Model-Based Radar Power Calculations for Ultra-Wideband (UWB) Synthetic Aperture Radar (SAR)

Transcription

1 odel-based Radar Power Calculaions for Ulra-Wideband (UWB) Synheic Aperure Radar (SAR) by Traian Dogaru ARL-TN-548 June 13 Approved for public release; disribuion unlimied.

2 NOTICES Disclaimers The findings in his repor are no o be consrued as an official Deparmen of he Army posiion unless so designaed by oher auhorized documens. Ciaion of manufacurer s or rade names does no consiue an official endorsemen or approval of he use hereof. Desroy his repor when i is no longer needed. Do no reurn i o he originaor.

3 Army Research Laboraory Adelphi, D ARL-TN-548 June 13 odel-based Radar Power Calculaions for Ulra-Wideband (UWB) Synheic Aperure Radar (SAR) Traian Dogaru Sensors and Elecron Devices Direcorae, ARL Approved for public release; disribuion unlimied.

4 REPORT DOCUENTATION PAGE Form Approved OB No Public reporing burden for his collecion of informaion is esimaed o average 1 hour per response, including he ime for reviewing insrucions, searching exising daa sources, gahering and mainaining he daa needed, and compleing and reviewing he collecion informaion. Send commens regarding his burden esimae or any oher aspec of his collecion of informaion, including suggesions for reducing he burden, o Deparmen of Defense, Washingon Headquarers Services, Direcorae for Informaion Operaions and Repors (74-188), 115 Jefferson Davis Highway, Suie 14, Arlingon, VA -43. Respondens should be aware ha nowihsanding any oher provision of law, no person shall be subjec o any penaly for failing o comply wih a collecion of informaion if i does no display a currenly valid OB conrol number. PLEASE DO NOT RETURN YOUR FOR TO THE ABOVE ADDRESS. 1. REPORT DATE (DD--YYYY) June 13. REPORT TYPE Final 4. TITLE AND SUBTITLE odel-based Radar Power Calculaions for Ulra-Wideband (UWB) Synheic Aperure Radar (SAR) 3. DATES COVERED (From - To) 1/1/13 5a. CONTRACT NUBER 5b. GRANT NUBER 5c. PROGRA ELEENT NUBER 6. AUTHOR(S) Traian Dogaru 5d. PROJECT NUBER 5e. TASK NUBER 5f. WORK UNIT NUBER 7. PERFORING ORGANIZATION NAE(S) AND ADDRESS(ES) U.S. Army Research Laboraory ATTN: RDRL-SER-U 8 Powder ill Road Adelphi, D PERFORING ORGANIZATION REPORT NUBER ARL-TN SPONSORING/ONITORING AGENCY NAE(S) AND ADDRESS(ES) 1. SPONSOR/ONITOR'S ACRONY(S) 11. SPONSOR/ONITOR'S REPORT NUBER(S) 1. DISTRIBUTION/AVAILABILITY STATEENT Approved for public release; disribuion unlimied. 13. SUPPLEENTARY NOTES 14. ABSTRACT In his sudy, we esablish a relaionship beween he radar ransmied power, he arge signaure and he signal-o-noise raio required for a specific arge deecion performance in a radar sysem. While his relaionship can be easily derived from he radar equaion in he case of narrowband waveforms, his echnical noe exends he analysis o wideband waveforms and applies i o synheic aperure radar sysems as well. The echnique is demonsraed hough a numerical example, where compuer daa modeling a hree-dimensional building imaging radar sysem is used in evaluaing he radar ransmied power for a given arge deecion performance. 15. SUBJECT TERS ulra-wideband radar, synheic aperure radar 16. SECURITY CLASSIFICATION OF: a. REPORT Unclassified b. ABSTRACT Unclassified c. THIS PAGE Unclassified 17. LIITATION OF ABSTRACT UU 18. NUBER OF PAGES 19a. NAE OF RESPONSIBLE PERSON Traian Dogaru 19b. TELEPHONE NUBER (Include area code) (31) Sandard Form 98 (Rev. 8/98) Prescribed by ANSI Sd. Z39.18 ii

