Range Migration Techniques for Short-Range MIMO Array Imaging

Size: px

Start display at page:

Download "Range Migration Techniques for Short-Range MIMO Array Imaging"

Richard Hampton
5 years ago
Views:

1 Pogess In Elecomagneics Reseach Lees, Vol. 64, , 2016 Range Migaion Techniques fo Sho-Range MIMO Aay Imaging Jing Yang, Xiaozhou Shang, and Zhi-Ping Li * Absac This pape pesens a sho-ange imaging algoihm fo muliple-inpu-muliple-oupu (MIMO) aay. One of he seps in a pevious mehod uilizes 2-D STOLT inepolaion o ansfom 3-D daa ino 2-D daa, which is no sic in he view of mahemaical deivaion and lack of physical meaning. The convoluion opeaion which is analyzed by physical pocess of angula specum popagaion is used o explain muli-saic configuaion and educe he 3-D daa ino 2-D ones. This pape gives he physical phenomena of he whole pocess of imaging. We also explain he diffeen physical meanings of FFT beween ansmies and eceives. Numeical simulaions show he consequence of STOLT inepolaion in he pevious algoihm and demonsae he pefomance of he poposed algoihm. 1. INTRODUCTION Nowadays, sho-ange human secuiy sceening equipmen is songly desied o have fas opeaional capabiliies and mobiliy [1, 13, 14]. Synheic apeue ada (SAR) [2] which ges he signal by elaive movemen beween age and ada is ofen used in imaging of saellies and aiplanes. The speed of imaging in hese sysems is slow because of mechanical of scanning. The anennas of a phased aay ada [3] ae disibued evenly and densely involving excessive communicaion bandwidh and cumbesome pocessing in hadwae. Muliple-inpu Muliple-oupu (MIMO) [4] ada is an emeging ada sysem. I is composed of aays of ansmies and eceives, and is Poin Spead Funcion (PSF) is muliplied beween paens of ansmies and eceives. On one hand, MIMO ada can acquie daa fo a sho by using muliple paallel channels, which esuls in a quick image; on he ohe hand, i can achieve he same esoluion using lowe numbe of physical channels making i easily poable, because a coheen MIMO ada uses closely spaced anennas and allows coheen signal evaluaion o impove esoluion. The geaes sengh of an MIMO ada is ha i can pefom well wih fewe hadwae esouces bu a he cos of puing moe buden o sofwae. Theefoe, a kind of sho ange and fas imaging algoihm is a key pa of an MIMO ada used in apid human secuiy insumen. Typical imaging algoihms ae Back Pojecion (BP) [6] and Range Migaion (RM) [5]. The esuls of BP algoihm based on ime and spaial domains ae vey accuae; howeve, i compues so slowly ha i canno saisfy apid imaging equiemens. On he ohe hand, RM algoihm is based on specal domain. I compues quickly and also keeps esul accepably accuae. Theefoe, RM algoihm will be a moe suiable choice o sudy such applicaions. A pesen, hee ae wo kinds of MIMO ada sandad algoihms, viual aay (VA)-RM [7] and MIMO-RM [8]. I is well known ha he phase cene of each goup of ansceives is a viual elemen fo fa-field siuaion. Regading he sho-ange secuiy applicaions, we need o compensae phase cene eo, bu he opion is limied. Since VA-RM algoihm canno saisfy he equiemen of Received 1 Sepembe 2016, Acceped 21 Ocobe 2016, Scheduled 13 Decembe 2016 * Coesponding auho: Zhi-Ping Li (zhiping li@buaa.edu.cn). The auhos ae wih he School of Eleconic and Infomaion Engineeing, Beijing Univesiy of Aeonauics and Asonauics, Beijing, Haidian , China.

