A CLUTTER SUPPRESSION ALGORITHM BASED ON OPTIMAL WAVEFORM DESIGN FOR SAR IMAGING

Bingqi Zhu, Hui Sheng, Yesheng Gao, Kaizhi Wang and Xingzhao Liu

School of Electronic Information and Electrical Engineering

Shanghai Jiao Tong University Shanghai, China

ABSTRACT

A clutter suppression algorithm for SAR imaging is proposed in this paper. The optimal waveform of the SAR system is designed according to the prior-knowledge of the target and clutter, an amplitude limiter set in frequency domain is used to suppress the clutter response and 2-dimentional pulse compression is then used to the SAR imaging. With the help of this algorithm, the SAR sensor has a strong adaptive capacity to the environment. Simulated results are presented based on our method and improvement in image is approached. Finally, the conclusions are drawn based on our analysis and simulations.

Index Terms— Optimal waveform, SAR imaging, clutter suppression, amplitude limiter

1. INTRODUCTION Synthetic aperture radar (SAR) is an active sensor that generates images to detect reflecting objects, and these images have provided wide applications in remote sensing. Most of the SAR systems employ chirp signal as transmit signal to illuminate imaging region despite of the content of the scene. However, the flat spectrum of the chirp signal has no selective effect for different objects. In fact, most of time the specific target what we want to detect is hidden in the clutter which is the prime composition of the scene, for example, tanks hidden in the forests. So we try to combine both the detection and the imaging for SAR systems.

Waveform design is a classic topic which has been investigated in many aspects of radar recently, and the goal is to learn about an object or environment by transmitting optimal waveforms while suppress both the clutter and noise signals simultaneously. Early investigations of detection in the presence of interference in space-time adaptive processing [1], and waveform design for clutter rejection [2], assumed that the clutter returns were independent, and identically Gaussian distributed. The problem of matching a known target response in a signal-dependent interference and additive channel noise was first investigated in [3], and

it was noted that traditional waveforms such as chirp signals, were inferior in SINR performance for extended targets. Earlier work in signal design for detection and identification includes the works [4] [5]. Goodman summarized and demonstrated a framework for implementation of closed-loop radar with adaptive waveforms in [6] [7]. S. Kay models the received signal in frequency domain and derives the optimum NP detector in [8] [9]. Recent work on optimal waveform design also contains [10], in which the writer consider the problem of knowledge-aided transmit signal and receive filter design for point-like targets in signal-dependent clutter.

This paper is organized as follows. Section II describes the signal model and its optimal waveform solution. An amplitude limiter is proposed to depress the clutter response in Section III, and chirp signal is then used to the SAR image formation. Section IV demonstrates the simulation experiments and conclusion is drawn in Section V.

Fig.1 The sketch of the algorithm

2. SIGNAL MODEL AND ITS OPTIMAL

WAVEFORM SOLUTION The transmit signal ( )f t excites the desired target which can be written as

( ) ( ) ( ) ( )cr t w t f t n t= ∗ + (1)

407978-1-4799-5403-2/14/$31.00 ©2014 IEEE ChinaSIP 2014

Fig.2 Model of received waveform

and the clutter is illuminated by signal simultaneously which is

( ) ( ) ( ) ( ) ( ) ( )cr t h t f t w t f t n t= ∗ + ∗ + (2)

which ( )f t is the transmitted signal with Fourier transform ( )F ω , ( )h t is the deterministic impulse response of the

target which has Fourier transform ( )H ω , ( )cw t is the Gaussian random process with power spectrum density (PSD)

( )cG ω , ( )n t is the Gaussian random process with PSD ( )nG ω , and the frequency band is assumed to be

/ 2 / 2W Wω− ≤ ≤ .

