An Extended Virtual Aperture Imaging Model for Through-the-wall Sensing and Its Environmental Parameters Estimation

Transcription

1 84 YONGPING SONG, TIAN JIN, BIYING LU, JUN HU, ZHIMIN ZHOU, AN EXTENDED VIRTUAL APERTURE IMAGING MODEL An Extended Vitual Apetue Iaging Model fo Though-the-wall Sensing and Its Envionental Paaetes Estiation Yongping SONG, Tian JIN, Biying LU, Jun HU, Zhiin ZHOU College of Electonics Science and Engineeing, National Univesity of Defense Technology, Changsha, 40073, China Abstact. Though-the-wall iaging (TWI) ada has been given inceasing attention in ecent yeas. Howeve, pio knowledge about envionental paaetes, such as wall thickness and dielectic constant, and the standoff distance between an aay and a wall, is geneally unavailable in eal applications. Thus, tagets behind the wall suffe fo defocusing and displaceent unde the conventional iaging opeations. To solve this poble, in this pape, we fist set up an extended iaging odel of a vitual apetue obtained by a ultiple-input-ultiple-output aay, which consides the aay position to the wall and thus is oe applicable fo eal situations. Then, we pesent a ethod to estiate the envionental paaetes to calibate the TWI, without ultiple easueents o doinant scattees behind-the-wall to assist. Siulation and field expeients wee pefoed to illustate the validity of the poposed iaging odel and the envionental paaetes estiation ethod. Keywods Though-the-wall ada, envionental paaete estiation, vitual apetue, ultiple-input ultipleoutput (MIMO).. Intoduction Though-the-wall sensing is highly desied in any civilian and ilitay applications. Though-the-wall iaging ada (TWIR) achieves good wall penetation by tansitting low-fequency electoagnetic waves and povides iaging desciption of tagets of inteest behind walls [-3] o the inside stuctue and layout of buildings [4-5]. Theefoe, it has attacted oe and oe attention [6-0]. Geneally speaking, two techniques, naely synthetic apetues and vitual apetues, ae adopted in TWIR. Copaed with the synthetic apetue foed by oving ada antennas, the vitual apetue obtained by the ultiple-input ultipleoutput (MIMO) aay can collect iaging data in a uch shote tie and is thus oe applicable fo eal-tie ipleentation. In this pape, we focus on the MIMO aay based TWIR. When electoagnetic waves popagate in a layeed ediu coposed of the ai and wall, eflection and efaction will occu at the ai-wall inteface. This equies though-the-wall iaging (TWI) to conside the non-linea popagation path of electoagnetic waves, whee soe wall paaetes, i.e., wall thickness and dielectic constant, ae equied to deteine the popagation path. Cuently, ost though-the-wall iage foations ae based on the pio knowledge of the afoeentioned wall paaetes [-3]. Howeve, pio knowledge about these wall paaetes is usually unavailable in pactical applications, and the easued o estiated eo of the wall paaetes will geatly affect iaging quality of behind-the-wall tagets [4]. Theefoe, accuate estiation of wall paaetes is an ipotant technique in TWI. The eeging techniques to estiate wall paaetes can be categoized into thee types. Fist, the iage autofocusing ethod seaches the easonable wall paaetes by assessing the iage focusing quality [5]. It is effective but affods heavy coputing buden. To ipove the efficiency, an estiation ethod by iniizing the coss-ange esolution of a special doinant scattee athe than assessing the whole iage was intoduced in [6]. The ethod is invalid if thee ae no doinant scattees behind the wall. Second, the wall paaetes can be estiated by adjusting the aay stuctue [7] o stand-off distance [8], both of which involve exta easueents. Thid, echoes eflected by the wall ae utilized to estiate the wall paaetes. The dielectic constant can be povided by the back and foth popagation tie if the wall thickness is known [9]. Moeove, seaching the axiu of the coelation coefficient between the easued etun and the coesponding estiating etun in diffeent wall paaetes is also valid [0], and the geatest difficulty is the indecisive seaching diection. Instead, using soe special infoation extacted fo echoes caused by the font suface and the ea suface of the wall is oe poising, e.g., the dielectic constant can be estiated using the aplitude infoation of the font suface eflection []. Because the aplitude estiation is easily influenced by noise, a oe pactical ethod is pesented by pefoing tie-delay-only easueents in []; howeve, to achieve adequately high accuacy, it equies adjusting the tansceive-eceive sepaation epeatedly.

