Time Reversal Synthetic Aperture Radar Imaging In Multipath

Transcription

1 Time Reversal Syntheti Aperture Radar Imaging In Multipath Yuanwei Jin, José M.F. Moura, and Niholas O Donoughue Eletrial and Computer Engineering Carnegie Mellon University Pittsburgh, PA 1513 Mihael T. Mulford and Alphonso A. Samuel Raytheon Missile Systems Tuson, AZ Abstrat Conventional spotlight Syntheti Aperture Radar (SAR) assumes a single refletion of transmitted waveforms from targets [1]. Multiple refletions of targets due to surrounding satterers appear as ghosting artifats in onventional SAR images, whih obsures true target image and leads to poor resolution. In this paper, we develop image formation tehniques using time reversal, Time Reversal SAR (TR- SAR), to remove ghosting artifats and ahieve high resolution. The TR-SAR algorithm is tested using phase history data olleted by a rail-mounted SAR sensor operated by Raytheon. 1 Introdution Many data adaptive high resolution approahes to syntheti-aperture radar (SAR) image reonstrution have been developed [, 3]. Our work is onerned with the exploitation of time reversal in spotlight syntheti aperture radar imaging in multipath rih environments. For targets in a rih sattering environment, onventional SAR results in ghosting artifats due to multiple bounes by surrounding satterers. To ounter this, we develop time reversal SAR algorithms to proess phase history data in rih multipath sattering. The ultimate goal of TR-SAR is to improve automated target reognition and to aid image analysts in identifying targets in dense multipath. We developed the TR-SAR algorithm in [4] for target fousing and ghost image removal. We show in [4], how, from a rough estimate of the target loation obtained from a onventional SAR image and using time reversal, TR-SAR fouses on the target with improved resolution, and redues or removes ghost images. TR-SAR uses two-pass olletions to perform a sensitive form of hange detetion deteting targets by using two SAR images that apture the same This work is funded by the Defene Advaned Researh Projets Ageny through the Army Researh Offie under grant no. W911NF syntheti aperture ground path Figure 1. Spotlight SAR imaging geometry. sene. In this paper, we fous on TR-SAR algorithms for linear frequeny modulated (LFM) hirp signals. For a SAR radar that uses LFM hirp signals, radar returns undergo streth proessing and IF sampling to obtain the phase history data. Streth proessing, a ommonly used tehnique for pulse ompression in radar, enables narrowband sampling for wideband waveforms and onverts range (i.e., fast time) into the spatial frequeny domain [5, 6]. We verify the proposed imaging algorithms suessfully using eletromagneti experimental data olleted by a rail-mounted SAR sensor at Raytheon in a rih sattering environment. Mathematial Desription of TR-SAR For illustration purposes, we use the mono-stati onfiguration shown in Fig. 1, where a SAR sensor images the ground path at range x and ross range y. For the SAR imaging platform at height h, ψ and θ are the depression angle and the squint angle, respetively; The symbols W r and W a denote the range swath and the azimuth swath, respetively. Next, we desribe the time reversal signal model in streth proessing.

2 .1 Time Reversal in Streth Proessing Linear frequeny modulated hirp signals take the form of s(t) = os ( πf t + πγt ), t / (1) where γ is the hirp rate in units of radian/se, is the waveform duration, and f is the arrier frequeny. The radar transmits a sequene of suh LFM signals with an interpulse period of T. The pulse repetition frequeny PRF is 1/T. These pulses have the form of Rs(n, t)}, where the omplex exponential form of the transmitted signal an be written as follows [1]: t nt s(n, t) = ret e j[πf t+πγ(t nt ) ]. () The quantity n is the pulse number; n = 0 represents the first transmitted pulse. Let = t nt denote the time within a signal reeived from a speifi transmitted pulse and referened to the time of pulse generation. The funtion ret(u) = 1 for u 1 is the retangular window funtion. The illuminating signal s(t) is emitted from the transmit antenna, propagates to the target sene, and is refleted bak to the reeive antenna. The reeived signal from a single point target an be written as s r (n, ) = A t ret e j[πf (t τ)+πγ(e t τ) ], (3) where A t is the target refletivity and τ is the round-trip propagation delay. Next, the SAR we use employs streth proessing for pulse ompression. Streth proessing is ommonly used in high resolution radar and target reognition [5, 6]. Streth