimum during search or track. Theoretical evaluation of single-pulse
detector in this case does not differ from the circuit of an opti- detection probability is widely used to estimate overall per-
mum filter of a signal detector with random phase. Only the formance of radar in target detection. SAL
optimum threshold Z changes, which will depend on the dis- Ref.: Blake (1980), p. 26.
0
tribution law of the random amplitude (quantity b). AIL
Single-scan [burst] detection is detection in a single scan
Ref.: DiFranco (1968), p. 298; Dymova (1975), pp. 57–63; Sosulin (1992),
pp. 48–55. (observation), obtaining the single-scan probability of detec-