2 RADIOENGINEERING, VOL. 3, NO. 3, SEPTEMBER Futheoe, all of the above ethods assue that the TWIR paallels the wall duing data collection in the iaging odel. When the aay is placed close to the wall, the assuption can be easily et. Howeve, in soe applications, e.g., fie escue, standoff opeation is equied. Theefoe, it is necessay to setup a oe easonable odel that consides the distance and inclination angle between the ada and wall. In such an extended iaging odel fo though-the-wall sensing, the unknown paaetes include not only the taditional wall paaetes, i.e., thickness and dielectic constant, but also the distance and the inclination angle. These fou unknown paaetes, denoted as the envionental paaetes in this pape, ae all equied to be estiated in pactical applications. In the next section, an extended iaging odel is poposed to fit the detection situation whee a linea MIMO aay sets in font of a wall with unknown distance and inclination angle. Then, in Section 3, we will show a novel envionental paaetes estiation algoith without any exta easueents o doinant scattes behind-thewall to assist. To ipove the iage quality, an effective copensation iaging ethod fo the poposed iaging odel is intoduced in Section 4. Section 5 & 6 show the coesponding pocessing esults of the siulation and field easued data, which veify the iaging odel and envionental paaetes estiation algoith. Conclusions will be dawn in Section 7.. Extend Vitual Apetue Iaging Model fo TWI The conventional linea MIMO aay though-thewall iaging odel assues an antenna aay stictly paallel to the wall, as shown in Fig.. At this point, the elative position of the antenna aay and the wall can be descibed with only one distance value R, which educes coplexity in iage pocessing. Howeve, in pactice, liiting factos, such as the pobe scene, ake it difficult to ensue that the antenna aay is stictly paallel to the wall, so it is necessay to extend the conventional odel and take into consideation the case in which the wall inclines the antenna aay. Fig.. Conventional linea MIMO aay TWI odel. R When the antenna aay is inclined to the wall, the elative position of aay and the wall needs to be descibed by both the distance and the inclination angle. Fo a linea MIMO aay, the inclination angle can be descibed by one inclination angle θ. Howeve, the aay eleents ae at diffeent distances to the wall. Because the aay stuctue is known, we can conside anywhee in the aay to be the efeence position and use the efeence position s distance to the wall to descibe the distance infoation R fo the aay to the wall. Hee we use the cente of the aay as the efeence position. Suppose we have a linea MIMO aay TWIR with M tansitting eleents and N eceiving eleents. To siplify ou poble, we assue that the aay is only inclined to the wall in the hoizontal plane. Consideing eflection and efaction caused by the wall, the iaging odel can be expessed as Fig.. A' L n C ' O ' Fig.. TWI odel of inclined linea MIMO aay. Fig. shows a tilted linea MIMO aay set in font of a wall with an inclination angle θ. When the left end point of the aay is futhe fo the wall than the ight one, we define 0, othewise 0. Obviously, Donate the th tansitting eleent as th Tx, and the n th eceiving eleent as n th Rx. Then, the distance fo th Tx to the wall is R. Without consideation of the diect wave, the fist two echoes ae caused by the font suface and the ea suface of the wall, and the intesections of thei popagation paths would be th Tx and n th Rx. Donate A to be the location of th Tx, B to be the location of n th Rx, and L n to be thei spacing. C is the font suface echo eflection point, and the coesponding ea suface echo eflection point is D. Thei espective efaction points ae E and F. BH is paallel to the wall. G is the intesection of BH & AE. A' is the idpoint of AG. BB ' is the extension line of FB, and A'B'/ / BH. DO ' A' B ', and C ' is the intesection of DO ' and the font suface. It can be poved that fo the echo popagation path of the font suface: AC CB A' C' C' B' () and fo the echo popagation path of the ea suface: AE ED FD BF A' E ED FD B' F () Futheoe, the spacing of A ' B' is L cos, and the n B '