proessing has two basi features: (1) it enables the use of wideband waveform with narrowband proessing. For example, for the rail-sar system we use, the sampling rate is 300 MHz while the hirp signals have 1 GHz bandwidth; () it onverts range into spatial frequeny. This is beause the reeived signal is mixed with a referene signal that has the same hirp rate as the transmitted waveform. Given the referene range R 0, i.e., the distane between the antenna phase enter to the target sene enter, the referene signal is s ref (n, ) = e j[πf(t R 0 )+πγ( e t R 0 ) ]. (4) The target returns are translated into tones by taking the differene frequeny out of the mixer. The frequeny of the tones denotes the ranges to the targets. The mixing operation results in a pulse ompressed signal s (n, ) = s r (n, )s ref(n, t) (5) = A t ret e jπ[f R +γ(e t 0 )] (R t R 0 ) }} phase term e j4πγ (R t R 0 ) } } RVP. (6) The residual video phase (RVP) is an unwanted artifat arising from the range dehirping proess and an be removed [1]. Ideally, the referene range R 0 = R 0 (nt ) is the exat range from the antenna phase enter to the seleted sene enter at eah pulse transmission time. In real SAR imaging systems, R 0 is not preisely equal to the round trip propagation time to the enter of the ground path. Thus, post-proessing tehniques, suh as autofous, or automati phase-error orretion, are employed [7]. For simpliity, in what follows, we ignore the quadrati phase term. Thus, we have s (n, ) = A t ret e jπ[f+γ( e R t 0 )] (R t R 0 ). where the ommon time window is given by + W r t nt R 0 (7) W r. (8) Furthermore, the phase term in (7) an be deomposed as a produt of the instantaneous spatial frequeny U n = 4 π(f + γ( R 0 )) and the range distane (R t R 0 ). By (8), the spatial frequeny (9) an be written as 4π (f + γ( + W r )) U n 4π (f + γ( W r )) with the spatial frequeny bandwidth (m 1 ) given by (9) B U = γ ( W r ) = (B B IF )/ B /. (10) The approximation is due to B B IF for pratial SAR systems using streth proessing. Closely examining (7) reveals that = e jπ(f R +γ(e t 0 )) (R t R 0 ) = e ju n(r t R 0 ) δ(u(n, ) (R t R 0 ))e juu n du = F u δ(u(n, ) (R t R 0 )) }. (11) It is well known that time reversal in the time domain is equivalent to phase onjugation in the frequeny domain. In our ase, time reversal of the demodulated signal an be treated as phase onjugation in the spatial frequeny domain. Use of linear FM hirp and streth proessing translates the pulse ompressed signal into Fourier transform in range (spatial) domain. Thus, range is onverted into spatial frequeny. As a result, phase onjugation an be applied diretly to the pulse ompressed signal. The time-reversed dehirped signal (after removing RVP) an be written as [s (n, )] = A t ret e ju n(r t R 0 ) (1)

3 with the target response filter A t e jun(rt R0) ( onfined et within the window speified by ret ). This observation enables a simple implementation of time reversal in SAR with streth proessing. The hirp signal will not be involved in the subsequent mathematial time-reversal transmission. Next, we disuss the TR-SAR proessing.. TR-SAR Desription The proposed spotlight mode TR-SAR onsists of four major steps: (1) Clutter probing; () Target probing; (3) Time reversal; (4) Multi-look averaging and TR-SAR image formation. Step-1: Clutter probing This is the first step in a two-pass data olletion proess. The target is not present. A LFM hirp signal is sent to probe the lutter environment. We then reord the phase history data as the referene data. Step-: Target probing This is the seond step in the twopass data olletion proess. The target is now present. A LFM hirp signal is sent to probe the target environment, whih results in the test data. The signal returns reorded in the first step will be subtrated out from this step. The subtration proedure will remove the strong refletions from dominant satterers in the viinity of the target. In a multipath rih environment, the ompressed return signal is the superposition of the diret path from the target and the multiple refletion due to the surrounding satterers, whih takes the form of L 1 s (n, ) = ret A l e ju n(r tl R 0 ), (13) where A l is the refletivity for eah refletion; R tl is the nominal slant range for eah refletion given by R tl (n, t) = [ (x l x a (n, t)) + (y l y a (n, t)) + (z l z a (n, t)) ] 1/ (14) where (x 0, y 0, z 0 ) is the (diret path) target loation; (x l, y l, z l ), l = 1,, L 1 are the oordinates of eah multipath refletion. x a (n, t), y a (n, t), and z a (n, t) denotes the antenna position at pulse n and time