Available online at www.sciencedirect.com
ScienceDirect IERI Procedia 4 (2013) 168 – 173
2013 International Conference on Electronic Engineering and Computer Science
Small Target Detection and Noise Reduction in Marine Radar Systems Md Saiful Islama, Hyungseob Hana, Jae-Il Leeb, Myung-Gook Jungb, Uipil Chonga* a
Department of Comp., Univ. of Ulsan,, Ulsan, Korea b Jin Information System Co., Itd, Ulsan, Korea
Abstract The most fundamental problem in radar signal is detection of an object or physical phenomenon. This problem became more challenging to the signal processing and radar communities to detect small targets (like small icebergs) in an oceanic environment. These small targets are difficult to detect for a marine radar system since they protrude only about a meter or so above the sea surface level. Unfortunately these small targets can cause severe damage to ships traveling in ice-ridden waters. In this paper, we make detection decision for small targets such as small fragments of icebergs using crosscorrelation instead of statistical decision theory. Then we recover a transmitted signal using matched filter. Our simulation results give the exact result even when the received signal is attenuated more than 90%.
© 2013. Published by Elsevier B.V. B.V. Open access under CC BY-NC-ND license. © 2013 The Authors. Published by Elsevier Selection and/or peer under review under responsibility AmericanResearch Applied Science Research Institute Selection and peer review responsibility of Informationof Engineering Institute Keywords: Target detection; marine radar; cross-correlation; matched filter; signal to noise ratio
1.Introduction In an oceanic environment, detection of small targets like small icebergs using microwave radar of great interest to the signal processing and radar communities [1]. This is due to the problems of detection of signals in chaos. Traditionally, signals (encompassing desired signals as well as interfering signals) can be classified as Deterministic signals, which waveforms defined precisely for all instants of time and Stochastic processes, which is defined by an underlying probability distribution [2]. These two broadly defined classes overlook * Corresponding author. Tel.: +82-52-259-2220; fax: +82-52-259-1687 E-mail address:
[email protected]
2212-6678 © 2013 The Authors. Published by Elsevier B.V. Open access under CC BY-NC-ND license. Selection and peer review under responsibility of Information Engineering Research Institute doi:10.1016/j.ieri.2013.11.024
Md Saiful Islam et al. / IERI Procedia 4 (2013) 168 – 173
another important class of signals, known as chaotic signals, which have very irregular waveform, but it is generated by a deterministic mechanism [3]. Current marine radars show the poor performance in detecting small surface targets such as small fragments of icebergs [4]. It is very difficult to detect such targets because they appear only about a meter or so above the waterline. To perform target detection, current marine radar systems use statistical decision theory. Since sea clutter seen at a low grazing angle as well as target seen by high resolution radar does not follow the Gaussian probability density function [5], it is difficult to obtain a statistically optimal detector for this application. Besides, the identically independent distributed (i.i.d.) condition which is usually assumed in statistical radar detection is invalid. Without the i.i.d. assumption, deriving the likelihood function for detection is quite complicated [2]. Here we make detection decision using cross-correlation and recover transmitted signal using matched filter. 2. Proposed method
Figure 1: proposed method
Figure 1 indicates the following procedures: (1) Transmitting the radar signal and add noise to the transmitted signal. (2) Then the received signal is correlated to take the detection decision. (3) Using the result of cross-correlation, recover transmitted signal by the matched filter. In section II-1, we briefly explain the cross-correlation using radar transmitted signal and received signal. The matched filter is presented in Section II-2. 2.1 Cross-correlation for detection decision Correlation is the process to determine degree of ‘fit’ between two waveforms and to determine the time at which the maximum correlation coefficient or “best fit” occurs. For the radar system, if we correlate between the transmitted signal and the received signal, then we get the time difference between transmitted and received signal, which is the most challenging work. In this section, we will proof the cross-correlation for the radar system. We consider the transmitted signal be x(n), then the returned signal r(t) may be modelled as: r(n)= ĮX(n-D)+w(n) Where w(n) is assumed to be the additive noise during the transmission, Į is the attenuation factor, D is the delay which is the time taken for the signal to travel from the transmitter to the target and back to the receiver. Now the auto-correlation of the transmitted signal x (n) with itself (constant shift l) be [6]
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Md Saiful Islam et al. / IERI Procedia 4 (2013) 168 – 173 n v
Cxx(l)=
¦ r n x n l
(1)
n v
The maximum value of the auto-correlation will be at the delay time l. The cross-correlation between the transmitted signal, x (n) and the received signal, r (t) be [6] n v
