RADAR SIGNAL EXTRACTION USING CORRELATION 1-2 1 1 ENST-Bretagne, Département Signal et Communication, BP 832, 29285 BREST CEDEX, e-mail :
[email protected] 2 THOMSON-CSF, DIVISION RCM, Centre électronique de Brest, 10 Avenue 1ère DFL, 29283 BREST CEDEX, Fax : (33)98312767, Tel : (33)98312705, e-mail :
[email protected] 1
amplitude and time of arrival of the pulse. The
In this paper we present post-integration processing
processor deinterleaves pulses and assigns samples to
in order
to
electronic
a pulse train which represents the radar signal. Using
support
measure
Correlation
a database, the processor identifies the emission.
methods take advantage of the periodic character of
Then information is presented to the defence systems.
improve
the
sensitivity
(ESM)
of
receivers.
radar signals. In such cases,
autocorrelation
and
A basic microwave receiver consists of a front-
cross-correlation improve the detection of signals
head filter followed by a detector and a video low-
with high repetition frequency. Furthermore, since
pass filter with Bv bandwidth.
the extraction of radar parameters is necessary to identify received signals, we study three types of estimators : straightforward
method,
interpolation
! Those
receivers
always
need
to
improve
the
method and maximum likelihood one. Simulation
probability of detection of radar signals. Using digital
studies with realistic models and real signals are
processing, we can extract signal from noise, keeping
carried
in mind that such a system must provide radar
out
to
validate
performances
of
such
parameters for identification.
processing. With a view to implanting correlation functions,
Sensitivity is defined in terms of the signal-to-
some architectures are studied. The choice of method
noise ratio at the output of the video filter. This paper
is of interest since we need a lot of samples to be
deals with correlation processing. Section 2 discusses
integrated.
the
To conclude, as radar ESM receiver requires most
autocorrelation processing, detection processing of
information on received signals, the enhancement of
those methods and exploitation of the results. Special
the sensitivity using correlation method is of great
attention is paid in section 3 to the application of
interest.
cross-correlation. Some simulations are presented in
support
gain
obtained
at
the
output
of
section 4 to validate the performances. Section 5
Electronic
sensitivity
describes
measure
systems
perform
the
function of electromagnetic area surveillance in order to determine the identity and direction of arrival of surrounding radar emitters. Automatic radar ESM
the
complexity
to
implanting
such
processing since many samples should be integrated.
"
Since the radar signal is periodic, autocorrelation
systems are passive receivers which receive emissions
processing seems to be of interest, because it keeps
from other platforms, measure the parameters of each
the repetitive character with the same pulse repetition
detected pulse and thus sort the emissions to enable
frequency. After quadratic detection, the received
the
signal is a pulse train in additive gaussian noise.
determination
of
the
radar
parameters
and
identification of each emitter. The contribution of our study is to improve the receiver sensitivity using post-integration processing such
as
autocorrelation
and
cross-correlation
methods.
In practice, the amplitude envelope received by the ESM system is a series of pulses modulated by the radar frequency carrier. After detection of radar pulses intercepted by the the
ESM
receiver
Given
takes
digital
measurements of frequency within the pulse, bearing,
a
finite
observation
interval
Ti,
the
autocorrelation is estimated by :
Γ (k ) =
antennas,
# 1
∑ X(i )X(i + k ) 0 ≤ k ≤ N − 1 N − k = 1 Γ (k ) = ∑ X(i )X(i + k ) N = Γ (k ) =
1 − ∑ X(i)X(i + k ) 0 ≤ k ≤ N − 1 N = corr
(1) (2) (3)
where N is the number of samples on the Ti interval. Ti has
to
be
sufficiently
long
for
the
estimated
correlation
to
be
Γ 2
(unbiased) and
accurate.
Both
Γ1
estimators
(biased) use all
the
samples,
frequency (HPRF signal). Furthermore with a low SNRi, the processing gain decreases quickly (Fig.2). 60
whereas the third one works with Ncorr samples out of 2Ncorr (Ncorr is a constant value, Ncorr=N/2). The third
40
estimator carries out the correlation function on a
sliding
temporal
window
but
its
decrease by 3dB in comparison with the two previous
Γ
20
performances
0
estimator gives the
- 20
first result when Ncorr samples have been integrated,
- 40
estimators. Despite this, the
3
whereas we have to wait for N samples with the first and
second
functions.