5 Conens Lis of Figures iv 1. Inroducion 1. Theoreical Calculaion of he Radar Transmied Power.1 Narrowband Radar, Far-Field Case.... Wideband Radar, Far-Field Case Wideband SAR, Far-Field Case Near-Field Case Numerical Example 7 4. Conclusions References 13 Lis of Symbols, Abbreviaions, and Acronyms 14 Disribuion Lis 15 iii

6 Lis of Figures Figure 1. Descripion of he single-sory building used in he 3-D radar image sudy....8 Figure. Schemaic represenaions of he airborne spoligh radar imaging sysem, showing (a) he radar plaform moving in a circular paern around he building and (b) he synheic aperure posiions (mared as yellow dos) placed on a sphere....8 Figure 3. The 3-D building image for he airborne spoligh configuraion and V-V polarizaion. The feaure colors correspond o heir brighness levels in he raw 3-D image....9 iv

7 1. Inroducion The radar modeling eam a he U.S. Army Research Laboraory (ARL) has developed a suie of simulaion ools and mehodologies ha have been successfully applied o predic radar sysem performance in complex scenarios. Among hese scenarios are ground peneraing radar and forward-looing radar for landmine and improvised explosive device deecion, as well as sensing hrough he wall (STTW) radar for deecion of arges inside buildings. In general, he main focus of our modeling wor has been on high-resoluion imaging applicaions of an ulra-wideband (UWB) synheic aperure radar (SAR). Specific o his sensing modaliy is he large range of frequencies and aspec angles for he daa collecion in he simulaion domain, ha ranslaes o a large amoun of compuaional resources. An example of a large-scale radar simulaion ha creaes he hree-dimensional (3-D) image of a one-sory building was repored in reference 1. One limiaion of our curren models is ha hey emphasize he arge scaering aspecs and mosly ignore oher imporan parameers of he radar sysem, such as anenna gain, sysem losses, receiver noise figure, ec. In some cases (far-field scenarios), he models even ignore he propagaion (pah) losses incurred by he radar waves. Addiionally, by design, he elecromagneic (E) scaering models do no include any exernal noise or radio frequency (RF) inerference (which can acually have a significan impac on he performance of an UWB radar). However, in evaluaing he overall radar performance, mos of hese effecs can be accouned for in he pos-processing of E scaering model daa. This sudy aemps o parially fill his gap, by maing he connecion beween quaniies obained via compuer modeling (such as he arge scaering parameers) and he more radiional radar sysem parameers, such as ransmied power and signal-o-noise raio (SNR). ore specifically, we evaluae he required pea ransmied power of he radar, based on he arge scaering parameers and he level of SNR required for a specific arge deecion performance. We apply his mehod o UWB SAR imaging scenarios, where nowledge of he arge response over a large range of frequencies and aspec angles is necessary. I is imporan o menion ha he equaions are valid regardless of he mehod employed in obaining he arge scaering parameers (which can be measuremen-based as well as model-based). The echnical noe is organized as following: secion discusses he heoreical aspecs of he radar power calculaion based on compuer models, secion 3 presens a numerical example, and secion 4 offers conclusions. 1

