Target detection probability of a wideband passive radar using correlation method

Target detection probability of a wideband passive radar using correlation method Dr.. When considering a wideband passive radar, target detection problem bases on the correlation te

Target detection probability of a wideband passive radar using correlation method

Dr Tran Cao Quyen

Faculty of Electronics and

Telecommunications

University of Engineering and

Technology (VNUH)

P204, G2, 144 Xuan Thuy, Cau Giay,

Ha Noi Tel: 0976753540 Email:

quyentc@vnu.edu.vn

Tiến sĩ Trần Cao Quyền

Bộ môn thông tin Vô tuyến Khoa Điện tử-Viễn thông Trường Đại học Công nghệ (ĐHQGHN) P204, G2, 144 Xuân Thuỷ, Cầu Giấy, Hà Nội

Tel: 0976753540 Email: quyentc@vnu.edu.vn

Abstract—The advantages of a passive

radar to an active radar in term of its

capability to blind enemy’s anti-radar

system was introduced in [1] When

considering a wideband passive radar,

target detection problem bases on the

correlation technique of the reflected

signal and its delay is presented in [2]

This paper investigates target detection

probability of the 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 of the proposed wideband

passive radar is compared to that of the

narrow band one

Keywords—Target target detection

probability, corrlation technique, OFDM,

wideband passive radar

Tóm tắt- Các lợi thế của radar thụ động

so với radar chủ động ở khía cạnh che

mắt hệ thống chống radar của đối phương

đã được giới thiệu ở [1] Khi xem xét một

radar thụ động dải rộng, việc phát hiện

mục tiêu dựa trên kỹ thuật tương quan

của tín hiệu phản xạ và trễ của nó được

trình bày trong [2] Bài báo này nghiên

cứu xác suất phát hiện mục tiêu của radar

thụ động băng thông rộng với giả thiết

rằng tín hiệu tán xạ từ các trạm phát

truyền hình số mặt đất và dùng kỹ thuật

tương quan ở trên Các kết quả mô phỏng

chỉ ra rằng chất lượng của radar thụ động băng rộng đề xuất so sánh được với chất lượng của radar băng hẹp cùng loại

Từ khoá- Xác suất phát hiện mục tiêu, kỹ thuật tương quan, OFDM (ghép theo tần số trực giao), radar thu động băng rộng

I INTRODUCTION

In the past, most of radar systems are active radar systems One shortcoming 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] In addition,

an ultra-wideband passive radar can applied not only in military field but also in commercial area such 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 of the transmitted signal The objective of radar processing algorithms is providing maximum SNR at the output of the processor without knowing the signal shape [2]

This paper is organized as follows Section II presents single dimension target detection probability The wideband passive

radar supporting OFDM (Orthogonal

Frequency Division Multiplexing) signal is

introduced next In section IV the simulations

are carried out We conclude the paper in

section V

II SINGLE DIMENTION TARGET DETECTION

PROBABILITY

probability

The classic detection theory is presented

in [3] The radar problem is considered as a

particular case in the detection problem The

elements of the decision theory problem are

shown in the Figure 1

Figure 1 The elements of a detection

theory problem

Source creates one output In the simplest

case the output is one of two choices We

called two choices are hypotheses and label

them as H and 0 H1

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 1

the case there is a target and H corresponds 0

to the case there is not

We assume that under H the output 1

receiver is a voltage m and under H the 0

output is a voltage 0 The output is corrupted

by AWGN noise with mean 0 and variance

2

 (having N samples)

1

0

The pdf of AWGN noise is

2 2

1

2 2

i n

x

P x





  (2) The likelihood ratio test is given by

1

2

2 2 1

2 2 1

1

2 2

( )

1

2 2

N

H i

i N

i H i

R





















Omitting the common terms and taking logarithm

1

0

2

1

2

H N

i i

H



Thus the sufficient statistic is

1

0

2

1

2

H N i i H

Nm

m



 