This
note
achieves
-8
-6
-4
-2
0
2
4
6
8
10
a
ρ= 0.5
compromise between SNR gain and extraction of
ρ= 0.2
ρ= 0.1
ρ= 0.01
ρ= 0.001
Variation of SNR with SNR and ρ (Ν=20000).
samples in a prominent position.
! $ #
45 40
The output process of a radar signal without noise is
35
as follows :
30
25
5 J
ρ.)
A
Γ(τ)
2
20 15 10 5
AUTOCORRELATION
-8
-6
-4
-2
0
2
4
6
8
10
J
29
29
241
241
Input
τ
Output Output signal where PRI = pulse repetition interval, PW = pulsewidth.
% & '' ( ) Fig.4
variance and Bv bandwidth.
noise with zero mean,
σ
Γ (τ) = 0 .
Γ (τ ) = Γ (τ ) + Γ (τ )
very low in comparison with Ti, thus low compared with
Γ S ( τ) .
Γ N (τ )
is very
2
2
where SNRi=A /σ - N
(5)
= π.B .T = π.B .N.T =
of
Probability of detection with SNR and N (P =1e-5).
# *
The aim of an ESM receiver is to identify emissions,
At a peak of correlation, the output SNR (SNRo) is :
N ρ SNR SNR = 1 + 2ρSNR
peak
(4)
As we suppose that the noise correlation duration is
a
, the output process is :
of
X(t ) = S(t ) + N( t)
detection
greater than PRI in order to decrease the error of the
Given
the
whole number of PRI.
determines
Furthermore, the observation interval should be much output signal since we integrate samples during a non
correlation.
Signal and noise will not correlate then
Variation of SNR with SNR and N (ρ=0,2).
The signal is mixed with an additive gaussian 2
number
so the system has to define its characteristics exactly. There are three parameters to estimate : amplitude, PW and PRI. We study three estimators. The sampling frequency (1/Ts) of the autocorrelation function is the same as the signal one. Indeed, the
of independent samples.
autocorrelation function of the signal with a band
The SNR gain depends on the integration window
limited spectral density, has the same limited band
(Fig.3), the duty cycle of the pulse train (ρ = PRI / PW) (Fig.2). That is why such processing is of interest for radar signals with high pulse repetition
since
Fourier
transform
of
the
autocorrelation
function is the power spectral density. In that case
Shannons
theorem
applied
to
the
signal
or
its
correlation function gives the same sampling rate.
Studying the output samples, we get : PRI = interval between two peaks. PW = width at the halfway up of a triangle of correlation.
amplitude = maxρ
$' . ( " +-, +-, +-, */ .0 */ .0 */ .0
+, E
1 1 2%3 2#3
0
0,5
0,4
0,6
0,3
0,5
5,7
3,8
3,3
2,4
2,3
2,5
13,8
7,2
10,7
6,5
5,5
6,6
13,9
7,1
10,1
6,3
5,6
5,5
PW and peak correlation accuracy.
(max is the peak value).
The parameter accuracy is defined as follows :
! At each triangle of correlation, we have to estimate
E[parameter ]
ε% =
variance
the two slopes in the mean-square criterion: PW
=
a b
− a b
and amplitude
2a a
% 2 "
2a a PRI
=
a
− a
The purpose of such a method is to recognise an a prior known signal Y(k) in the received noisy signal.
y(i)
The cross-correlation estimators are the y1(i) = a1.i + b1
Γ (k ) =
J −1
MAX
∑
^
MV
=
i = J − k 29
=# − PW # −
=# − PW
= #
i = J − k 29
T PW (i − J ) + 1 y T PW (i − J ) + 1 S
S
i 2
=
∑ Y(i )X(i + k )
(6)
= N ρSNR
(7)
interval and of the duty cycle. Thus we obtain a
constant improvement (Fig.6).