2 112 Yang, Shang, and Li sho ange, his algoihm will no be fuhe exploed in his pape. Wheeas, MIMO-RM appoach can achieve fas imaging using Fas Fouie Tansfom (FFT) ove ansmie and eceive aays. Thee have aleady been some papes [8, 12] discussing his appoach; howeve, hey do no explain he physical phenomena in much deail. This pape descibes he physical phenomena of MIMO-RM algoihm and is oganized as follows. Secion 2 pesens he fomulaion of he MIMO ange migaion algoihm and is mahemaical fomulaion. Then he pocess of convoluion is deailed as a pefeed alenaive poducing moe pecise esuls. Secion 3 descibes he algoihm implemenaion and daa pocessing seps, in which we explain he diffeen meanings of FFT ove ansmi aays and FFT ove eceive aays. Secion 4 gives simulaion esuls. Secion 5 is he conclusion. 2. FORMULATION AND OPERATION OF CONVOLUTION The essence of ada imaging is elecomagneic invese scaeing, which means ha ansmi aays send elecomagneic waves o illuminae age which scaes he incoming adiaion. Then, we measue he scaeed field o ge he geomeic chaaceisics of his objec. In ode o quickly compue he poblem, specal domain imaging algoihm based on Discee Fouie Tansfom (DFT) is used commonly. So he ada imaging pocess can be undesood as finding he Fouie ansfom elaionship beween he ada echo daa and he age chaaceisic funcion. The MIMO linea aay imaging geomey is illusaed by Figue 1. The Caesian coodinae sysem O-XZ is esablished. x-axis and z-axis denoe he azimuh and ange diecions, especively. The locaions of he age and anenna ae boh pesened in he coodinae sysem. Assuming ha he age s chaaceisic funcion is A(x 0,z 0 ), he locaions of ansmi and eceive aays ae x and x, especively. Figue 1 shows he wo-way popagaion pah of an MIMO ada sysem. Rx (, x, k) Rk (, k, k) z x ( x0, z0) Rk ˆ(, k ) x z o Rk (, x, k) x Rk (, k, k) exp( jdk z ) Figue 1. Imaging sysem geomey of he linea MIMO aay. Figue 2. Block diagam of pevious mehod of MIMO ange migaion. Accoding o Huygens-Fesnel pinciple [9], MIMO ada echo daa R(x,x,k)isinegalofall age scaes along vaious popagaion diecions. Since we cae abou focus posiion, he following deivaion will ignoe he influence of ampliude. R(x,x,k)= A(x 0,z 0 )e jkr e jkr dx 0 dz 0 (1) x 0,z 0 whee k =2πf/c is he wave numbe wih c denoing he speed of ligh, f he fequency, and he exponenial em epesens a spheical wave popagaion model. R and R ae he disances fom he ansmie and eceive o he age, especively, as given in he following. R = (x x 0 ) 2 +(d + z 0 ) 2 R = (x x 0 ) 2 +(d + z 0 ) 2 (2)

3 Pogess In Elecomagneics Reseach Lees, Vol. 64, whee d is he disance beween ansmi/eceive elemen and he cene of age and z 0 he disance beween he cene of age and ohe poins on age. Fouie ansfom is done along x and x, hen he mehod of saionay phase (MSP) [12] is used o solve inegal as follows: R(k x,k x,k)= A(x 0,z 0 )e jkz(z0+d) e jkxx0 dx 0 dz 0 (3) x 0,z 0 Afe acquiing specal domain daa, he fom of no elaion wih inegal vaiae is moved o he lef of he equaion. R(k x,k x,k)exp(jk z d)= A(x 0,z 0 )e jkxx0 e jkzz0 dx 0 dz 0 (4) x 0,z 0 whee k z = k 2 k 2 x + k 2 k 2 x, k x = k x + k x (wave dispesion elaion). Accoding o wave dispesion elaion, he pevious mehod uses STOLT inepolaion o ansfom 3-D echo daa (k,k,k) o 2-D age spaial specum (k x,k z ), hen consuc he age image using 2-D invese fas Fouie ansfom (IFFT). Figue 2 shows a daa flow diagam of he whole imaging pocess. Howeve, i is achieved by mahemaic pocess. As we can see, i loses 1-D infomaion because igh-hand side of fomula (4) is a 2-D inegal wheeas he lef-hand side is 3-D echo daa. Though descibing MIMO ada imaging pocess, his pape will show he physical pocess of elecomagneic waves popagaion clealy, and explain how o solve he poblem of ansfomaion fom 3-D echo daa o 2-D age spaial specum. The convoluion mehod is esified in he following ex. Figue 3 shows a linea MIMO aay which has seveal ansmies and eceives. In fac, ansmi and eceive anennas ae se in he same line. In ode o pesen he physical pocess of scaeing in wo-way popagaion clealy, ansmies and eceives ae dawn on opposie sides. Moeove, A is an inciden field face and C a scaeing field face, and boh ae close o B age. Tansmies T emi signal (e jkxx, only phase em peseved) which illuminaes he age aea B, and he inciden field is scaeed by he isoopic scae poins in age aea which is eceived by eceive R. R( x, x, k) R( k, k, k ) z k z k R( k, x, k) R( k, k, k) Rˆ( k, k ) x z k exp( jdk z ) age Figue 3. Elecomagneic wave popagaion fo MIMO ada. Figue 4. Block diagam of poposed appoach of MIMO ange migaion.

