Hr3114661470

Umoh, Gabriel Etim, Akpan, Aniefiok Otu / International Journal of Engineering Research
and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 1, January -February 2013, pp.1466-1470
Extraction Of Radar Signal Using Auto-Correlation Functions
Umoh, Gabriel Etim, Akpan, Aniefiok Otu
Department Of Electrical/Electronics Engineering Faculty Of Engineering, Akwa Ibom State University
Ikot Akpaden, Mkpat Enin, L.G.A. Akwa Ibom State, Nigeria
Department Of Physics Faculty Of Natural Andapplied Sciences, Akwa Ibom State University
Ikot Akpaden, Mkpat Enin, L.G.A. Akwa Ibom State, Nigeria

ABSTRACT
This research seeks to present post- 1.1 Radar ESM System
integration processing in order to improve In practice, the amplitude envelope
the sensitivity of electronic support measure received by the ESM system is a series of pulses
modulated by the radar frequency carrier.
(ESM) receivers. Correlation methods take
After detection of radar pulses intercepted by the
advantage of the periodic character of radar antennas, the ESM receiver takes digital
signals. In such cases, autocorrelation and measurements of frequency within the pulses,
cross-correlation improve the detection of bearing, amplitude and time of arrival of the pulse.
signals with high- repetition frequency. The processor de-interleaves pulses and assigns
Furthermore, since the extraction of radar samples to a pulse train which represents the radar
parameters is necessary to identify received signal. Using a database, the processor identifies the
signals, we study three types of estimators: emission. Then information is presented to the
straightforward method, interpolation defense systems.
method and maximum likelihood one. A basic microwave receiver consists of a front-head
filter followed by a detector and a video low-pass
Simulation studies with realistic models and
filter with Bv bandwidth.
real signals are carried out to validate
performances of such processing. With a 1.2 Need for Sensitivity
view to implanting correlation functions, Those receivers always need to improve the
some architecture are studied. The choice of probability of detection of radar signals. Using
method is of interest since we need a lot of digital processing, we can extract signal from noise,
samples to be integrated. To conclude, as keeping in mind that such a system must provide
radar ESM receiver requires most radar parameters for identification.
information on received signals, the Sensitivity is defined in terms of the signal-to-noise
enhancement of the sensitivity using ratio at the output of the video filter. This paper
deals with correlation processing. Section 2
correlation method is of great interest.
discusses the sensitivity gain obtained at the output
of autocorrelation processing, detection processing
Keywords: Electronic support measure, of those methods and exploitation of the results.
autocorrelation, estimators, sensitivity, signal-to- Special attention is paid in section 3 to the
noise ratio, cross-correlation, simulation, recursive application of cross-correlation. Some simulations
structure are presented in section 4 to validate the
performances. Section 5 describes the complexity to
Introduction implanting such processing since many samples
Electronic support measure systems should be integrated.
perform the function of electromagnetic area
surveillance in order to determine the identity and 2. Autocorrelation
direction of arrival of surrounding radar emitters. Since the radar signal is periodic,
Automatic radar ESM systems are passive receivers autocorrelation processing seems to be of interest,
which receive emissions from other platforms, because it keeps the repetitive character with the
measure the parameters of each detected pulse and same pulse repetition frequency. After quadratic
thus sort the emissions to enable the determination detection, the received signal is a pulse train in
of the radar parameters and identification of each additive Gaussian noise.
emitter.
The contribution of our study is to improve the 2.1 Estimators
receiver sensitivity using post-integration processing Given a finite observation interval Ti, the
such as autocorrelation and cross-correlation autocorrelation is estimated by:
methods.

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1 N - k -1 As we suppose that the noise correlation duration is
ˆ
1 (k ) 
N-k
 X(i)X(i  k) 0  k  N - 1
i 0
very low in comparison with Ti, thus N ( ) is very
. . . . (1) low compared with S ( ) .
N-k -1 At a peak of correlation, the output SNR (SNRo) is:
1
ˆ
2 (k ) 
N
 X(i)X(i  k) . .
N i p 2SNRi2
i 0 SNRO 
. . . . (2) I  2pSNRi
Ncorr-1
1 Where, SNRi =
ˆ
3 (k) 
Ncorr
 X(i)X(i  k) 0  k  N
i0
corr -1
A /   N i   .B V .Ti   .B V .N.TS 
2 2