8 . Theoreical Calculaion of he Radar Transmied Power.1 Narrowband Radar, Far-Field Case Throughou his sudy, we mae he disincion beween near-field and far-field radar-arge configuraions. While we do no discuss he specific quaniaive crieria ha separaes he wo cases (more deails can be found in reference ), we menion ha he far-field assumpion allows us o use he radar equaion (3) for power calculaion, whereas in he near-field case, he model on which he classic radar equaion is derived, is generally no valid. In his secion, we consider a narrowband radar (wih a bandwidh much smaller han he carrier frequency), operaing in a far-field, monosaic configuraion, wih idenical ransmier and receiver anennas. A simple form of he radar equaion is he following (3): P r PG, (1) R where P r is he received power, P he pea ransmier power, G he anenna gain, he wavelengh of he carrier, he radar cross secion (RCS) of he arge, and R he radar-arge range. Throughou his sudy, he arge is considered saionary. In he following, we ignore cerain facors ha usually appear in he radar equaion, such as sysem losses and receiver noise figure (3). We also assume ha he deecion is performed based on a single ransmied pulse (no pulse inegraion performed), by comparing he magniude of a pos-deecion sample wihin he range gae of he arge wih a hreshold. The effec of sysem losses, receiver noise figure, and pulse inegraion can be accouned for by adding corresponding facors o he radar equaion; however, heir omission does no change he principle of he mehod oulined here. Compuer programs ha model radar far-field scaering scenarios, such as AFDTD (4), FEKO (5), or Xpach (6), perform calculaions of he complex arge scaering parameer S, which lins he elecric field inensiies inciden o and scaered by he arge (for a more precise definiion, see reference 7). The relaionship beween S and is 4 S. Throughou his noe, we assume ha he radar performance is limied by he hermal noise a he receiver anenna (3), so we ignore oher sources of noise or inerference. The hermal noise is usually modeled as having a consan power specral densiy (PSD) in he band of ineres, equal o B T, where B is Bolzmann s consan and T is he emperaure. The average power of he noise is hen B T B, where B is he receiver noise bandwidh (which we assume equal o he ransmied pulse bandwidh).

9 Now assume ha we require a specific SNR for a desired arge deecion performance. Then we formulae our problem as following: given he S parameer calculaed via he compuer model, find he ransmier power P in order o obain he specified SNR. For his, we wrie he SNR as From here, we derive SNR P P PG S r. () T B B 4 4 R T B 4 4 R T BSNR B B. (3) G S. Wideband Radar, Far-Field Case The calculaions in he previous secion are valid for a ransmied radar signal wih a narrow bandwidh (long duraion). Now we consider he case of a wideband pulse, which ypically has a shor duraion. For he presen discussion, we assume ha he pulse consiss of an ampliudemodulaed (A) carrier, and no pulse compression echnique (3) is used (he pulse compression case is menioned briefly a he end of his secion). A ypical relaionship beween duraion and bandwidh for such a pulse is (3) 1 B. In his sudy, we wor wih discree (sampled) signals in boh ime and frequency domains. The conversion of signals from one domain o he oher can be made via discree Fourier ransforms (DFTs), which involve sequences of lengh N in boh domains. Noice ha N is also indicaive of he number of range resoluion cells covered by he receiver ime gae (ime when he receiver is urned on), as well as he number of samples colleced by he receiver during ha ime (assuming ime domain sampling a Nyquis rae [8]). We furher assume ha he specral conen of he ransmied pulse is relaively fla over he signal bandwidh. Then, he magniude of each of he N specral componen equals he ransmied pulse pea power (defined as he average power of he pulse over is duraion; his should no be confused wih he average ransmied power of he radar, where he average is calculaed over a pulse repeiion inerval). The radar equaion can be wrien separaely for each specral componen (indexed by, wih from 1 o N) as P r, 4 4 R PG S. (4) Noice ha in equaion 4 we used he index for G, and S, o represen he fac ha hey vary wih frequency. However, he value of P was considered consan over he bandwidh. Nex we consider he signal a he receiver, which is made of a arge-scaered componen and an addiive noise componen. For he former, we call he power of each ime-domain sample p r,n, and he power of each frequency-domain componen P r,, wih indexes n and running from 1 o N. For he laer, we call he power of he ime-domain samples w n, and he power of 3