4 114 Yang, Shang, and Li In ode o discuss he elaion of popagaion of elecomagneic wave, le a epesen inciden field, b epesen age scaeing chaace, and c epesen scaeing field. The FFT noaions of hese vaiables ae A, B and C, which indicae he angula specum of inciden field, age fom and scaeed field, especively. The Fouie ansfom elaions can be expessed as follows: A = FFT(a),B = FFT(b),C = FFT(c) Accoding o scala diffacion heoy [10], he elaion beween field and age chaace is: A B = C whee epesens convoluion. The convoluion can be solved by Fouie ansfom. Moeove, if a is a pue phase em, he following fom is saisfied: b = c a Now he age can be expessed in specum domain as follows: B = C A ( x) (5) Theefoe, he convoluion of C and A ( x) is he soluion of age B. Accoding o he angula specum soluion of Helmholz equaion [11], he inciden field A and scaeed field C can be expessed by he specum of ansmie and eceive signal: A = e jkxx e j k 2 k 2 x (d+z 0) C = R(x,k x,k) e j k 2 k 2 x (d+z 0) Subsiuing hese elaions ino fomula (5), he imaging pocess can be wien as: b= R(x,k xa,k) e j(kx kxa)x dx e j k 2 kxa 2 (d+z0) e j k 2 (k x k xa) 2 (d+z 0 ) dk xa e jkxax 0 dk x dk The fis inegal on x indicaes he coheen supeposiion of all ansmies, and he inegal on ohe vaiables can be seled o saisfy a Fouie elaion as follow: b = R (k x k xa,k xa,k)e jkz(d+z0) e jkxax 0 dk xa dk x dk (6) whee R (k x k xa,k xa,k)= R(x,k xa,k) e j(kx kxa)x dx, k z = k 2 k 2 xa+ k 2 (k x k xa ) 2 In fomula (6), he fis inegal on x is eplaced by Fouie ansfom along ansmies, and e jkzd is consideed as he efeence funcion. A 2-D inegal on k xa and k x is demanded o acquie he inegal of k z. Afe hese pocedues, he age can be solved fom a 2-D Invese Fouie ansfom of R. 3. ALGORITHM IMPLEMENTATION This secion deals wih he pacical implemenaion of he poposed MIMO-RM. The image econsucion pocedue is sepaaed ino seven seps as shown in he flow cha in Figue 4. Because he basic elemen of an MIMO ada is sepaaed ino ansmie-eceive pai, he wo-way popagaion heoy should be aken ino accoun as in he pevious secion. Accoding o fomula (6), he fis sep akes FT along ansmi aays, o calculae he inegal of R. Fo he eceive secion, we use FT o ansfom he incoming echo daa ino is angula specum domain in he second sep, and hen we muliply efeence funcion. The Fouie ansfom elaion beween k z and z 0 can be ealized by STOLT inepolaion fo he discee daa; howeve, k z is deemined by wo vaiables k xa and k x hee and esolved afe he convoluion, hus he STOLT inepolaion mus be opeaed befoe he convoluion pocedue. Theefoe, he fouh sep is 1-D STOLT inepolaion along boh k xa and k x. Nex sep deals wih he convoluion. A discee convoluion can be calculaed by flip and shif of he inpu veco, and he vaiable mus be pojeced o he igh coodinae. As menioned peviously, he ansfom vaiable is k x k xa in he fis sep of FT pocess. To acquie daa se in k x k xa k coodinae fo he convoluion, he esul is pojeced o he coec coodinae hough a flip and shif pocedue fo he discee daa fom if he discee ineval is appopiae. Since he opeaion of flipping has no influence on symmeic daa, his sep is ignoed. Theeby, afe daa shif in he fifh sep, he

