COHERENT PHASE COMPENSATION METHOD BASED ON DIRECT IF SAMPLING IN WIDEBAND RADAR

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1 Progress In Eletromagnetis Researh, Vol. 136, , 2013 COHERENT PHASE COMPENSATION METHOD BASED ON DIRECT IF SAMPLING IN WIDEBAND RADAR Qianqiang Lin, Zengping Chen *, Yue Zhang, and Jianzhi Lin Automati Target Reognition (ATR) National Defense Siene and Tehnology Key Lab, National University of Defense Tehnology, Changsha , China Abstrat In order to eliminate the negative influene of the rotational phase omponent (RPC) of target prominent sattering entres on the performane of Doppler entroid traking (DCT) method, a oherent phase ompensation method is proposed. The oherene of eho pulses sampled diretly in intermediate frequeny (IF) is firstly analyzed and proved. Based on the oherene property, the proposed approah improves the translational phase omponent (TPC) estimation auray of DCT. Compared to the modified Doppler entroid traking (MDCT) algorithm, the proposed method ahieves better phase ompensation performane with simpler operations. Both the theoretial analysis and experimental results based on the real ISAR data prove the effetiveness and effiieny of the presented strategy. 1. INTRODUCTION The inverse syntheti aperture radar (ISAR) an obtain high resolution images of moving targets by utilizing the information inherent in differential target Doppler and is greatly ontributive in target reognition [1 6]. Generally, ISAR aims at non-ooperative moving target, whose motion an be deomposed into rotational motion and translational motion. The rotational motion is benefiial to ISAR imaging whereas the existene of translational motion deteriorates the performane and must be aurately determined and ompensated [7, 8]. Therefore, translational motion ompensation is the fundamental requirement in ISAR imaging, whih an usually be Reeived 22 Deember 2012, Aepted 4 February 2013, Sheduled 4 February 2013 * Corresponding author: Zengping Chen (atrhen@163.om).

2 754 Lin et al. arried out by two steps: envelop alignment and phase ompensation. ISAR imaging raises a high demand on phase ompensation. Thus, improving the preision of phase ompensation plays an important role in improving the quality of ISAR image. So far, there have been lots of researh works fousing on phase ompensation, the researh diretions of whih generally fall into two ategories: parametri methods and non-parametri methods [9 12]. Among these numerous methods, Doppler entroid traking (DCT) [13 15] algorithm is one of the state-of-the-art methods. DCT algorithm is the optimal one based on maximum likelihood riterion and an redue the traking loss aused by sintillation and obsuring while traking the whole objet instead of whihever sattering point [14]. It also has less omputation load and is feasible to real-time imaging. However, the DCT algorithm has poor translational phase omponent (TPC) estimation auray beause of the rotational phase omponent (RPC) of target prominent sattering entres. The modified Doppler entroid traking (MDCT) [15] algorithm an eliminate the effet of the RPC on the estimation of the TPC, but the omputational omplexity aused by multi-time iteration makes the MDCT method hard to be applied in real systems. With the development of analog-to-digital onverter (ADC), diret intermediate frequeny (IF) sampling for wideband radar beomes realisti and is widely employed in engineering [16]. Compared to STRETCH proessing [17, 18], diret IF sampling raises a high demand on sampling frequeny. It also brings obvious advantages, one of whih is the oherene of eho pulses. By adopting this oherent property, a oherent phase ompensation method is developed in this paper, whih eliminates the negative influene of the RPC on the estimation auray of the TPC and improves the quality of ISAR image with simpler operations. The remainder of this paper is organized as follows. In Setion 2, the DCT algorithm is briefly introdued, as well as its limitation. Further, we analyzed the oherene of eho pulses sampled diretly in IF, and plae an emphasis on oherent phase ompensation method in Setion 3. Experimental results and performane analysis are reported in Setion 4 and Setion 5 onludes the paper. 2. DCT ALGORITHM AND ITS LIMITATION DCT algorithm is the embodiment of target entroid traking method first proposed by Prikett [19]. It traks the target entroid and fores the average Doppler to be zero. Its onrete implementation steps an be desribed as follows: After envelope alignment, the weighted mean