10 he frequency-domain componens W. We define he SNR of he received signal as he raio of he average ime-domain arge-scaered sample o he average ime-domain noise sample. Now, i is reasonable o assume ha he arge response exends over resoluion cells, wih < N. Then, we compue he SNR as he average SNR over hose resoluion cells. Using Parseval s heorem (8) and he fac ha he average power of a ime-domain noise sample is B T B, we obain SNR N N 1 1 pr, n pr, n Pr, n1 n1 1. (5) 1 1 N BT B wn wn n1 n1 In he above equaion, we used he following discree version of Parseval s heorem: N p 1 N r, n n1 N 1 P r,, (6) as well as he fac ha he p r,n samples are zero ouside he resoluion cells ha mae up he arge response. I is very imporan o emphasize ha, in equaion 5, we compue he SNR sricly over he spaial exen of he arge response we canno use he SNR over he enire range swah sensed by he radar (corresponding o N resoluion cells), or he SNR over one paricular resoluion cell eiher. Finally, from equaions 4 and 5, we can derive he required ransmied pea power for a given SNR: In general, can be compued as P 4 4 R T BSNR N 1 B G S N. (7) R R BR, (8) c where R is he arge exen in range, and R is he range resoluion. Noice ha he case when = N corresponds o a frequency-domain sampling of he S sequence a he Nyquis rae (he receiver ime gae corresponds direcly o he range exen of he arge response). An ineresing conclusion we draw from equaion 7 is ha here is no advanage or disadvanage in increasing he widh of he receiver ime gae (or, equivalenly, increasing N), since boh he numeraor and he denominaor in he expression of he ransmied power increase by a proporional amoun (he denominaor via he sum from 1 o N). 4

11 The pea power of he ransmied signal can be brough down significanly if a pulse compression scheme is employed (3). For such a pulse, he produc beween duraion and bandwidh B (also nown as he compression raio [CR]) is much larger han he uniy (a ypical value would be 1). In his case, he required ransmied pea power is reduced by a facor CR (9): P 4 4 R T BSNR CR B N 1 G S N 4 4 R T SNR N 1 B G S N. (9) Noice ha he final form of equaion 9 is valid in general for any ype of pulse, regardless of wheher compression is used or no..3 Wideband SAR, Far-Field Case In his secion, we consider he model of a SAR imaging scenario, where he E simulaion program compues he S parameers (or received signal) over a range of frequencies and aspec angles. To be more specific, we consider a circular spoligh SAR daa collecion geomery (1), where he radar operaes monosaically in he far-field. For now, we analyze a wo-dimensional (-D) imaging geomery; a 3-D imaging geomery example is shown in secion 3. The derivaion of he ransmied pea power for his case largely follows he procedure in secion., wih he difference ha we now wor wih -D (sampled) signals, boh in spaial (or image) and frequency-angle domains. As shown in reference 1, a -D Fourier ransform relaionship can be esablished beween he signals in he wo domains. The E simulaion sofware compues he received -D signals in he frequency-angle domain. The SAR image can hen be inerpreed as a -D inverse Fourier ransform of hese daa samples (deails of he numerical calculaion of his Fourier ransform are no rivial, bu are no discussed here). Wihou going again hrough every sep as in secion., we menion ha he daa in he frequency-angle domain are ransformed o he image domain, and he image SNR for a desired arge deecion performance is found. As previously, we emphasize he fac ha he SNR is compued as an average of he signal power o he average noise power over he arge image exen, which is assumed o comprise D resoluion cells in down-range and C resoluion cells in cross-range. By analogy wih he one-dimensional case presened in secion., he equaion ha expresses he oal pea power ransmied by he radar o obain an image wih a given SNR is P oal 4 4 R T BSNR N B 1 L l1 S, l image NL G D C. (1) 5