3 844 YONGPING SONG, TIAN JIN, BIYING LU, JUN HU, ZHIMIN ZHOU, AN EXTENDED VIRTUAL APERTURE IMAGING MODEL distance to the wall is R 0.5 nlnsin. When th Tx is futhe than n th Rx fo the wall,, othewise (See Appendix ). n Thus, fo the echo popagation paths of the font suface and the ea suface, the tilted linea MIMO aay can be equivalent to seveal vitual eleent pais whose connections ae paallel to the wall. 3. Envionental Paaetes Estiation of the Linea MIMO Aay TWI Model Aleady entioned in the intoduction, fo ou poposed linea MIMO aay TWI odel, the envionental paaetes should include the distance of the aay to the wall R, the inclination angle, the wall thickness d and the dielectic constant ε. We will use the conclusions in Section to show the estiation ethod of the envionental paaetes. 3. Estiation of R and θ By the geoetic elationship in Fig. we get: ( ct (, n)) ( L cos ) (R L sin ) (3) f n n n whee, c is the light velocity in ai, and t f (,n) is the font suface echo delay caused by th Tx and n th Rx. It can be futhe conveted to: set then get whee: ct ( n, ) L 4R 4 L R sin (4) n f n n n g n c, (5) t f (, n) Ln E R R, (6) (, sin ) T h (4,4 L ), (7) n n n g h E (8) n n Consideing all the echoes geneated by th Tx, we Accodingly, That is, fo G H E (9) G ) T ( g, g,, g, (0) N H ( h, h,, h ). () E T T T T N E ( H H ) H G. () T T e R e R sin (3) we obtain the estiation of the distance R and the inclination angle on th Tx: Rˆ e. (4) ˆ acsin( e / e ) By pefoing the sae pocessing on the echo data of the eaining M tansitting eleents we will get R ˆ ( R ˆ, R ˆ,, R ˆ ) T, (5) E M ˆ ( ˆ, ˆ,, ˆ ) T. (6) E Taking the aveage of eleents in vecto ˆ E as the final estiation of ˆ : M M M ˆ ˆ. (7) Then, if the left end point of the aay is futhe fo the wall than the ight end point: ˆ ˆ, (8) else ˆ ˆ. (9) Accodingly, Rˆ, which epesents the distance between the aay and wall, can be estiated as: M Rˆ w Rˆ (0) wheein w is the weighting coefficient, which depends on the geoety of the antenna aay. 3. Estiation of d and ε It has been poved in Section that th Tx and n th Rx can be equivalent to a vitual eleent pai fo the echo paths of the font suface and the ea suface. Denoting the vitual eleent pai as 'n', with the estiation Rˆ and ˆ in Section 3., the spacing of 'n' can be expessed as: Lˆ L cosˆ () ' n' and the distance of 'n' to the wall Rˆ ' n' is: Rˆ Rˆ 0.5 L sin ˆ. () n n ' ' n n So that the echo path odel of the vitual eleent pai 'n' can be showed as Fig. 3. Because 'n' is paallel to the wall, we have the following equation [3]: d Lˆ cos ˆ d 0.5 c t (, n) n ' ' ˆ ˆ ˆ d Ln ' ' cos 4Rn ' ' (3) whee t (, n) t (, n) t (, n). (4) d f

