XAC SUAT PHAT HIEN MUC TIEU

SCIENCETECHNOLOGYl

XAC SUAT PHAT HIEN MUC TIEU CUA RADAR THU DONG BANG RONG DUNG PHl/ONG PHAP TI/0NG QUAN

TARGET DETECTION PROBABILITY OF A WIDEBAND PASSIVE RADAR USING CORRELATION METHOD

Tran Cao Quyen

Tom t i t

Cac I d the cua radar thu dong so vdi radar chu dgng is khi'a canh che mat he thong chong radar cOa doi phucmg da daac gidi thieu Is [ l ] . Khi xem xet mgt radarthu ddng d^i rong, viec phat hien muc tieu dua tren ky thuat tuong quan cua tin hieu phan xa va tre cua no di/gc trinh bay troi^g [2]. Bai bao nghien c i ^ xac suat phat hien muc tieu cOa radarthu dgng bang thong rong vdi gia thlet rang tin hieu tan xa til cac tram phat truyen hinh sd mat dat va diing ky thuat tuang quan d tren. Cac ket qua mo phong chi ra rang chat li/gng cila radar thu dong bang rdng de xuat so sanh dUflc vdi chSt lugng cilia radar bang hep cung loai.

Ttf khoa: Xac suat phat hidn muc tieu, ky thuat tumig quan, OFDM Ighep theo tan so true giao), radarthu dpng bang rong.

Abstract

The advantages of a passive radar to an active radar in term of its capability to blind enemy's anti-radar system wasintroduced in [1], When considering a wideband passive radar, target detection pmblem bases on the correlation technique ofthe reflected signal and its delay is presented in [2J.This paper investigates target detection probability ofthe wideband passive radar with assumption that the scattered signal coming from DVB-T (Digital Video Broadcasting-Terrestrial) stations and using the above correlation technique. The simulation results show that the performance ofthe proposed wideband passive radar is comparable to that ofthe narrow band one.

Keywords: Target detection probability, corrlation technique, OFDM, wideband passive radar.

TS-Tran Cao Quyen

Khoa flien tii-Viin thong,TrUifng 6H Cong nghe, flHQGHN Email. quyentc@vnii.edii.vn

1. INTRODUCTION

Inthepast, most of racJar systems are active radar systems. One shorteoming of an active radar is that the enemy can find its location by its transmitted sequence. Therefore, a passive radar becomes a high priority in term of its safety [1].lnaddition,an ultra-wideband passive radar can applied not only in military field but also in commercial

Ngaynhanbai: 14/01/2014 Ngay chap nhan ffang: 21/03/2014

area sueh as in transportation, income tax management, medical imaging, all weather sensing and communication over short ranges, etc [2]. The principle which is already presented in [1] for a narrow band passive radar should be investigated for a wideband system.

With a wideband radar signal, there is a change not only in its parameters but also in its shape at signal processing

stage. As a result, the signal shape at the input of the processor is different to the shape ofthe transmitted signal.

The objective of radar processing algorithms is providing maximum SNF^

at the output of the processor without knowing the signal shape [2].

This paper is organized as follows.

Section 2 presents single dimension target detection probability. The wideband passive radar supporting OFDM (Orthogonal Frequency Division Multiplexing) signal is introduced next.

In section 4 the simulations are carried out We conclude the paper in section 5 2. SINGLE DIMENTION TARGET DETECTION PROBABILITY

The classic detection theory is presented in [3]. The radar problem is considered as a particular ease in the detection problem. The elements of the decision theory problem are shown in the Figure 1.

Source creates one output. In the simplest ease the output is one of two choices. We called two choices are hypotheses and label them as H^ and H,.

in a radar system, we look at a particular range and azimuth and try to decide whether a target presents or not; H, corresponds to the case there is a target and H^, corresponds to the ease there is not.

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Transition Probabihty Mechanism

Figure 1. The elements of a detection theory problem Figure 2. The probability densities R^ under two hypotheses

We assume that under H, the output receiver is a voltage m and under H^

the output is a voltage 0. The output is corrupted by AWGN noise with mean 0 and variance o^ (having N samples).

H,:r=m-i-n, i-1,...N Ho:r, =n, = 1,... (1) The pdf of AWGN noise is:

P.W = - i = - e x p ( - ^ ) V2Tta 2 0 '

A(R)

The likelihood ratio test is given by:

A 1 , (R,-m)' „ 2 g ' > , ,.fV2iia 2<j'

T|(3)

Omitting the common terms and taking iogarithm:

. . , . , . m ^ „ Nm^ > . lnA(R) = - - - y R , r Inii (4)

a ^ 2o <

Thus the sul^cient statistic is:

I(R) = £ R , > a , Nm

— I n i i + — - = r

< m 2 (5)

The probability density R^ under hypothesis H^ is:

(R,-m)' 2 o ' (6) The probability density R^ under hypothesis H^^ is:

p(RJH,) = - = ^ e x p ( ~ V27rCT

PW,|H,) = ^ = = - e x p ( - e y ) V27[a 2a (7) The probability densities R under

these two hypotheses are described in the Figure 2 as follows.

Therefore, the target detection probability is given by:

PD-jp(R,|H,)dr (8)

The false alarm probability is written by:

(2) pF=jp(R,|HJdr

(9)

3 . W I D E B A N D P A S S I V E R A D A R S U P P O R T I N G O F D M S I G N A L

3 . 1 . D V B - T s y s t e m ' s p a r a m e t e r s As i n [ 4 - 5 ] t h e p a r a m e t e r s o f a D V B - T s y s t e m a r e g i v e n i n T a b l e 1 as f o l l o w s

Table 1. Main DVB-T system parameters NoofFFT

TDFDM (guard) FEC Bandwidth Modulation

2048 1/32 2/3CC+RS 8MHz

64 AM

p a s s i v e r a d a r is s h o w n i n F i g u r e 3. Firstly, t h e s c a t t e r e d s i g n a l r{t) is d e l a y e d b y l which is the multiple of transmitted pulse duration T (at least one OFDM).