12 where l is he aspec angle index ha runs from 1 o L; also, no pulse compression was considered here. The anenna gain G depends on frequency only for he spoligh SAR mode. However, if we wan o adap his equaion o a srip-map daa collecion geomery (1), we may need o ae ino accoun he gain variaion wih angle as well (if his variaion is significan wihin he angular range employed in he image formaion algorihm). To compue he pea power of one ransmied pulse (or he pea power of he radar), we need o ae ino accoun ha L pulses are employed in creaing he SAR image. Tha means he pea power of one individual pulse is P divided by L, or P oal 4 4 R T BSNR N B 1 L l1 S, l image N G D C. (11) Noice in equaion 11 ha increasing he number of daa collecion poins along he synheic aperure (L) helps o bring down he ransmier power for a given image SNR (via increasing he number of erms in he sum from 1 o L ha appears in he denominaor), or, equivalenly, increases he image SNR for a fixed ransmier power..4 Near-Field Case For a near-field radar scaering scenario, he direc applicaion of he radar equaion is no valid any longer, since some of he quaniies and conceps used in is derivaion only mae sense for far-field geomeries. oreover, he equaion connecing he ransmied and received radar powers depends srongly on he ype of radar anennas, and in mos cases, canno be expressed in analyic form. Even when his connecion is evaluaed via E compuer models, here is no sandardized way of implemening he ransmier and receiver anennas or characerizing he arge scaering (by comparison, he S parameer for he far-field case is a well-defined quaniy and does no depend on he evaluaion mehod). Despie hese difficulies, we derive he equaion of he pea ransmied power for he case when he near-field radar scenario is simulaed wih he NAFDTD sofware (11), and he ransmier and receiver anennas are provided by infiniesimal dipoles. We firs consider he narrowband case. According o he heory of his ype of anennas (), we have l I P Z, (1) 3 E 3 P r r Z 8, (13) where Z is he free-space impedance, I l is he curren momen of he ransmier (), and E r is he elecric field a he locaion of he receiving dipole. The NAFDTD program compues he 6

13 arge response for an exciaion wih I l 1; le us call he field a he receiver in his case Then, for a general exciaion, we have E r. P r r E Z. (14) 3 E A he same ime, he SNR can be wrien as SNR P Er 3 r. (15) BT B 16Z BT B By exracing r E from he las equaion and replacing i in equaion 14, we obain P 4 Z T BSNR B. (16) 4 9 Er Noice ha, as compared o equaion 3, his expression does no explicily conain parameers such as he anenna gain G and he range R. This is because, unlie he S parameer (from he far-field case), he E parameer implicily conains all he oher facors. r Now le us exend he mehod o an UWB SAR scenario. In his case, we assume ha he radar moves along a cerain rajecory and measures he arge response from L pairs of ransmierreceiver locaions. Le us call E o r,, l he field a he receiver compued by he NAFDTD code, for frequency index and radar locaion index l. Then, by applying argumens similar o hose in secion.3, we obain P 4 Z T BSNR 9 B N 1 L l1 E image r,, l 4 N D C. (17) 3. Numerical Example In his secion, we presen a numerical example demonsraing how o esimae he pea power required by a STTW radar sysem in order o obain 3-D images of a building wih a given SNR meric. The calculaions are relaed o he wor in reference 1, where he 3-D images were obained from simulaed radar daa. The building has a single floor and conains four saionary human arges (figure 1). For his sudy, we assume an airborne radar sysem, placed in he farfield, and collecing daa in a circular spoligh mode over cerain ranges of azimuh and elevaion angles from one side of he building (figure ). The 3-D image obained for verical- 7

14 verical (V-V) polarizaion is shown in figure 3, where we represen only he oupu of a consan false alarm rae (CFAR) deecor. Figure 1. Descripion of he single-sory building used in he 3-D radar image sudy. (a) (b) Figure. Schemaic represenaions of he airborne spoligh radar imaging sysem, showing (a) he radar plaform moving in a circular paern around he building and (b) he synheic aperure posiions (mared as yellow dos) placed on a sphere. 8