Then detection problem can be described using NP detector

0

1

: ( ) ( ) ( ) ( ): ( ) ( ) ( ) ( ) ( ) ( )

c

c

H r t w t f t n tH r t h t f t w t f t n t

= ∗ += ∗ + ∗ +

(3)

The NP detector is derived as

21

1 dD FAP P += (4)

where DP denotes the probability of detection, and FAP is a fixed false alarm rate, and 2d is given by

22/22

2/2

( ) ( )( ) ( ) ( )

W

c nW

F Hd d

G F Gω ω

ωω ω ω−

=+∫ (5)

So, the transmit signal energy spectrum density (ESD) that maximizes 2d is given by

122

2 ( ) ( ) ( )( ) max( ,0)

( )n n

optc

G H GF

Gλ ω ω ω

ωω

−−

= (6)

where λ is a constant, and is determined by the total transmit energy Ε

/22

/21

2/2 2

/2

( )

( ) ( ) ( )max( ,0)

( )

W

optW

Wn n

cW

F d

G H Gd

G

ω ω

λ ω ω ωω

ω

−

−

−

Ε =

−=

∫

∫

(7)

Fig.3 Clutter suppression process

It can be seen that under the above modeling assumptions, optimal detection performance is independent of the spectral phase of the transmit waveform, and hence there is an unlimited number of possible time domain waveforms ( )optf t that are “optimal”.

3. CLUTTER SUPPRESSION ALGORITHM FOR SAR

IMAGING Conventional SAR imaging algorithm is developed based on pulse compression of chirp signals on both range and azimuth directions, but the flat spectrum of the chirp signal has no selective effect for different objects. What we really want is to separate the target from clutter and then image the target. So, the optimal waveform design discussed above is a useful method to suppress the clutter and separate the target from it. 3.1. Details of the Clutter Suppression Algorithm Because of its basic properties of SCR maximization, we use optimal waveform to suppress the clutter. Fig.3 is the schematic figure of the clutter suppression process. In fig.3,

( )optf t is the optimal waveform that has been designed

before, and 1( )opt

f t−

is its inverse form. ( )r t is the total impulse response of the scene and can be written as

( ) ( ) ( )cr t h t w t= + (8)

K is an amplitude limiter which is designed in frequency domain and its threshold is denoted as Aσ

(9)

where ( )S f are the Fourier transform of ( )s t and

( ) ( ) ( )opts t f t r t= ∗ (10)

So the final response after optimal waveform and the

amplitude limiter is ( )r t∧

1( ) ( ) [ ( ) ( )]opt optr t f t K f t r t∧

−= ∗ ∗ (11)

'( )S f =( ), ( ) max[ ( )]AS f if S f S fσ≥

0 , ( ) max[ ( )]Aif S f S fσ<

408

As is shown in (9), the response of ( )optf t and the ( )r t in frequency domain suppresses the clutter response

while maintain most of the target response. After limited by amplitude limiter K, most of the clutter response is set to zero, and we convolute the result by 1( )optf t− , what left is almost all target impulse response which has few clutter impulse response in it. Thus, the clutter is successfully been suppressed by our optimal waveform and amplitude limiter. 3.2. SAR Imagimg After the clutter suppression process, we can move on to the SAR image process. In the range direction, the radar sends out a chirp signal, and the reflected energy at any illumination instant is a convolution of the chirp signal and

the impulse response ( )r t∧

that has been derived before, which is

20( ) ( ) [ ( ) cos(2 )]r rc t r t t f t K tω π π

∧

= ∗ + (12)

where ( )r tω is the pulse envelope function, 0f is the center frequency of the transmitted signal and rK is the FM rate of the range pulse.

In the azimuth direction, the subsequent chirp signals are transmitted and received by SAR sensor as it advances along its path. And after matched filtering in two dimensions, we can obtain the SAR image with few clutters and high SCR.

4. SIMULATION EXPERIMENT 4.1. Clutter Suppression Test We now consider the following scenario. The bandwidth is

5W = MHz, the signal pulse width is 10T us= , the signal energy is 610E = J, the noise constant is 1210− w/Hz. The clutter suppression process is shown in fig.4. In fig.4 (a), optimal waveform is designed based on target and the clutter response. Then we set an amplitude limiter and after limited by amplitude limiter (fig.4 (b), black point line), and most of the clutter response is set to close zero. We then convolute the result by 1( )optf t− , what left is almost all target impulse response which only has few clutter impulse response in it (fig.4 (c), the solid line and dotted line).