. . . (3) Number of independent samples.
where N is the number of samples on the T i interval. The SNR gain depends on the integration window
Ti has to be sufficiently long for the estimated (Fig.3), the duty cycle of the pulse train
(p=PRI/PW) (Fig.2). That is why such processing is
correlation to be accurate. Both estimators
ˆ
1 of interest for radar signals with high pulse
repetition frequency (HPRF signal). Furthermore,
ˆ
(unbiased) and 2 (biased) use all the samples, with a low SNRi,, the processing gain decreases
whereas the third one works with Ncorr samples out quickly (Fig. 2).
of 2Ncorr (Ncorr is a constant value, Ncorr = N/2). The
third estimator carries out the correlation function
on a ‘sliding temporal window’ but its performances
decrease by 3dB in comparison with the two
ˆ
previous estimators. Despite this, the 3 estimator
gives the first result when Ncorr samples have been
integrated, whereas we have to wait for N samples
with the first and second functions. This note
achieves a compromise between SNR gain and
extraction of samples in a prominent position. Fig. 2: Variation of SNRo with SNRi and ρ
(N=20000).
2.2 Sensitivity Gain
The output process of a radar signal without noise is
as follows:

Fig. 1: Output signal where PRI = pulse repetition Fig. 3: Variation of SNRo with SNRi and N(ρ=0,2).
interval, PW = pulse-width
2.3 Detection threshold
The signal is mixed with an additive Fig.4 determines the detection of a peak of
Gaussian noise with zero mean, σ2 variance and Bv correlation.
bandwidth. Signal and noise will not correlate then
SN ( )  0 .
Furthermore, the observation interval should be
much greater than PRI in order to decrease the error
of the output signal since we integrate samples
during a non whole number of PRI.
Given X(t) = S(t) + N(t), the output process is:
X ( )  S ( )  N ( ) . . .
. (4)
Fig. 4: Probability of detection with SNRi and N
(Pfa=1e-5).

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J  k PW
2.4 Parameter Estimation J -1
 TS  T 
The aim of an ESM receiver is to identify PW  PW 
(i - j)  1 y i    S (i - j) - 1 y i
 i  J  PW 
emissions, so the system has to define its ˆ
MAX MV 
i  J -k
characteristics exactly. There are three parameters to 2 Jk 2
J -1
 TS   TS 
  (i - j)  1 - J  PW (i - j) - 1
PW
estimate: amplitude, PW and PRI. We study three
estimators i  J -k PW  PW  i  
The sampling frequency (1/Ts) of the
autocorrelation function is the same as the signal where JTs is the time of arrival of the peak,
one. Indeed, the autocorrelation function of the yi the signal value at iTs, kLI the number of samples
signal with a band since Fourier transform of the used in a slope. We check that the pulse-width
autocorrelation function of the signal with a band estimator and the peak value one are both efficient
limited spectral density, has the same limited band in the maximum likelihood criterion.
since Fourier transform of the autocorrelation Note: We could estimate the PRI parameter with the
function is the power spectral density. In that case maximum likelihood criterion using the Fourier
Shannon’s theorem applied to the signal or its transform. We will have an efficient estimator.
correlation function gives the same sampling rate. Despite this, to implant the method we need an
additional transform of the output process, and
2.4.1 Straightforward Method consequently more calculus.
Studying the output sample, we get:
PRI = interval between two peaks 2.4.4 Simulation
PW = width is the halfway up of a triangle of A computer simulation was conducted to
correlation. compare the performances of the different
aplitude  maxp (max is the peak value). estimators. The first method is the easiest one to
implant, whereas the last estimator has the best
accuracy thanks to the maximum likelihood
2.4.2 Interpolation method
principle as can be seen in Table 1.
At each triangle of correlation, we have to estimate
the two slopes in the mean-square criterion:
SNRi Straight est. Interpol est. ML est.(%)
a 2 b1 - a 1 b 2 (db) (%) (%)
PW = and amplitude =
2a 1 a 2 PW peak PW peak PW peak
10 0 0,5 0,4 0,6 0,3 0,5
2a1a 2 PRI 0 5,7 3,8 3,3 2,4 2,3 2,5
a 2 - a1 -3,6 13,8 7,2 10,7 6,5 5,5 6,6
-4,6 13,9 7,1 10,1 6,3 5,6 5,5
Table 1 PW and peak correlation accuracy
The parameter accuracy is defined as follows:
E[parameter]
c/o  .100
varianceparameter