3 Progress In Eletromagnetis Researh, Vol. 136, of the omplex exponential funtion of adjaent eho phase differene on weighted amplitude is alulated. In other words, the omplex exponential funtion of Doppler entroid phase differene is obtained as follows [15]: exp [j ζ(m)] = / N N s m,ns m+1,n s m,ns m+1,n (1) n=1 where m = 1, 2,... is the frame number, s m,n and s m+1,n are the sub-ehoes of range ell n in the adjaent ehoes (Frame m and Frame m + 1), ζ(m) stands for the TPC indued by envelope motion. The phase ompensation is aomplished by alibrating the phase of all range ells via this funtion. However, the RPC of target motion may redue the TPC estimation auray and deteriorates the ompensation performane of DCT method mentioned above. In [15], based on irular shifting, windowing and iteration steps, the authors proposed the MDCT method whih applies the phase gradient autofous (PGA) [20, 21] algorithm to solve this problem. Unfortunately, it needs 8 to 10 times of iteration to ahieve good ompensation performane, whih result in huge omputation load and make this method hard to be applied in real systems. 3. PHASE COMPENSATION METHOD BASED ON THE COHERENCE OF ECHO PULSES Most of modern radars utilize not only the amplitude, but also the phase and frequeny information for their main funtions. Thus, radar oherene plays a more and more important role in the system performane. However, the oherene of eho pulses is usually destroyed in STRETCH proessing. With the development of ADC, ultra-high speed diret IF sampling for wideband radar is no longer an inextriable problem and is employed widely in engineering. Diret IF sampling is the preondition for maintaining the oherene in pulse ompression radar Coherene of Diret IF Sampling The linear frequeny modulation (LFM) signal transmitted by radar an be expressed as ( ) [ t s(t) = ret exp j2π (f t + 12 )] γt2 (2) T t n=1

4 756 Lin et al. where T t is the pulse duration, f the arrier frequeny, t time variable, and γ the hirp rate. It is assumed that the amplitude of the LFM signal is 1 for the onveniene of analyzing. Using R i as the distane between the target and radar, the target eho return s r (t) an be written as ( t 2Ri / s r (t)=ret T t ) exp { ( j2π [f t 2R ) i + 12 ( γ t 2R ) ]} 2 i where is the veloity of light. After mixing proessing, the eho return is onverted down to IF signal s I (t). s I (t) ( ) { t 2Ri / = ret exp( j4πf R i /) exp j2π [f I t+ 12 ]} γ(t 2R i/) 2 (4) T t where f I stands for the entre frequeny of IF eho signal. Then the baseband signal s B (t) an be written as ( ) t 2Ri / s B (t) = ret exp( j4πf R i /) exp [ jπγ(t 2R i /) 2] (5) T t Aording to the stationary phase priniple, we obtain the frequeny domain expression of s B (t) from (5). S B (ω) = 1 ( ) [ ω ret exp j ( ω2 γ 2πγT t 4πγ + π )] ( exp j 2R ) ( iω exp j 4πf ) R i (6) 4 The mathed filter of signal expressed by (6) an be written as H(ω) = 1 ( ) [ ω ret exp j ( ω2 γ 2πγT t 4πγ + π )] 4 So the output signal of the mathed filter an be expressed as s p (t) = s B (t) h(t) = 1 2π = 1 ( 2πγ exp j 4πf R i = T t 2 exp is ( j 4πf R i + ) + S B (ω)h(ω) exp(jωt)dω ) sin ( ) ( ω ret exp 2πγT t ( [πγt t t 2R )] i j 2R iω (3) (7) ) exp(jωt)dω We an see from (8) that the phase of signal after mathed filtering (8) φ d = 4πf R i / (9)