t in range, ross range, and elevation, respetively. Next, we onstrut the target impulse response funtion (IPR) based on the initial target range estimation s 0 (n, ) = ret  0 e ju n(b Rt0 R 0 ) (15) where Â0 and R t0 is the refletivity and the distane of the estimated target to be foused on. The estimation requires the multilook proessing disussed in setion.3. In pratie, the antenna moves along the trak ontinuously. For simpliity, we make assume that the antenna is stationary during pulse transmission and reeption while moving in disrete inrements between pulses. For SAR, the measurement data are olleted via a platform that arries the radar. Suppose that the speed of this platform is v, the slow-time interval between suessive radar transmissions is the pulse repetition interval (PRI) (pulse repetition frequeny or PRF is 1/T ) T = y v, where y is the distane that the radar travels during eah transmission. In a pratial radar system, the PRF is usually small. For example, the rail-sar system at Raytheon has PRF = 8 Hz, and v = 6 m/se. Hene, y = 0.75 m. This implies that the position of the antenna at eah pulse an be written as x a (n, t) = x a (n) = v PRF (n+n o), n = 0,, N 1 (16) where n o is an offset and needs to be determined by alibration. We further assume that all targets are in the ground plane with z t = 0. Thus, the range term takes the form of R t0 (n, t) = ( x t (n + n o )vt ) + ŷt + (R sinψ) (17) Step-3: time reversal In the time reversal step, the return signal is time-reversed, phase onjugated, and energy normalized. Let µ(n) be the energy normalization fator for eah pulse, thus, the time-reversed signal beomes L 1 s tr (n, ) = µ(n)ret A l e ju n(r tl R 0 ). (18) The returned signal of this re-transmitted signal beomes ( s tr r(n, ) = ret ) L 1 µ(n) A l e jun(rt l R0). (19) Step-4: TR-SAR proessing The TR-SAR proessing is onfined to a seleted window illustrated in Fig. 3. The image is proessed in small image hips. We use windowing to remove the interferene aused by very strong refletors, for instane, trihedral orner refletors, and to loalize the multipath refletion in the region of interest (ROI). The seleted image hip undergoes the windowed inverse Fourier transform to extrat the signal for subsequent time reversal proessing. By mathing the returned time-reversed signal by the estimated target impulse response filter, we obtain the following data for image reonstrution: x re (n, ) = s tr r(n, )s 0 (n, ). (0).3 Multi-look Averaging Multilook averaging is a neessary step in the proposed TR-SAR algorithm to remove random ghost patterns in SAR images with multipath [8]. In multi-look (subaperture) proessing, different subapertures of a ground sene

4 Spotlight SAR Image Chip target satterer Range [meter] Figure. Ghost artifats in rih sattering form different subaperture images [7]. In a rih sattering environment where there are many sattering objets in the viinity of the target, the ghost patterns aused by the multipath will be look angle dependent. The independene between various subaperture images an redue or remove ghost pattern artifats aused by multipath refletions..3.1 Analysis of Ghost Patterns Fig. shows the effet of multipath due to random plaement of a satterer near a target. The single refletion returned signal travels a total distane of d + d t + d t. This returned signal indues ghost artifats. To haraterize the loation of the ghost artifats that appear on a SAR image, we alulate the ghost range x g and the ross range y g. We define the target oordinates x t = d t osα, y t = d t sinα (1) where α is the aspet angle of the target with respet to the syntheti aperture. Hene, the satterer oordinates are x = d osθ, y = d sinθ () where θ is the aspet angle of the satterer with respet to the antenna. By Taylor series expansion, we have os(α + θ) = osα sinα θ + O( θ) sin(α + θ) = sinα + osα θ + O( (3) θ) Let d g = (d t + d + d t )/ and define we have xg = x t+x x g = d g osα, y g = d g sinα (4) y g = yt+y + y x θ + d t osα dt θ + sinα (5) In a SAR senario, the ross range y x, and α is a small angle, i.e., osα 1, sinα α. Therefore, we have the following approximation x g xt+x + dt y g yt+y x θ }} + sattering spread d t α }} sattering density (6) Cross Range [meter] Figure 3. SAR image Chip Eqn. (6) shows that the ghost artifats in ross range y g depend on the sattering spread ( θ) and the sattering density (α and d t ). The analysis demonstrates that the appearane of the ghost pattern artifats is look angle α dependent. Sine the true target loation is fixed, averaging multi-look images, either oherently or non-oherently, will redue or remove the ghost patterns and enhanes the intensity of the target. Hene, from the averaged multilook images, we obtain a rough estimate of the target loation with a oarse resolution. Later, the estimated target loation an be used for reonstruting the TR-SAR images in the full aperture domain to retain full resolution. 