3. Cross-correlation
The purpose of such a method is to recognize an
Fig. 5: Slopes of the triangle interpolation. a prior know signal Y(k) in the received noisy
signal. The cross-correlation estimators are the same
as those of autocorrelation where:
2.4.3 Maximum likelihood method
1 N-k -1
J -1 J  k PW
ˆ
1 (k )   Y(i)X(i  k) .
N - k i 0
(6)

 (i - j)  (i - j)
2 2

ˆ
PWMV  maxTS
i  J - k PW iJ 3.1 Sensitivity Gain
J -1 J  k PW With same working hypothesis as 2.2, we get:
 ( y - max)(i - j) -  ( y - max)(i - j)
i  J - k PW
i
iJ
i
SNRo =
.
NiρSNRi .
(7)
. .

The gain is a linear function of the
observation interval and of the duty cycle. Thus, we
obtain a constant improvement (Fig. 6).

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Fig. 6 Variation of SNRo with SNRi and N (ρ=0,2)
Fig. 9. Autocorrelation output signal.
3.2 Detection Probability.

Fig. 10: Cross-correlation output signal.
Fig. 7 Detection probability with SNRi and N
(Pfa=10e-5).
5 Implanting Correlation Function
Fig. 7 shows that the more samples we integrate, the
5.1 Classical Structure
easier the detection of a signal with
additive noise is.

3.3 Autocorrelation and cross-correlation
comparison
The use of cross-correlation function provides
sensitivity gain, but special attention is given to such
applications. Indeed, the operator of the ESM
system has no information on the received signal.
Fig. 11 Classical structure
That is why the aim of this method is to search for a
given radar in the surrounding area in order to
5.2 Recursive structure
perform the warning function.
Each correlation sample is the result of a recursive
calculus (Eq. 8-9)
4 Simulation description and results
Simulation studies with realistic models (k )  Rk(N) . . .
and real signals were conducted to corroborate the N
theoretical performance predictions. . . . . (8)
The scenario presented here (Fig. 8-9-10) is a Where, Rk (N) = Rk (N – 1) + X(N)X(N+k)
mixture of three signals. . . . (9)

The recursive method uses one multiplier-
accumulator cell (Fig.12) per correlation point. The
correlator is designed as a macro-cell.

Fig. 12 Recursive structure.

Fig. 8 Input signal with S1: HPRF signal with SNRi 5.3 Fast correlation’ Structure
= 0dB; ρ=0,1 – S2” LPRF (low PRF) signal with Using a Fourier transform, we compare correlation
SNRi=13dB; ρ=5,1.1e-4 - S3: LPRF signal with and convolution (Eq. 10):
SNRi=13dB; ρ=6.1e-4 - σ=1 - N = 2000. s ( )  S(t) * S* ( t )   s ( )   s ( ) s ( )
FT

. . . . .
(10)

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The advantage of such method is the use of a Fast 2. M. Bellanger, Traitement numerique du
Fourier transform algorithm. signal: theorie et pratique, 4o edition,
MASSON, 1990.
6. CONCLUSION
To conclude, as the function of a radar ESM 3. T. G. KINCAID, ‘Estimation of periodic
receiver is surveillance to determine radar activity, signals in noise’, J.A.S.A, Vol. 46, no6,
the system requires most information on received 1969, p. 1397-1403.
signals. So the enhancement of sensitivity achieved
by correlation methods is of interest. Those 4. J. MAX, Methodes et techniques du
functions contribute to the increased detection of traitement du signal et applications aux
HPRF signals with low SNR. This processing also measures physiques, physiques, Tome 1,
carries out parameter estimation of radar signals. MASSON, 1981, p. 173-181.
Future ESM system could incorporate such
functions. 5. A. PAPULIS, Probability, random
variables and stochastic processes, Mc.
REFERENCES GRAW-HILL BOOK COMPANY, 1965.
1. V. Albrieux, ‘Compilateur de 1a function
de correlation’, Conferencfes radar, Vol. 1, 6. R. G. WILEY, Electronic intelligence: the
1989, p. 319-322. analysis of radar signals, ARTECH
HOUSE Inc., 1982.

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