5 Progress In Eletromagnetis Researh, Vol. 136, In (9), φ d is related to R i only and hanges when hanges take plae in R i. That means the eho phase keeps a strit and stable relationship with the phase of transmitted signal. In other words, the eho pulses are oherent. For STRETCH proessing, the target eho signal an be expressed in frequeny domain as [22]: ( S p (f i ) = T t sin [T t f i + 2 γ )] R exp( j4πf R /) exp [ j4πf i R /] exp ( j4πγr 2 / 2) (10) where R = R i R ref, R ref is the referene distane. The seond exponential term in (10) is residual video phase (RVP) term, and the third exponential term is the envelop sideling term when R 0. This two exponential phase term an be eliminated by phase ompensation at the envelope peak point where f i = 2 γ R [17]. The first phase term is the eho phase brought by translational motion: φ d = 4πf R / = 4π f (R i R ref ) (11) As shown in (11), the phase of STRETCH proessing eho pulse is related to the radial distane R i of target and the referene distane R ref. R ref is losely related to the time-delay of the narrowband eho, whih is not preise enough. Thus, the phase term in (11) an not be obtained preisely and finally indues the inoherene of eho returns of STRETCH proessing Coherent Phase Compensation Method Equation (8) shows that, for the 1-D range profile of mathed filtering based on diret IF sampling, phase ompensation means to eliminate the exponential term exp( j4πf R i /) whih truly reflets the phase variation indued by translational motion of the target. Even though there may be aelerated motion during observation, the phase transformation urve aused by motion should be ontinuous and smooth beause of the inertial of the target. The non-ideal fators suh as system distortion and radio propagation path an just superimpose little ripple on the smooth urve. STRETCH proessing destroys the oherene of eho pulses and does not have this property. By employing DCT method, Fig. 1 shows the phase differene urves of adjaent eho pulses ahieved by diret IF sampling and STRETCH proessing respetively in a phased array radar. We an see from Fig. 1(a) that the phase differene urve of adjaent return ehoes sampled diretly in IF is ontinuous and approximately smooth. The little ripple is indued by the non-ideal

6 758 Lin et al. (a) Figure 1. Phase differene urves of adjaent eho pulses ahieved by diret IF sampling and STRETCH proessing. (a) Diret IF sampling. (b) STRETCH proessing. fators suh as system distortion and radio propagation path. Also we an find from the figure that the phase differene has an inreasing trend whih indiates the aelerated motion of the target. For the return ehoes reeived by STRETCH proessing, its phase differene urve shown in Fig. 1(b) undulates tempestuously and annot reflet the motion states of the target. This is due to the oherene destroying by STRETCH proessing. Based on the oherene of diret IF sampling, we an smooth the phase differene urve and eliminate the phase error using the least squares urve fitting method. Then we ahieve the aurate phase differene urve and an improve the phase ompensation effet. The onrete steps of the algorithm are shown bellow. 1. Ahieving the omplex exponential funtion of Doppler entroid phase differene shown in (1) using DCT method, so we an obtain the phase differene urve of adjaent return ehoes (urve of ζ(m)); 2. Implementing the urve fitting using the least squares urve fitting method, we obtain the aurate phase differene funtion ζ (m); 3. Reonstrut the phase ompensation exponential funtion C(m) using ζ (m). C(m) an be expressed as C(m) = exp ( j m 1 m=1 ζ (m) ) (b) (12) 4. Aomplish the phase ompensation by multiplying the 1-D range profile data with the orresponding C(m).

7 Progress In Eletromagnetis Researh, Vol. 136, As an be seen from the steps above, the algorithm proposed in this paper is on the basis of DCT method, and improves the TPC estimation auray using only one time of urve fitting. In Step 2, it is important to hoose a proper polynomial order when using urve fitting. Numerous experiments show that, in order to reflet the atual phase hanges indued by motion of the targets as muh as possible, the polynomial order should be set to EXPERIMENTAL VERIFICATION AND ANALYSIS 4.1. Algorithm Verifiation In order to verify the algorithm presented above, the performane of phase ompensation employing the proposed method is ompared with that of unmodified DCT method in this setion. Airraft eho data sampled by experimental phased array radar is adopted. Fig. 2 shows the phase differene urve after urve fitting using the least squares urve fitting method, while Fig. 3 shows the differene between pre- and post urve fitting. As shown in Fig. 2, the phase differene urve tallies with the motion states of the target. Meanwhile, urve in Fig. 3 indiates that there are errors between the phase estimated by DCT method and that indued by target motion. The differene, whih is just the negative influenes of the RPC and other system fators on the TPC estimation auray, lies within the sope of ±0.6 radian. ISAR imaging is proessed after phase ompensation whih uses the phase differene funtion ahieved by the least squares urve fitting method. Fig. 4(a) shows the ISAR imaging results obtained by using unmodified DCT method, while Fig. 4(b) are the ISAR images obtained by adopting the MDCT method and Fig. 4() via the oherent Figure 2. Post fitting phase differene urve. Figure 3. Differene between pre- and post fitting.