The probability density R under i

hypothesis H is 1

2

1

2 2

i i

p R H







The probability densityR under i

hypothesis H is 0

2

1

2 2

i i

R

p R H





  (7)

The probability densities R under i

these two hypotheses are described in the Figure 2 as follows

Source Transition Probability

Mechanism

Observation Space

1

H

Decision

Decision Rule

0

H

0  m

1 ( i| )

p R H

0 ( i| )

p R H

Figure 2 The probability densities R under i

two hypotheses

Therefore, the target detection probability

is given by

1

( | )







(8)

The false alarm probability is written by

0

( | )







(9)

III WIDEBAND PASSIVE RADAR

SUPPORTING OFDM SIGNAL

A DVB-T system’s parameters

As in [4-5] the parameters of a DVB-T

system are given in Table 1 as follows

Table 1 Main DVB-T system parameters

TOFDM(guard) 1/32

B 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 DVB-Thus, the scattered signal from a

target is OFDM signal forwarding to the

proposed passive radar

C Detection scheme

Detection scheme of the proposed passive

radar is shown in Figure 3 Firstly, the

scattered signal r t( )is delayed by T which r

is the multiple of transmitted pulse duration

 (at least one OFDM) In this case, T can r

be equal from 20 to 200 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 of the incoming signal

Figure 3 Detection using modified

correlation method

D Probability densities after the correlation process

The received signal at the front end of the 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 Noise (AWGN)

After the correlation process, the output is written by

( ) ( ) ( ) ( )

(11)

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

T r



Threshold comparing

R (T)

Decision r(t)

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( ) 12 K0( n2)

 (12)

where K is the second kind, zero order 0

Bessel function

E 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,P , is lower than that of the F

conventional correlation method In the other

hand, the dispersion is the distribution of the

deterministic signal plus noise make the

detection region,P , even become longer D

than that of the conventional approach

(Figure 4)

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 ( i| 1)

conventional case can be expressed by a

value 

probability with the false alarm level,  , is written by

1

( | )







IV SIMULATIONS Firstly, we simulate the conventional case which is fully known signal as in [1] For example we change the false alarm rate value from 103to 108 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  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 case and even it has approximately 2dB better than the fully known signal case

0  m+Δ

1 ( i| )

p R H

0

(i| )

p R H

Figure 5 Detection probabilities with

fully known signal: a) blue line is with the

false alarm probability 108 b) green line is

with the false alarm probability 6

10 c) red line is with the false alarm probability 3

Figure 6 Detection probabilities: a) the

proposed scheme with deviation 0.5 (green

line) b) the fully known signal with the false

alarm rate 108(blue line)

Figure 7 Detection probabilities: a) the

proposed scheme with deviation 0.5 (green line) b) the fully known signal with the false alarm rate 6

10 (blue line)

Figure 8 Detection probabilities: a) the

proposed scheme with deviation 0.5 (green line) b) the fully known signal with the false alarm rate 103 (blue line)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Signal to Noise Ratio-SNR(dB)

with PF=10E-8 with PF=10E-6 with PF=10e-3

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SNR(dB), False alarm rate=1E-8

the conventional correlation the proposed scheme

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

SNR(dB), False alarm rate=1E-6

the conventional correlation the proposed scheme

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

SNR(dB), False alarm rate=1E-3

the conventional correlation the proposed scheme

V CONCLUSIONS From the simulation results, it can be seen

that when 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 compared to the fully

known signal

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

REFERENCES

[1] Tran Cao Quyen et al, “ An approach for passive radar using a smart antenna system”, International conference on advanced technologies on communications (ATC08), pp.270-274, 8-9 Oct, Hanoi, Vietnam

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

[3] H L 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, 200

[5] ETSI Standard: EN 300 744 V1.5.1 , Digital Video Broadcasting Framing Structure, channel coding and modulation for digital terrestrial television