(a)

(b)

(c)

Fig.4 Clutter suppression process

4.2. Threshold Test The different values of threshold Aσ are listed in Table 1, and different target-clutter peak-to-peak powers are calculated via these threshold. As can be seen, with the increase of the threshold value, the result of

Peak PeakTar Clutter− is increase as well, from 1dB to 40dB, but at the expense of the decrease of resolution. Fig.5 shows

409

us these changes vividly, and when 0Aσ = , the point target is hidden in the clutter and cannot be distinguished correctly; when 0.2Aσ = , almost all clutter is suppressed and over 40dB improvement is gained.

Fig.5 Performances comparison of different threshold values

TABLE I. PERFORMANCES COMPARISON OF DIFFERENT Aσ

Threshold Aσ −Peak PeakTar Clutter

0 1dB

0.05 8dB

0.1 20dB

0.2 40dB

4.3. SAR Image Test We now expand the result to the SAR image formation. The target is a five-point target, and 9 targets are contained in the illuminated scene which is heavily cluttered. Fig.6 (a) shows the result using only chirp signal and filtered by matched filter, and we can see that the targets are buried in the clutter and cannot be distinguished from the clutter. Fig.6 (b) is the result after clutter suppressed by optimal waveform and 2-dimentional SAR image formation, and most of the clutter is removed and the targets can be seen correctly.

5. CONCLUSION A new method has been proposed to reduce the influence of the clutter while forming SAR images. The knowledge about the target and clutter response has been used to design optimal waveform and then an amplitude limiter is set to suppress the clutter while maintain most of the target response. Simulated results which are presented based on our method show the effectiveness of our algorithm. What's more, we should notice that the prior knowledge of the

target impulse response or the clutter impulse response is not so easily to be obtained, and feedback process might be added to our algorithm in the near future.

(a)

(b)

Fig.6 SAR image simulation before and after clutter

suppression

6. REFERENCES

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[2] M.R. Bell, "Information theory and radar waveform design," IEEE Trans. Inform. Theory, Vol. 39, pp.1578-1597, Sept. 1993.

[3] S.U. Pillai, D.C. Youla, H.S. Oh, and J.R. Guerci, "Optimum transmit-receiver design in the presence of signal-dependent interference and channel noise," IEEE Trans. Inform. Theory, Vol. 46, pp.577-584, 2000.

[4] J.R. Guerci, S.U. Pillai, "Theory and application of optimum transmit-receive radar," In Proceedings of the IEEE 2000 International Radar Conference, Washington, D.C., pp.705-710, 2000.

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[5] D.A. Garren, M.K. Osborn, A.C. Odom, J.S. Goldstein, S.U. Pillai, and J.R.Guerci, "Enhanced target detection and identification via optimised radar transmission pulse shape," Radar, Sonar and Navigation, IEE Proceedings, Vol. 148, pp.130-138, Jun. 2001.

[6] N.A. Goodman, "Closed-loop radar with adaptively matched waveforms," International Conference on Electromagnetics in Advanced Applications, Torino, pp.468-471, Sept. 2007.

[7] N.A. Goodman, P.R. Venkata, and M.A. Neifeld, "Adaptive waveform design and sequential hypothesis testing for target recognition with active sensors," IEEE Journal of Selected Topics in Signal Processing, Vol. 1, pp.105-113, Jun. 2007.

[8] S. Kay, "Optimal signal design for detection of Gaussian point targets in stationary Gaussian clutter/reverberation," IEEE Transactions on Selected Topics in Signal Processing, Vol. 1, pp.31-41, Jun. 2007.

[9] S. Kay, "Waveform design for multistatic radar detection," IEEE Transactions on Aerospace and Electronic Systems, Vol. 45, pp.1153-1166, July. 2009.

[10] A. Aubry, A. Demaio, A. Farina, and M. Wicks, "Knowledge-aided (potentially cognitive) transmit signal and receive filter design in signal-dependent clutter," IEEE Trans. Aerosp. Electron. Syst, Vol. 49, pp.93-117, Jan. 2013.

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