8 760 Lin et al. (a) (b) Figure 4. ISAR imaging results via unmodified (a) DCT method, (b) MDCT method and () method presented in this paper. phase ompensation algorithm proposed in this paper. It an be seen from the figures that, the image fousing quality of Fig. 4() are better than that of Fig. 4(a) and Fig. 4(b). Thus the method proposed in this paper is effetive Performane Analysis The performane of phase ompensation diretly affets the quality of ISAR image whih an be quantitatively evaluated by image entropy [23 25]. Therefore, image entropy is adopted for the ()

9 Progress In Eletromagnetis Researh, Vol. 136, Table 1. The ISAR image entropy of Fig. 4. Phase ompensation method ISAR image entropy (1) (2) (3) Unmodified DCT method (Fig. 4(a)) MDCT method (Fig. 4(b)) Method proposed in this paper (Fig. 4()) performane evaluation of phase ompensation in this setion. On the basis of the same algorithms for other proessing (suh as distortion ompensation, envelope alignment, image reonstrution, et al.), the better phase ompensation performane, the higher image quality and lower image entropy, and vie versa. The ISAR image entropy of Fig. 4 are obtained and shown in Table 1. (Coherent envelope alignment method [26] and RD imaging method are adopted for envelope alignment and image reonstrution respetively.) As shown in Table 1, the ISAR images obtained by adopting the unmodified DCT method have the highest image entropy, while the ISAR images obtained by using the algorithm proposed in this paper have the lowest entropy. This indiates that the phase ompensation method proposed in this paper has the best performane. It is assumed that the frame ount of ehoes used for one ISAR image is M, and the sample number of one frame eho is N. Aording to the steps of MDCT algorithm desribed in [10], we an obtain the total omputation load of the MDCT algorithm. That is 9(M 1)(8N + 2M) + 34NM log 2 M + 24NM times of multipliations with 9(M 1)(5N + 1.5M 1) NM log 2 M + 16(N M 1) times of additions. In the same way, the total omputation load of the method proposed in this paper is obtained, whih is (M 1)(8N + 2M + 42) + 2NM log 2 M times of multipliations with (M 1)(5N + 1.5M + 21) + 2.5NM log 2 M + 18 times of additions. In Setion 4.1, the sample number of one frame eho is And 512 frames of ehoes are used for one ISAR image. Then aording to the analysis aforementioned, the omputation loads of the MDCT method and strategy proposed in this paper are obtained and shown in Table 2. We an see from the table that the omputation load of MDCT method is about 16 times as muh as that of the method proposed in this paper. In a word, ompared with the MDCT method, our method improves the unmodified DCT method and ahieves better performane of phase ompensation with simpler operations.

10 762 Lin et al. Table 2. The omputation loads of MDCT method and the method proposed in this paper (the approximate value). Phase ompensation method multipliation (times) addition (times) MDCT method Method proposed in this paper CONCLUSIONS The oherene plays a more and more important role in radar system performane. In this paper, the oherene of eho pulses sampled diretly in IF is proved. The signal model of eho pulses is presented. And the mathematial formula for the oherene of eho pulses is derived. By omparing the phase differene urves of eho pulses sampled diretly in IF with that of STRETCH proessing, the validity of this theoretial analysis is onfirmed. Based on the oherene property, a oherent phase ompensation algorithm is proposed in this paper. Compared to MDCT method, the proposed algorithm improves the TPC estimation auray and ahieves better ISAR image quality with less omputation load. The experimental results based on the real ISAR data show that the proposed strategy is an effetive and effiient phase ompensation method. ACKNOWLEDGMENT This work was supported by the National Natural Siene Foundation of China (No ). The authors would like to thank the anonymous reviewers and the editors for improving the manusript. REFERENCES 1. Park, S. H., J. H. Lee, and K. T. Kim, Performane analysis of the senario-based onstrution method for real target ISAR reognition, Progress In Eletromagnetis Researh, Vol. 128, , Kaya A. and M. Kartal, Point satterer model for RCS predition using ISAR measurements, Proeedings of 4th International Conferene on Reent Advanes in Spae Tehnologies, , Park, J. I. and K. T. Kim, A omparative study on ISAR imaging algorithms for radar target identifiation, Progress In Eletromagnetis Researh, Vol. 108, , 2010.

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