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 A. Single dimention target detection 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 0 H and 1 H . In a radar system, we look at a particular range and azimuth and try to decide whether a target presents or not; 1 H corresponds to the case there is a target and 0 H corresponds to the case there is not. We assume that under 1 H the output receiver is a voltage m and under 0 H the output is a voltage 0. The output is corrupted by AWGN noise with mean 0 and variance 2  (having N samples). 1 0 : 1, : 1, ii ii H r m n i N H r n i N     (1) The pdf of AWGN noise is 2 2 1 ( ) exp( ) 2 2 i n x Px    (2) The likelihood ratio test is given by 1 2 2 2 1 2 2 1 () 1 exp( ) 2 2 () 1 exp( ) 2 2 N H i i N i H i Rm R                R (3) Omitting the common terms and taking logarithm 1 0 2 22 1 ln ( ) ln 2 H N i i H m Nm R          R (4) Thus the sufficient statistic is 1 0 2 1 ( ) ln 2 H N i i H Nm lR m          R (5) The probability density i R under hypothesis 1 H is 2 1 2 () 1 ( | ) exp( ) 2 2 i i Rm p R H     (6) The probability density i R under hypothesis 0 H is 2 0 2 1 ( | ) exp( ) 2 2 i i R p R H    (7) The probability densities i R under 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 i R under two hypotheses Therefore, the target detection probability is given by 1 ( | ) Di P p R H dr     (8) The false alarm probability is written by 0 ( | ) Fi P p R H dr     (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 No of FFT 2048 TOFDM(guard) 1/32 FEC 2/3CC+RS Bandwidth 8MHz Modulation 64 QAM 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. 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 ()rt is delayed by r T which is the multiple of transmitted pulse duration  (at least one OFDM). In this case, r T can 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 ()st is the useful signal and ()nt is the Additive White Gaussian Noise (AWGN). After the correlation process, the output is written by 00 00 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) TT TT r t r t T s t s t T dt s t n t T dt n t s t T dt n t n t T dt             (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 r T  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] 0 22 1 ( ) ( ) n p n K    (12) where 0 K is the second kind, zero order 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, F P , is lower than that of the conventional correlation method. In the other hand, the dispersion is the distribution of the deterministic signal plus noise make the detection region, D P , even become longer than that of the conventional approach (Figure 4). Figure 4. The probabilities i 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 1 ( | ) i p R H to that of the conventional case can be expressed by a value  . The modified target detection probability with the false alarm level,  , is written by 1 ( | ) Di P p R H dr      (13) 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 3 10  to 8 10  . 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 8 10  b) green line is with the false alarm probability 6 10  c) red line is with the false alarm probability 3 10  . Figure 6. Detection probabilities: a) the proposed scheme with deviation 0.5 (green line) b) the fully known signal with the false alarm rate 8 10  (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 3 10  (blue line). 0 5 10 15 20 25 30 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Signal to Noise Ratio-SNR(dB) Pd-Detection Probability with PF=10E-8 with PF=10E-6 with PF=10e-3 0 5 10 15 20 25 30 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 Pd-Detection Probability the conventional correlation the proposed scheme 0 5 10 15 20 25 30 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-6 Pd-Detection Probability the conventional correlation the proposed scheme 0 5 10 15 20 25 30 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 Pd-Detection Probability 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. . 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. 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] 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