4 RADIOENGINEERING, VOL. 3, NO. 3, SEPTEMBER Rˆ ' n ' ' ˆ L ' n ' Fig. 3. The echo path odel of a vitual eleent pai. t (, n) is the ea suface echo delay caused by th Tx and n th Rx. Then, we get: Ap b (5) whee: then: A Lˆ '' cos ˆ Lˆ '' cos ˆ 4Rˆ Lˆ ˆ '' cos ˆ L ˆ ˆ '' cos 4R ˆ L cos ˆ Lˆ ˆ 4Rˆ p b M ' N ' M ' N ' cos d d p p 0.5 ctd(,) 0.5 ctd(,) 0.5 d (, ) '' '' M ' N ' ct M N MN MN n' (6) (7) (8) T T p ( A A) A b. (9) Finally, we can obtain the estiates of the left two envionental paaetes: dˆ p, (30) ˆ p p. (3) 4. Copensation Iage Foation Based on the Extended Vitual Apetue Iaging Model / Vitual apetue ada, such as MIMO ada using ulti-eleents, geatly ipoves detection pefoance. Accodingly, the iaging odel becoes oe coplicated, which akes any taditional synthetic apetue ada iaging algoiths no longe applicable [4]. Due to the absence of any estictions on the antenna aay, the BP algoith is widely used in vitual apetue ada iaging systes. We will use the envionental paaetes estiated in Section 3 to show the copensation BP algoith fo the extended vitual apetue iaging odel. The BP algoith eplaces phase copensation by calculating the exact popagation delay of the taget to the antenna eleents [5]. In taditional though-the-wall BP iaging algoith, the antenna aay cente is usually set as the oigin, wheeas the aay itself is the abscissa. The diection pependicula to the linea MIMO aay is the odinate. We nae this coodinate syste the antennacoodinate-syste. Coespondingly, the coodinate syste that sets the font suface of the wall as the hoizontal axis and the wall pependicula as the longitudinal axis is called the wall-coodinate-syste. The pupose of TWI is usually to descibe tagets behind the wall. When the tagets position infoation is elative to the wall, intepetation of tagets is easie. Theefoe, using the wall-coodinate-syste to show the esults of TWI is oe suitable. Assuing the aay cente is located in the cente on the connection of th Tx and n th Rx, we can obtain the TWI odel in the wall-coodinatesyste: Ai y Rea suface Wall ˆd 墙体 (0,0) E F Ai x i ni Font suface B n Th Rx A (0.5L ˆ ˆ ˆ th n cos, R nln sin ) Tx ( 0.5L cos ˆ, ˆ n R ) Fig. 4. TWI odel in wall-coodinate-syste. C (x, y) Accoding to the BP algoith, the iage value I(x,y) of a point taget (x,y) behind the wall could be calculated as follows: n TE M N I( x, y) s ( t (, n)) (3) n n whee, s ( t (, n)) epesents the sapling at tie t TE (, n) in the echo geneated by th Tx and n th Rx. t TE (, n) is the popagation delay fo the point taget to n. As shown in Fig. 4, (, n) can be obtained as: t TE t TE TE lac lbc (, n) (33) c

5 846 YONGPING SONG, TIAN JIN, BIYING LU, JUN HU, ZHIMIN ZHOU, AN EXTENDED VIRTUAL APERTURE IMAGING MODEL l AC is the popagation path fo the taget to th Tx, and l BC is the popagation path fo the taget to n th Rx. The key to obtaining l AC and l BC is to deteine the position of efaction points E and F in Fig. 4. Using the estiated thickness and dielectic constant of the wall, a quatic equation with one unknown quantity can be ceated to obtain the analytical solutions of the efaction point accoding to Snell's law [6] o to seach fo the location of efaction points by the iniu tie citeia [7]. Both algoiths have high accuacy but costly calculations. To avoid calculation esouce depletion in solving the exact solutions, l AC can be appoxiated by the expession [3]: l AC ˆ d( ˆ sin cos ) (34) AC whee AC is the staight-line distance fo the taget to th Tx, and i is the incident angle of l AC. i can be appoxiately obtained by: x 0.5L cos ˆ n i actan( ). (35) y Rˆ Siilaly: l BC ˆ d( ˆ sin cos ) (36) BC whee BC is the staight-line distance fo the taget to n th Rx, and ni is the incident angle of l BC. In suay, fo the point taget ( x, y) in the iaging scene, set: ˆ d( ˆ sin cos ), (37) ˆ i d( ˆ sin cos ), (38) n then the popagation delay in the echo geneated by th Tx and n th Rx is calculated as follows: AC BC n tte (, n) (39) c whee is a scale facto to distinguish the positional elationship between the point taget and the wall: ni i 0, y 0 y/ dˆ, 0 ydˆ, y dˆ ni i ni i ni (40) Cobining foula (3), the pixel value on (x,y) can be obtained. By tavesing evey point in the iaging scene we can achieve the copensated iage fo the entie scene. Copaed with conventional algoiths, the coputation geatly educes. 