15 Figure 3. The 3-D building image for he airborne spoligh configuraion and V-V polarizaion. The feaure colors correspond o heir brighness levels in he raw 3-D image. To obain he image in figure 3, a cerain amoun of complex-valued whie Gaussian noise was added o he daa direcly in he image domain. The noise average power is aen relaive o he maximum inensiy voxels (in our case, hese can be found along he lower edge of he fron wall). By inspecing he image in figure 3 we find ha he sronges feaure (he lower edge of he fron wall) has a power of 1 db, while he weaes feaure ha we wan o deec (he human closes o he fron wall) has a power of abou 5 db. In a ypical deecor, he arge would need o be abou 1 db above he average noise level in order o pass he deecion es, meaning ha he noise average power should be 6 db. This gives us a raio beween he maximum inensiy voxel and he noise average power of 5 db. Now, according o he discussion in secion.3, we recognize ha his power raio (which ulimaely deermines he radar sysem performance in deecing he human arges) is no he same quaniy as he image SNR used in equaion 11. Insead, as an inermediae sep, we need o numerically compue he average SNR over all he image voxels, when he image noise average power is 6 db (as deermined in he previous paragraph). This calculaion yields SNR image = 15 db. Equaion 11 can be adaped o a 3-D imaging geomery as follows: 9

16 P 4 4 R T BSNR N B L Q 1 l1 q1 S image, l, q N D G C E, (18) where his ime he S parameers are compued over hree dimensions (q indicaes he elevaion angle index), while D, C and E represen he numbers of resoluion cells wihin he image, in down-range, cross-range, and elevaion range, respecively. These numbers can be compued according o he following formulas (see reference 1): In hese equaions, we used he following noaions: DR he image dimension in down-range (along x-axis) CR he image dimension in cross-range (along y-axis) ER he image dimension in elevaion range (along z-axis) B eff he effecive bandwidh of he radar daa eff he effecive azimuh angle range for he radar daa eff he effecive elevaion angle range for he radar daa C E f he cener frequency for he radar daa c he speed of ligh D Beff DR, (19) c eff 4 f sin CR, () c eff 4 f sin ER. (1) c In he numerical sudy performed in reference 1, he following parameers were used: B =. GHz, f = 1.4 GHz, B eff = 1.1 GHz, eff, eff,dr = 9 m, CR = 1 m,er =.75 m, N = 331. Addiionally, we assume ha R = 1 m and he anenna gain is given by f.3 f 1 / G, () where f is he frequency in GHz. This expression indicaes ha he anenna gain varies beween 5 and 1 dbi in he frequency band of ineres, which is ypical for a SAR sysem operaing in 1

17 he spoligh mode a hose frequencies. The oal power of he scaering parameers S (added 6 over all hree daa dimensions) is 6.81 square-meers. For he B T consan we ae he usual value of J. Afer plugging all hese parameers in equaion 1, we obain P = W. This is an unreasonably high value for he ransmied pea power in an airborne radar sysem. However, his figure assumes ha we do no use any pulse compression echnique. As menioned in secion., if we use pulse compression, he pea power is reduced by a facor proporional o he compression raio. For insance, for CR = 1, we obain P = W, which is a more manageable figure. In fac, mos airborne radar sysems employ some ind of pulse compression echnique in order o eep he pea power o low values. Also, eep in mind ha he pea power calculaion is very sensiive o he choice of he range R; hus, operaing he radar a smaller ranges can dramaically reduce he required ransmied power. One cavea regarding his calculaion is he fac ha he 3-D images creaed in reference 1 are no based on he received radar signals, bu on he S-parameers. The received signals differ from he S-parameers by a scaling facor ha can be easily derived from he radar equaion. As long as his scaling facor does no depend on frequency and aspec angle, he wo images (obained from he wo ses of daa) are simply scaled up/down versions of one anoher. Since he only way he power of he image voxels appears in he radar pea power expression is hrough SNR image, scaling up or down he image inensiy by a facor does no change he final calculaion. However, he scaling facor ha lins he received signals o he S-parameers generally depends on frequency hrough he anenna gain G and he wavelengh ; herefore, he SAR images based on he wo ses of daa may loo slighly differen, which can, in urn, lead o differen values of he pea ransmied power. This issue can be resolved by re-creaing he images wih a se of correced S-parameers ha accoun for he variaion of G and wih frequency. Neverheless, we did no pursue his procedure in his sudy, which is only mean o illusrae he general mehod for pea power calculaion. 4. Conclusions In his noe, we derived equaions for he radar pea ransmied power as a funcion of radar sysem parameers, he arge scaering srengh and he desired SNR a he oupu of he radar processing chain. The mehod was applied o SAR images obained by UWB radar. The arge scaering is characerized by he scaering parameers S (whose magniude square is equivalen o he arge RCS), wih his quaniy deermined separaely by compuer simulaions or measuremens. For UWB SAR sysems, an imporan fac is ha S depends on boh frequency and aspec angle. In secions. and.3 we paid paricular aenion o he way we define he 11

