Computational Method and Experimental Meaurement XV 43 Synthetic aperture radar raw ignal imulator for both puled and FM-CW mode P. Serafi C. Lenik & A. Kawalec Intitute of adioelectronic, Military Univerity of echnology, Poland Abtract Simulated raw radar ignal prove to be very ueful at the firt tage of teting radar ignal proceing algorithm and procedure. hi i particularly true for ynthetic aperture radar (SA), where the cot of real ignal acquiition are very high due to the cot of building the ytem a well a the cot of miion (air or pace-borne). hi paper decribe a multifunctional SA raw ignal imulator that ha been ued for the verification of SA image ynthei algorithm. Generated ignal can be imitated for puled a well a FM-CW radar both in SLA and quinted cae, it i alo poible to chooe between video and intermediate frequency ignal. he imulator allow u to generate echo ignal from tationary and moving target. he uer i able to differentiate the tatitic propertie of received echo ignal for each target, thu allowing u to generate different type of reflecting urface. If preent, a real raw SA ignal can be merged with a imulated one to produce more complicated cenario. he paper preent reult of the imulation of raw ignal and their image after SA proceing. Keyword: ynthetic aperture radar, SA ignal imulator, FM-CW SA. 1 Introduction Airborne and pace borne radar imaging allow u to collect the picture of a terrain fragment independently of the time of the day, the weather or viibility condition over the imaged cene. Unfortunately, due to relatively long wave ued by the radar (compared to photography), it need to employ large antennae in order to achieve the deired image reolution. hi can make the ytem impoible to build onboard an airplane or a atellite. he olution to thi problem i the technique of the ynthetic aperture radar (SA) that i able to doi:10.495/cmem110371
44 Computational Method and Experimental Meaurement XV generate virtual antenna by canning the oberved area along a known route. After covering a deired ditance gathered ignal are proceed a though they came from a real antenna giving a radar image with the reolution comparable with the wavelength of ued ignal. Due to it advantage, SA ytem became very ueful and widely applied reconnaiance tool and thank to the rapid development of the computational technique, their capabilitie have grown teadily over pat year. he development of SA ignal proceing algorithm require the verification of their reult with tet ignal. hi can be difficult in the early tage of the project, epecially during ytem feaibility verificatio when no phyical realiation of the radar that would provide data exit. Acquiring the ignal from third party intitution if poible i rather expenive due to the expene put into building the ytem a well a conducting the miion. herefore one of the baic ource of radar ignal ued in SA image ynthei algorithm teting i the computer imulation. Simulated ignal are incomparably cheaper than real one and their additional advantage i the ability to configure the oberved cene and the radar miion arbitrarily, which allow u to tet the algorithm in a wide range of parameter. he main drawback of imulation, however, i the implification made in order to keep computational cot a low a poible, which ometime render the reult unreliable. he imulation deign mut be then optimied for maximum reality and minimum complexity. hi paper preent a imulated SA raw ignal generator developed for the verification SA image ynthei algorithm in Military Univerity of echnology (MU) in Waraw, Poland. Principle of SA A SA ytem i typically a radar intalled onboard an airplane or a pacehip whoe antenna ytem i illuminating the Earth urface perpendicularly or at ome quint angle to the carrier route. A typical SA configuration for the airborne cae i Side-looking Airborne adar (SLA) whoe geometry i preented in fig. 1. he carrier i moving along a et, well known and, preferably, traight, route. During the operatio a it carrier move the radar emit the electromagnetic energy and receive echo ignal reflected from the terrain object. eceived ignal are then pre-proceed and tored in ytem memory. hi ignal pre-proceing include filtration and down-converion to intermediate frequency or can be extended to baeband converion and ubequently range compreio depending on the type of the algorithm ued. After the radar ha covered the ditance equal the antenna length L needed to achieve the deired azimuth reolution A, ignal tored in memory are proceed a if they were received by a real phaed array of a length L.