∑ (y − max)(i − J ) − ∑ (y − max)(i − J )
The gain is a linear function of the observation # + PW
= # # + PW
J −1
∑
SNR
∑ (i − J ) + ∑ (i − J )
1 N−k
With same working hypothesis as 2.2, we get :
Slopes of the triangle interpolation. # −
as
% ! $ #
i
" #$ % &
same
those of autocorrelation where :
y2(i) = a2.i + b2
PW !" = maxT
.100
J + k 29 + ∑ i =J J + k 29 − ∑ i =J
T PW (i − J ) − 1 y T PW (i − J ) − 1
45
40
S
i
35
2
S
30
25
where JTs is the time of arrival of the peak, yi the signal value at iTs, kLI the number of samples used in
20 -8
-6
-4
-2
a slope. We check that the pulsewidth estimator and
0
2
4
6
8
10
the peak value one are both efficient in the maximum
Variation of SNR with SNR and N (ρ=0,2).
likelihood criterion.
' ( ) % * +, ! $ % & ) %* % * -". ( / ) * *! * ! * %!% ! ) ** ) * 0% 1 ))%%*
% & . 44 ( 1
0,8
0,6
0,4
0,2
% A computer simulation was conducted to compare the
0 0,05
0,15
0,25
method is the easiest one to implant, whereas the last estimator
has
the
best
accuracy
thanks
to
the
0,35
0,45
0,55
0,65
0,75
performances of the different estimators. The first
Detection probability with SNR and N (P =10e-5).
maximum likelihood principle as can be seen in
Fig.7 shows that the more samples we integrate, the
Table 1.
easier the detection of a signal with additive noise is.
%% 5 & ( & 2& ( & . The
use
of
cross-correlation
function
provides
) *" 6 " 7
) ( &( 5&5 X(i)
X(N)
X(0)
sensitivity gain, but special attention is given to such
*
applications. Indeed, the operator of the ESM system
k weighting
has no information on the received signal. That is why the aim of this method is to search for a given radar in the surrounding area in order to perform the
X(N+k)
X(k)
Classical structure.
warning function.
# " * "
) &5 ! 5&5
Simulation studies with realistic models and real
calculus (Eq.8-9) :
signals were conducted to corroborate the theoretical
Γ(k ) =
performance predictions. The
scenario
Γ(k)
* *
presented
here
(Fig.
8-9-10)
is
a
mixture of three signals.
Each correlation sample is the result of a recursive
( )
R N
(8)
N
( ) = R (N − 1) + X(N )X(N + k )
where R N The
(9)
recursive
method
uses
one
multiplier-
accumulator cell (Fig.12) per correlation point. The correlator is designed as a macrocell.
X(i)
k
Γ (k)
weighting
+
*
CLK
Recursive structure.
)% 87 & ( 9 5&5
Input signal with S1 : HPRF signal with SNR=0dB; ρ=0,1 -
S2 : LPRF (low PRF) signal with SNR=13dB; ρ=5,1.1e-4 - S3 : LPRF signal with SNR=13dB; ρ=6.1e-4 - σ=1 - N=2000.
Using a Fourier transform, we compare correlation and convolution (Eq.10 ) :
&Γ (τ ) = S( t ) * S, ( t ) ← → γ (υ ) = γ (υ )γ I
I
I
*
I
(υ )
(10)
The advantage of such method is the use of a Fast Fourier transform algorithm.
"
To conclude, as the function of a radar ESM receiver is surveillance to determine radar activity, the system Y(t)
requires most information on received signals. So the
) ) *) %
enhancement of sensitivity achieved by correlation methods is of interest. Those functions contribute to the increased detection of HPRF signals with low time
$%& '(
SNR. This processing also carries out parameter +%& '(
Autocorrelation output signal.
estimation of radar signals. Future ESM system could incorporate such functions.
Z(t)
time
HPRF
Cross-correlation output signal.
1 V. ALBRIEUX, Compilateur de la fonction de corrélation, , Vol.1, 1989, p.319-322. 2 M. BELLANGER, , 4° édition, MASSON, 1990. 3 T.G. KINCAID, Estimation of periodic signals in noise, ., Vol.46, n°6, 1969, p.1397-1403. 4 J. MAX, , Tome 1, MASSON, 1981, p.173-181. 5 A. PAPOULIS, ! " , Mc GRAW-HILL BOOK COMPANY, 1965. 6 R.G. WILEY, # , ARTECH HOUSE Inc., 1982.