18 SNR ha appears in he final equaion of he pea power, as well as he number of resoluion cells ha need o be considered in he calculaion. The heoreical derivaions were followed by a numerical example ha applies he mehod o esimae he pea power of an airborne radar ha creaes he 3-D image of a building. The desired SNR level is based on he requiremen ha we deec all four human arges inside he building. The large pea power obained from his calculaion for unmodulaed pulses underscores he challenges faced by any STTW radar sysem, where he arge signaure is severely aenuaed by he round-rip hrough-wall ransmission of he radar waves. I also jusifies he need o use a pulse compression echnique in order o eep he pea ransmier power down. In his example, we assumed ha he radar deecion performance is limied by hermal noise. However, in a scenario involving hrough-he-wall deecion of saionary arges, he performance is mos liely limied by oher facors such as cluer, image sidelobes and mulipah propagaion, and scaering. Neverheless, hese issues canno be miigaed by increasing he ransmied power, bu insead by he correc choice of imaging geomery and advanced signal processing algorihms. 1

19 5. References 1. Dogaru, T.; Liao, D.; Le, C. Three-Dimensional Imaging of a Building; ARL-TR-695; U.S. Army Research Laboraory: Adelphi, D, December 1.. Balanis, C. Anenna Theory Analysis and Design; Wiley: New Yor, Solni,. I. Inroducion o Radar Sysems; cgraw Hill: New Yor, Dogaru, T. AFDTD User s anual; ARL-TR-5145; U.S. Army Research Laboraory: Adelphi, D, arch FEKO E Simulaion Sofware Web page. hp:// (accessed Ocober 11). 6. Science Applicaions Inernaional Corporaion (SAIC) Web page. hp:// (accessed December 11). 7. Ruch, G.; Barric, D. E.; Suar, W. D.; Krichbaum, C. K. Radar Cross Secion Handboo; Plenum Press: New Yor, Oppenheim, A. V.; Schafer, R. W. Discree-ime Signal Processing; Prenice Hall: Englewood Cliffs, NJ, ahafza, B. R. Radar Sysems Analysis and Design Using ATLAB; CRC Press: Boca Raon, FL, Soumeh,. Synheic Aperure Radar Signal Processing; Wiley: New Yor, Dogaru, T. NAFDTD A Near-Field Finie Difference Time Domain Solver; ARL-TR- 611; U.S. Army Research Laboraory: Adelphi, D, Sepember 1. 13

20 Lis of Symbols, Abbreviaions, and Acronyms -D wo-dimensional 3-D hree-dimensional A ARL CFAR CR DFT E PSD RCS RF SAR SIRE SNR STTW UWB V-V ampliude modulaion U.S. Army Research Laboraory consan false alarm rae compression raio discree Fourier ransform elecromagneic power specral densiy radar cross secion radio frequency synheic aperure radar Synchronous Impulse Reconsrucion signal o noise raio sensing hrough he wall ulra-wideband verical-verical 14

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