Computational Method and Experimental Meaurement XV 45 X max min G 0 Y Figure 1: he geometry of a SA ytem. Let u aume the tranmitted ounding ignal to be of form j t t A t e 0, (1) where: A t i a modulation ignal, 0 i the centre angular frequency. hen the echo ignal reflected from a ingle point target at the range will take form [1] t t e 4 j, () where: i the wavelength of ounding ignal, i a two way electromagnetic wave propagation time between the radar antenna and the target given by, (3) c where c i the wave propagation velocity. If one take into account that the radar i moving and denote the time t aociated with wave propagation a fat-time and the time aociated with the radar movement, a low-time one will obtain the complete equation decribing received ignal j, e. (4) t t 4
46 Computational Method and Experimental Meaurement XV In the above equation the intantaneou (in the low-time) range i defined a follow x x y y z z, (5) where: x, y z i the intantaneou radar poition and x, y, z, i the poition of the target. Auming the coordination ytem from fig. 1 one can define the coordinate a: z x x v cont 0 cont H 0, (6) y, (7), (8) where: x 0 i the initial radar poition along the X axi, v i the radar peed and H i the radar height above the ground. It i alo aumed that the target lie on the ground meaning herefore one can reduce eqn (5) to z 0. (9) x v x y H (10) 0 and then ubtitute the reult to eqn (4) which take then the following form, t 4 j x0 v x y H t e. (11) c If the ignal i ampled with ampling frequency f and define the range reolution cell dimenion a c d, (1) f one can obtain m, l 4 j x0 ld x y H l e d, (13)
Computational Method and Experimental Meaurement XV 47 where: m i a number of the ounding impule emitted by the radar with the Pule epetition Frequency ( PF ), l i a number of range cell and d i ditance between two conecutive ounding poition of the radar v d. (14) PF In order to obtain a high reolution radar image one hould compre the ignal in the range (fat-time) and azimuth (low-time) domain. he range compreion i performed by a filter matched to the form of the ounding ignal and can be done either before the azimuth compreion or after it. Some of the SA image ynthei algorithm combine thoe two compreion in one block. hey will be, however, conidered here a eparate proceing tep. eceiver with a quadrature detector I Q Memory A Complex raw ignal ange Migration correction A Output * h Complex SA image Figure : Structure of the DC SA proceor. It will be aumed that the obtained raw SA ignal i already rangecompreed. he azimuth compreion i in fact matched filtering [1, ], where filter impule repone i o called azimuth chirp being actually the complex conjugate to the exponential form in eqn (13). herefore the operation of azimuth compreion of the SA image would be a convolution of the ignal with the azimuth chirp. However imultaneouly with the change of ignal phae due to the change of range the ignal poition in ytem memory change a well. hi phenomeno called ange Migration (M), if not compenated for eriouly decreae maximum achievable ynthetic aperture length and conequently the maximum image reolution. ange Migration correction procedure conit of computing the actual number of range
48 Computational Method and Experimental Meaurement XV cell where the ignal for a given image pixel for each element of the ynthetic aperture. herefore the tructure of the SA proceor (hown in fig. ) conit the above mentioned convolution block following the M correction tep. he decribed algorithm i called ime Domain Correlation (DC) and although it i computationally very expenive, it i alo the mot accurate due to the lack of any implifying aumption. hi make thi algorithm a ueful reference tool for verification of other SA algorithm. 3 he imulation trategy he imulated raw SA ignal generator developed in MU wa deigned to evaluate the accuracy and efficiency of SA algorithm implemented in an FPGA tructure. he generator can provide the ingle- or multi-channel raw SA ignal reflected from uer-defined object placed in the oberved pace. Object are flat and lay on the Earth urface. hey ca however, move in the X and Y direction. Each object conit of a number of elementary catterer ditributed within it boundarie. Uer can define the hape (rectangle, ellipe or line) of the object, it ize, the number of catterer within the object and the v x and v y velocity component. here are three type of object in the program: 1) with randomly ditributed catterer that have defined parameter uch a minimal and maximal value of the adar Cro Section (CS) over the object, variance of CS and phae fluctuation of all catterer from pule to pule; additionally each catterer can have omnidirectional cattering characteritic in the azimuth and elevation domain or it can have an eight haped one in azimuth domain; in the latter cae uer can alo define the range of angle for azimuthal poition of the catterer; the probability denity function (PDF) for CS fluctuation i aumed to be Gauia wherea the phae ditribution i uniform and thoe fluctuation are uncorrelated, ) with uniformly ditributed elementary reflecting urface; the tatitical propertie of uch object are decribed by PDF and autocorrelation function (AF) of thoe urface, 3) jamming ource emitting white Gauian noie with an omnidirectional characteritic. he uer ha alo to define all the radar parameter uch a number of receiving channel q max, ditance between the antenna element d a, centre frequency f 0 and wavelength, pule repetition frequency PF, LFM deviation frequency f, pule duration i, ampling frequency f, intermediate f and the emitted peak power. Alo the carrier parameter uch a IM