5 Pogess In Elecomagneics Reseach Lees, Vol. 64, daa is supeposed along k x o complee he convoluion, which esuls in 2-D daa fom. The final sep is 2-D IFFT o ansfom back o space domain o ge he age. Duing he inepolaion, k z should be a eal value, because he inciden field should be consiued by avelling waves fom he ansmie, so do he consain of he eceived field. Theefoe, he following elaion mus be me; ohewise, he evanescen wave should be ignoed. k 2 k 2, k2 k 2 In pacical implemenaion, he daa ha do no saisfy he cieia in he wavenumbe domain ae valued zeo. Anohe deail is o calculae he convoluion fo discee daa in fomula (6). Tansmi and eceive aays ae fused ino he same gid and sampled wih he same ae and quanizaion, which can be compued by simple shif and summaion. The image of esoluion is deemined by seveal paamees. The ange-diecion esoluion and azimuh-diecion esoluion can be wien especively as: δ z = c 2B δ x = λ cr L T + L R whee B epesens bandwidh, R he disance fom anennas o he age, λ c he cuoff wavelengh, L T he lengh of ansmie aay, and L R he lengh of eceive aay. 4. SIMULATIONS AND ANALYSIS In ode o veify his poposed appoach and explain he confusion of pevious MIMO-RM mehod, his pape gives 1-D aay simulaion esuls fo compaison using MATLAB. The MIMO ada echo daa ae geneaed by using Huygens-Fesnel pinciple o calculae he popagaion phase shif, which can be ecognized as a simplificaion of daa afe mached fileing in eal scenaio. Boh ansmi and eceive apeues of a linea MIMO aay ae locaed a a disance of 1.5 m fom age aea. Boh ansmi and eceive anennas ae spaced wih 0.01 m sep wih a span of 0.44 m in oal, and he numbe of anennas is 45. This indicaes a esolving capabiliy of m in azimuh diecion. The age consiss of a cluse of en poin scaees disibued wihin an aea of 0.1m 0.1m, five poins along azimuh diecion and wo poins along ange diecion. The fequency anges fom 28 GHz o 32 GHz, sampling a oal of 201 poins wih a sep of 20 MHz, which means m of esoluion in ange diecion. Figue 5 compaes he images obained fom pevious mehod and he poposed mehod o show he focusing pefomance. The figue shows ha he scaee poins in he pevious mehod have high side-lobe and ae no focused well. The eason is shown by hei specum in Figue 6. We can see he lack of specum value of he pevious mehod. This is caused by 2-D STOLT inepolaion in 3-D daa, x-azimuh (m) x-azimuh (m) z-ange (m) (a) z-ange (m) (b) Figue 5. Imaging esuls of (a) pevious mehod, (b) poposed mehod.