In this case, T can be equal from 20r to 200T. Then the scattered signal is correlated with its delay. Next the output of the correlator is integrated and compared to a threshold level to make a decision whether a target present or not. As far as correlation concerned, the only different to the conventional correlation method is that the reference signal in this case is delay version ofthe incoming signal.

m

TJ

3.2. Wideband passive radar supporting OFDM signal

In Vietnam, there are many DVB-T stations placing all over the country from the North to the South. When a plane (target) flies into the country's airspace region it comes into the coverage of the above DVB-T stations.

Thus, the scattered signal from a target is OFDM signal forwarding to the proposed passive radar.

3.3. Detection scheme Detection scheme o f t h e proposed

J

^Rm

^{> )}

Threshold

''

companng

, i 1

^Decision

Figure 3. Detection using modified correlation method

3.4. Probability densities after the correlation process

The received signal at the front end o f t h e passive radar in white bandpass noise is given by:

r(t) = s(t) + n{t) (10}

where s(t) is the useful signal and n(t) is the Additive White Gaussian

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SCIENCETECHNOLOGYl

Noise (AWGN). distribution of the deterministic signal After the correlation process, the plus noise maite the detection region, output is written by: p^ even become longer than that of r I the conventional approach r ( t ) ® r ( t - T ) ^ | s ( t ) s ( t - T ) d t - . J s ( t ) n ( t - T ) d t + (ngure4).

in(t)s(t - T)dt -i-jn(t)n(t - T ) d t The different with the conventional method are the third and the fourth term in (11 ).The third term represents a product of OFDM signal with Gaussian noise then it accumulates a deviation to the total probability density distribution (signal plus noise).

The fourth term is a product of Gaussian noises and thus its distribution become a Bessel function as in [2]:

p(n) = AK.(4)

⁽¹²⁾

where K^ is the second kind, zero order Bessel function.

3.5. The target detection probability of the proposed radar

With the above described correlation method, the noise distribution becomes narrower than the single Gaussian noise; the institution meaning is that the false alarm rate, Pp is lower than that o f t h e conventional correlation method. In the other hand, the dispersion is the

Figure 4. The probabilities R under two hypotheses for the modified correlation method

Assuming that the threshold level is maintained in both cases. Thus, the deviation of the mean of p(R/H,) to that of the conventional case can be expressed by a value A.

The modified target detection probability with the false alarm level, y, is written by:

P D - Jp(R,|H,)dr (13)

4. SIMULATIONS

Firstly, wesimulate the conventional case which is fully known signal as in [1]. For example we change the false alarm rate value from 10"^ to 101 As results, the detection probabilities depending on the SNR at each given false alarm probability are depicted in Figure 5. From the figure, we easily

find out that lower the false alarm rate required more SNR at a certain target detection probability.

Secondly, we compare the performance of the conventional correlation method with the modified correlation method. We use (8) and (13). In this simulation, the normal distribution with error function (erfc) in MATLAB is used. Thus the standard deviation is 1 and the value A = 0,5.

Many simulations on detection probabilities are performed (Figure 6 to Figure 8) with different false alarm rates. The important thing is that in all cases the performance of the target detection probability of proposed scheme is compared to the conventional ease and even it has approximately 2dB better than the fully known signal ease.

5 . C O N C L U S I O N S

From the simulation results, it can beseenthatwhen using the correlation of the reflected signal with its delay and using the transmitted signal from DVB-T broadcasting stations the passive radar can deal with wideband signals. Moreover, the performance of the detected probability of the proposed scheme is comparable to the fully known signal. In view of the target detection probability the merit of 2dB is achieved.

Figure 5. Detection probabilities with fully known signal a) solid line Is with the false alarm probability 10^

b) solid-dot line is with the false alarm probability 10-^

c) solid-drde line is with the false alarm probability 10'

Figure 6. Detection probabilities

a) the proposed scheme with deviation 0,5 (solid-dot line)

b) the fully known signal with the false alarm rate lO'(solidline)

Figure 7. Detection probabilities a) the proposed scheme with deviation 0,5 (solid-dot line)

b) the fully known signal with the false alarm rate 10"'(solid line)

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Acknowledgement

The author would like to thank for the Faculty of Electronics and Telecommunications, University of Engineering and Technology (Viet Nam National University, Hanoi), This paper is completed with partially supported from the project No CN.13,03.

Phan bien khoa hoc: TS. Duflinh Vien

Figure 8. Detection probabilities

a) the proposed scheme with deviation 0,5 (solid-dot line)

b) the fully known signal with the false alarm rate 10-* (solid line).

REFERENCES

[1]. Tran Cao Quyen et al, "An approach for passive radar using a smart antenna system",

International conference on advanced technologlB on communications (ATC08), pp 270-274, 8-9 Oct, Hanoi, Vietnam.

[2]. T D. Taylor, Ultra-Wideband Rada Technology, CRC Press, 2001.

[3]. H. I. Van Trees, Detection, Estimation and Modulation, Vol 3, John Wileys and Sons Inc, 1971.

[4]. R. V. Nees and R. Prasad, OFDM for Wireless Multimedia Communications, Artech House, London, 2000.

[5]. ETSl Standard: EN 300 744 V1.S.1, Digital Video Broadcasting Framing Structure, channel coding and modulation for digital terrestrial television.

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