Cxr(l) =
¦ r n x n l
(2)
n v n v
=
¦ >D x ( n D ) w ( n ) @>x n l @
n v
=
¦ ^Dx(n D) x(n l ) w(n) x(n l )`
Now using Equation (1) and (2) (3) Cxr(l)=Į Cxx(l-D)+ Cwx(l) Since the noise signal w (n) and the transmitted signal, x(n) are uncorrelated then, Cwx(l)=0. Therefore equation (3) will be (4) Cxr(l)=ĮCxx(l-D) Comparing the equation (4) with equation (1), the maximum value of the cross-correlation will occur at l=D, which is our interest in cross-correlation from which we can detect our target. 2.2 Noise Reduction Using Matched Filter Matched filter is not a specific type of filter, but a theoretical frame work. It is an ideal filter that processes a received signal to minimize the effect of noise. Therefore, it optimizes the signal to noise ratio (SNR) of the filtered signal. Matched filter is characterized by its impulse response, so now we want to find an expression for impulse response which will maximize this SNR. We describe the matched filter as a linear time-invariant system which has an impulse response of h(t) and frequency response H(f). The signal part of the output is [6] v
ro(t) = h(t)*r(t) = F-1{H(f)R(f)} =
³ H ( f ) R( f ) Exp( j 2St )df
v
The output power is proportional to the square of this signal amplitude. 2
v
| ro(t)|2 =
³ H ( f ) R( f ) Exp( j 2St )df
(5)
v
Now, we consider the case where the interference is white noise with power spectral density N0/2 watts per hertz. The total out power noise is then [1]
Np Now using equation (5) and (6)
No 2
2
³ H( f )
df
(6)
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Md Saiful Islam et al. / IERI Procedia 4 (2013) 168 – 173 2
v
³ H ( f ) R( f ) Exp( j 2St )df
v
SNR
N0 2
v
³ H( f )
2
(7)
df
v
The maximum SNR can be determined vai Schwarz inequality. 2
^ `^B `
³ AB d A
2
2
But this true if and only if B(ȍ)= ĮA*(ȍ), with Į any arbitrary constant. Apply this condition to equation (7), we can say the SNR is maximized when H(f)= ĮR*(f)Exp(j2ʌft), in time domain h(t)= Įr(td-t). So, the matched filter maximizes the SNR of the filtered signal and has an impulse response that is reverse timeshifted version of the input signal. 3. Simulation Results transmitted signal
only noise 4 magnitude
magnitude
1
0.5
0
0
1
2 (a)
2 0 -2 -4
3
0
x 10 received signal without noise
3000
4000
5
0.6
magnitude
magnitude
2000 (b)
received signal(echo+noise)
0.8
0.4 0.2 0
1000
-7
0
1000
2000 (c)
3000
4000
0
-5
0
1000
2000 (d)
3000
4000
Figure 2 (a) transmitted signal; (b) received signal without noise; (c) noise signal; (d) received signal (echo + noise).
For simulation purposes, the following parameters were assumed: sampling frequency=10 GHZ, pulse duration=8 ns, pulse repetition frequency=.24 GHz. The receiver receives the return from the target in the present of AWGN. Although the attenuation is too high like more than 90%, our simulation provides the exact time delay. Here we use 50% attenuation and 90% attenuation, every time we get the same time difference (Figure-3(a), 3(b)). By using this time delay, we recover our transmitted signal from the received signal using the matched filter. We also take different attenuations of the received signal and consistently get the same result except for magnitude (Figure-3(c), 3(d)).
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Md Saiful Islam et al. / IERI Procedia 4 (2013) 168 – 173 recovery signal at 50% attenuation 4
200
magnitude
magnitude
correlated signal(50% attenuation) 300
100 0 -100 -4000
-2000
0 (a)
2000
1
2
0 2000
4000
3 -7
x 10 recovery signal at 90% attenuation 0.5 magnitude
magnitude
20
0 (b)
0
(c)
40
-2000
0 -2
4000
correlated signal(90% attenuation) 60
-20 -4000
2
0
-0.5
0
1
2 (d)
3 -7
x 10
Figure 3 (a) correlated signal at 50% attenuation; (b) correlated signal at 50% attenuation; (c) recovery signal at 50% attenuation; (d) recovery signal at 50% attenuation.
4. Conclusions In this paper, detection of small marine targets (iceberg) and recovery of transmitted signal in Addition white Gaussian noise is studied and algorithms are proposed based on cross-correlation and matched filter respectively. The result of simulations indicate that algorithms are effectives even the receiver receives a very weak signal. Acknowledgement This work (Grants No C0006188) was supported by business for academic-industrial cooperative establishments funded Korea small and medium business administration in 2012. References [1] K. D. Ward, C. J. Baker, and S. Watts, “Maritime surveillance radar Part 1: Radar scattering from the ocean surface,” Proc. Inst. Elect. Eng., pt. F, vol. 137, pp. 51–62, 1990. [2] Simon Haykin, Xiao Bo Li,” Detection of Signals in Chaos”, PROCEEDINGS OF THE IEEE, VOL. 83, NO. 1, JANUARY 1995 [3] T. S. Parker and L. 0. Chua, “Chaos: a tutorial for engineers,” Proc. IEEE, vol. 75, no. 8, pp. 982-1008, Aug. 1987 [4] Wang G., Xia X.G., Root B.T., Chen V.C., Zhang Y. and Amin M. (2003) IEEE -Radar Sonar Navig, 150(4). [5] E. Jakeman and R. J. A. Tough, “Non-Gaussian models for the statistics of scattered waves,” Adv. Phys., vol. 37, pp. 471–529, 1988.
Md Saiful Islam et al. / IERI Procedia 4 (2013) 168 – 173
[6] Mark A. Richards. Fundamentals of Radar Signal Processing, 1st edition, McGraw-Hill; 2005.
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