116 Yang, Shang, and Li 20 40 60 80 100 120 140 160 180 200 20 40 60 80 100 120 140 160 180 200 (a) (b) Figue 6. mehod.

6 116 Yang, Shang, and Li (a) (b) Figue 6. mehod. Specal disibuion diagam afe inepolaion of (a) pevious mehod, (b) poposed Table 1. Compae he pefomance beween pevious and poposed mehod. algoihm/pefomance side-lobe 3dB beam-widh compuaional ime specum pevious mehod 9.96 db s missing poposed mehod db s inegiy because he specum should be calculaed by a cuve inegal in he 3-D specum daa and canno be eplaced by a single value of inepolaion. Howeve, he inegal cuve calculaed in he convoluion pocess in he poposed mehod acquies coec specum of age as shown in Figue 6(b). Table 1 shows he compaison of hese wo mehods. Compaed o he poposed mehod, he side-lobe level is highe and compuaional ime is moe wih he pevious mehod. Pevious mehod consumes moe ime because of 2-D STOLT inepolaion. The specal disibuion of pevious mehod has some zeo values, which esul in high side-lobe level. 5. CONCLUSION This pape pus fowad he pocess of MIMO imaging accoding o physical phenomenon. The convoluion elaion is eviewed o inepe he implemenaion of STOLT inepolaion in MIMO- RMA. The diffeen meanings of FT beween ansmi and eceive aays ae discussed. Finally, he esuls of simulaion of he pevious mehod and poposed appoach ae analyzed. The simulaion demonsaes ha he poposed mehod pefoms well on focusing and is an available algoihm fo MIMO image. REFERENCES 1. Kischne, A. J., J. Guelein, S. Bel, e al., A millimee-wave MIMO ada sysem fo hea deecion in paol o checkpoin scenaios, SPIE Secuiy + Defence, Inenaional Sociey fo Opics and Phoonics, 85440I-85440I-11, Chen, C. C. and H. Candews, Tage-moion-induced ada imaging, IEEE Tansacions on Aeospace & Eleconic Sysems, Vol. 16, No. 1, 2 14, Geenwald, R. A., K. B. Bake, R. A. Huchins, e al., An HF phased-aay ada fo sudying small-scale sucue in he high-laiude ionosphee, Radio Science, Vol. 20, No. 1, 63 79, Li, J. and P. Soica, MIMO ada wih colocaed anennas, IEEE Signal Pocessing Magazine, Vol. 24, No. 5, , 2007.

7 Pogess In Elecomagneics Reseach Lees, Vol. 64, Zhuge, X. and A. Yaovoy, Nea-field ula-wideband imaging wih wo-dimensionalspase MIMO aay, Poc. 4h EuCAP, 1 4, Ap Cui, G., L. Kong, and J. Yang, A back-pojecion algoihm o sepped-fequency synheic apeue hough-he-wall ada imaging, Asian and Pacific Confeence on Synheic Apeue Rada, 2007, Apsa 2007, , Caaa,W.G.,R.S.Goodman,andR.M.Majewski,Spoligh Synheic Apeue Rada Signal Pocessing Algoihms, Aech House, Boson, MA, Zhuge, X. and A. G. Yaovoy, Thee-dimensional nea-field MIMO aay imaging using ange migaion echniques, IEEE Tansacions on Image Pocessing, Vol. 21, No. 6, , Goodman, J. W. and M. E. Cox, Inoducion o Fouie Opics, 2nd Ediion, McGaw-Hill, 66 73, Goodman, J. W. and M. E. Cox, Inoducion o Fouie Opics, 2nd Ediion, McGaw-Hill, 32 42, Goodman, J. W. and M. E. Cox, Inoducion o Fouie Opics, 2nd Ediion, McGaw-Hill, 55 61, Wang, H. J., MIMO ada imaging algoihm, Naional Univesiy of Defense Technology, Dayi, F., R. Boehnke, M. Tesa, e al., Mehod fo displaying an acive ada image and handheld sceening device, US [P], Gonzalez-Valdes, B., Y. Alvaez, S. Manzavinos, e al., Impoving secuiy sceening: A compaison of mulisaic ada configuaions fo human body imaging, IEEE Anennas & Popagaion Magazine, 1 1, 2016.

, on the power of the transmitter P t fed to it, and on the distance R between the antenna and the observation point as. r r t

, on the power of the transmitter P t fed to it, and on the distance R between the antenna and the observation point as. r r t Lecue 6: Fiis Tansmission Equaion and Rada Range Equaion (Fiis equaion. Maximum ange of a wieless link. Rada coss secion. Rada equaion. Maximum ange of a ada. 1. Fiis ansmission equaion Fiis ansmission