Computational Method and Experimental Meaurement XV 49 height, velocity, obervation ditance or initial coordinate need to be etablihed. adar can have a number of receiving channel whoe antennae are uniformly ditributed along the carrier movement direction. he ounding ignal in the imulated SA ytem can be either puled or continuou wave with linear frequency modulation (LFM-CW), the raw ignal after imulation will differ in each cae. For the puled radar it i either video or IM ignal with or without range compreio and for the LFM-CW cae it i the Dicrete Fourier ranform (DF) of dechirped (down-converted) received ignal. Both type of ignal are tored in a text or a binary file a complex ample arranged in range line (ignal received during one ounding). he uer can alo define the tandard deviation of the receiver thermal noie, which will have added to the ignal at the end of the imulation. 4 he imulation algorithm he echo ignal reflected from each element i computed accordingly to the following algorithm 1) For each m -th poition of radar (for each ounding) the ditance m, n between the radar antenna and the n -th catterer i computed accordingly to the following equation x x y y H h, (15) m, n m m, n m m, n m, n where: x m and y m are the radar poition coordinate in the m -th ounding, and x m, n and y m, n are the coordinate of the n -th catterer in the m -th ounding, H i the height of the carrier above the ground. If the poition of no. 0 antenna element would be aumed a the poition of radar x m, then the poition of the q -th antenna element can be defined a x aqm x qd. (16) m a A it wa mentioned all the object are flat and are placed at the height equal h h 0. (17) m Conidering the above and the radar movement the tatement for the ditance between n -th catterer and q -th antenna element in the m -th ounding can be rewritten a follow x qd md x y y H. (18) m, q 0 a m, n m m, n
430 Computational Method and Experimental Meaurement XV A in accepted model the radar Y coordinate y m i contant and equal to zero, and the object can be moving with the velocity having component v x and v y the eqn (18) hould take the following form mvnx mvny m, q x0 qd a md x n0 y n0 H PF PF, (19) where: x n0 and y n0 are the coordinate of the n -th catterer. ) he received echo ignal reflected from the imulated object are created either a impule with linear frequency modulation (LFM) or the LFM-CW ignal after dechirping. he puled ignal can have zero central frequency (video ignal) or ele their pectrum can be centred around a non-zero intermediate frequency f IM. he video ignal are aumed to be after quadrature down-converion and therefore are tored a complex ample wherea ignal with nonzero f IM are real with imaginary part equal to zero. 3) After having computed the ditance m, n, q, voltage ample in receiving channel are determined where: t U 4 m, n, q j m, q lt Am, q lt tm, q e, (0) i the function decribing the tranmitted ounding ignal, t m, q i the time of the two way propagation of the electromagnetic wave from the q -th antenna element to the n -th catterer and back to antenna in the m -th ounding and i equal t m, q m, q, (1) c A m, n, q i the amplitude of the echo ignal dependant on catterer reflecting characteritic m, q (CS), antenna characteritic G A, range and the tranmitted power P N and i equal to [] G P A N m, q A m, q. () m, n, q 4 3
Computational Method and Experimental Meaurement XV 431 he form of the tranmitted ounding ignal t i dependant on radar parameter et by the uer. In particular if the value of f IM i non-zero thi ignal i generated a a erie of real valued ample having the form of l f f co f IM lt lt. (3) i In the cae of the baeband (i.e. video) ignal it take the form of a erie of complex valued ample l f f f f co lt lt j in lt lt. (4) i i If the catterer under conideration i not fluctuating and it ha an omnidirectional reflecting characteritic the m, q parameter i contant. However for catterer with eight-haped reflecting characteritic a m, q angle between radar-target line and the azimuthal poition of the catterer characteritic i etablihed and then on it bai the m, n m, n i computed. he ignal can be range compreed by matched filtering in a FI filter whoe coefficient are the ample of the ounding pule replica. he filtering itelf if done in the form of o called fat convolution employing the Fat Fourier ranform (FF) on both ignal and the impule replica, then multiplication of the pectra, and finally the Invere Fat Fourier ranform (IFF). In the cae of LFM-CW radar the received ignal i computed a the reult of downconverion with the tranmitted ignal and for a ingle catterer it take the form of real valued erie of ample [3] lt U m, q lt Am, q co f 0 lt. (5) After computing the value of the ignal ample and their poition in the ytem memory the ignal are added to the repective cell (their value are ummed with thoe already exiting it the memory). If imulated radar i working a LFM-CW the FF in the range domain i performed in order to obtain the range compreion. he program ha the functionality of yntheiing the SA image uing decribed earlier the DC algorithm, which can be ued a the tool for verification of the generated raw ignal. It i alo poible to merge new ituation with earlier generated ignal or even with real radar ignal if only all of the needed parameter are known.
43 Computational Method and Experimental Meaurement XV Figure 3: Program window with radar parameter for the imulation tab. Fig. 3 preent the program window with radar parameter tab howing alo the ditribution of the imulated object. In fig. 4 the tab with generated raw SA ignal i preented and in fig. 5 the tab with SA image computed with the DC SA image ynthei algorithm. Figure 4: Program window with SA raw ignal generated.
Computational Method and Experimental Meaurement XV 433 Figure 5: Program window with SA image yntheied. 5 Concluion A Synthetic Aperture adar raw ignal generator developed in Military Univerity of echnology in Waraw, Poland wa decried in thi paper. Algorithm of the generation of echo ignal from both tationary and moving target wa preented a were the imulation reult. Acknowledgement hi work wa upported by the Polih Minitry of Science and Higher Education from ource for cience in the year 009-011 under project O00007509. eference [1] Cumming, I.G. & Wong, F.H., Digital Proceing of Synthetic Aperture adar Data. Algorithm and Implementatio Artech Houe: London and Boto 005. [] Skolnik, M., adar Handbook, Second Editio McGraw-Hill Book Company: New York, 1990. [3] Stove, A.G., Linear FMCW radar technique. IEE Proceeding F adar and Signal Proceing, 139(5), pp. 343-350, 199.