3 Field Experiments at the Raytheon Site We test the proposed algorithms using the phase history data olleted by a rail-mounted radar system in a desert area at Raytheon, Tuson, Arizona. The data olletion was onduted in August - Otober 007. The target area is an open field at 440 meters down range of the radar. In the open field, we onstruted a square-shaped test site of 0 meters wide and 7 meters deep. Four trihedral orner refletors are plaed at the four orners of the test site for registration purposes. Within this test area, we have installed satterers that onsist of a mix of in diameter solo PVC pipes, 11 pipe bundles of whih has in diameter PVC pipes, and in diameter opper pipe. The target is in diameter opper pipes bundled by dut tapes. All the pipes are 10 tall and fixed by anhors. The target is surrounded by the satterers. When testing, we first measure the SAR phase history data for the lutter without the presene of the target. Then the seond run of the data olletion is onduted when the target is put bak in. 4 Imaging Results by Experimental Data Fig. 3 shows a SAR image of the target after the lutter subtration. The ghost artifats are visible around the target at loation 14.5 meter in azimuth and meter in range. The four orner refletors are shown as four strong peaks.

5 Range (m) Time Reversal Foused Image Conventional TR Range Projetion Azimuth (m) Figure 4. Time reversal foused SAR image We proess the image first by windowing the image in the image domain. We implement the windowing in order to remove the interferene from the orner refletors and to loalize the multipath effet in the viinity of the target of interest. The image hip will undergo TR-SAR proessing to reonstrut the target image. Fig. 4 depits the TR-SAR reonstruted image. To view the resolution, we plot the image projetions in range and azimuth. In Fig. 5, the upper panel shows the range projetion of the TR-foused image and the onventional image. The plots show that the TRfoused image has a deeper null and slightly narrower main beam, whih shows a better resolution. The lower panel shows the range resolution; the differene is very small. This is beause the system bandwidth remains the same for the two image formation methods. 5 Conlusion and Continuing Work This paper desribes and demonstrates time reversal algorithms for spotlight SAR under streth proessing in a rih sattering multipath environment. The rail-sar data olleted at the Rayethon test site show the benefits of TR-SAR that inlude improved resolution and redued sidelobes and ghost artifats. Further development will fous on the integration of TR-SAR into an automated target reognition (ATR) module in the SAR proessing hain. 6 Aknowledgement The authors would like to thank Dr. John Campbell, Ms. Laura Santos and other engineers at the Raytheon Missile Systems with experimental data olletion. Referenes [1] W. G. Carrara, R. S. Goodman, and R. M. Majewski, Spotlight Syntheti Aperture Radar: Signal Proessing Algorithms. Boston, MA: Arteh House, [] S. R. Deraaf, SAR imaging via modern -D spetral estimation methods, IEEE Transations on Image Proessing, vol. 7, no. 5, pp , May Azimuth (m) Conventional TR Azimuth Projetion Range (m) Figure 5. Image projetions. Upper - Range projetion; Lower - Azimuth projetion. [3] G. Benitz, High definition vetor imaging, Linoln Laboratory Journal, vol. 10, no., pp , [4] Y. Jin and J. M. F. Moura, TR-SAR: time reversal target fousing in spotlight SAR, in ICASSP 07, IEEE International Conferene on Signal Proessing, vol.. Honolulu, HI: IEEE, April 007, pp [5] W. J. Caputi, Streth: A time transformation tehnique, IEEE Transations on Aerospae and Eletroni Systems, vol. AES-7, pp , Marh [6] P. Tait, Introdution to Radar Target Reognition. United Kingdom: The Institution of Eletrial Engineers, 005. [7] C. V. Jakowatz, D. E. Wahl, P. H. Eihel, D. C. Ghiglia, and P. A. Thompson, Spotlight-Mode Syntheti Aperture Radar: A Signal Proessing Approah. Boston, MA: Kluwer Aademi Publishers, [8] Y. Jin, J. M. F. Moura, Y. Jiang, J. Zhu, and D. Stanil, Time reversal target fousing in spotlight SAR, in 15th Adaptive Sensor Array Proessing (ASAP) Workshop. Lexington, MA: MIT Linoln Lab, June 007.