5. FDTD Siulations Finite-diffeence-tie-doain (FDTD) siulations ae conducted to test the pefoance of ou ethod. The MIMO aay can be egaded as seveal associated singleinput ultiple-output (SIMO) aays. To siplify the siulating coplexity, a SIMO aay is set in font of the wall: Fig. 5. The siulating scene. It is excited by a Gaussian deivative pulse with 0.6 ns width. The white noise is added to the siulating echoes. The signal to noise atio (SNR) is 5 db. The estiation esults ae shown in Tab. and Tab.. () ˆ( ) R ˆ() d ˆ() ˆ Tue value Tab.. Estiation esults of the siulation data when R =.4. R () R ˆ() ˆ( ) d ˆ() ˆ Tue value Tab.. Estiation esults of the siulation data when θ = 5. The esults ae satisfactoy. To indicate the benefits of ou vitual apetue iaging odel, an iaging pocess is pefoed on the siulation data of R =.4 and θ = 5 : Range / Coss / Fig. 6. BP iaging unde the antenna-coodinate-syste

6 RADIOENGINEERING, VOL. 3, NO. 3, SEPTEMBER Without consideing the aay position to the wall, diect BP iaging has to be pefoed on the antennacoodinate-syste, esulting in whole scene bias. To ake the scene easie to undestand, the wall-coodinate-syste should be built with the envionent paaetes R and ˆ : Range / Fig. 0. Expeient layout Coss / 0.5 Fig. 7. BP iaging unde the wall-coodinate-syste. Then, the defocusing and displaceent of the taget behind the wall can be fixed by the left two envionent paaetes d and ˆ : Range / Coss / 0.5 Fig. 8. BP iaging based on the extended vitual apetue iaging odel. Finally, benefiting fo the extended vitual apetue iaging odel, the quality of TWI is successfully enhanced. The antenna aay and the st wall ae cente-aligned. The distance fo the aay cente to the wall is, and the easued inclination angle is 3.. The thickness of the st wall is 0.8, but the dielectic constant is unknown. In addition, thee is a etal beaing in the cente of the st wall, and we will see its shadowing effect in the late iaging esult. The deivation in Section 3 shows that the envionental paaetes estiation depends on the echo tie delay estiation of the font suface and ea suface. Fo the font suface echo, thee ae only eflections on the aiwall inteface, so the dispesion effect is not seious. Theefoe, by extacting the peak position of the echo pocessed by the atched-filte, we can obtain an effective echo tie delay estiation of the font suface. Afte the echo tie delay estiation of the font suface is finished, we can obtain the elative position of the aay and the st wall by R and ˆ. Using these two envi- onental paaetes to build the wall-coodinate-syste, we can achieve the BP iaging esult without copensation, as shown in Fig.. To validate the poposed iaging odel and envionental paaete estiation algoith, we have designed a vehicle vitual apetue ada syste with tansitting eleents and eceiving eleents. The tansitted signal is a stepping-fequency signal fo 0.5 GHz to 3 GHz, and the step fequency is MHz. The expeient scene and coesponding layout ae shown in Fig. 9 and Fig. 0. Range / 6. Measueent Results st wall font suface Vitual apetue ada syste Fig. 9. The vehicle vitual apetue ada syste and expeient scene. Fig.. BP iaging esult without copensation unde the wall-coodinate-syste. In Fig., we obtain a elatively clea iage of the building s inne stuctue. To show the poposed envionental paaetes in this pape, we pay close attention to the st wall and the nd wall. By the shielding effect of the etal beaing, we find that the st wall ea suface and the

7 848 YONGPING SONG, TIAN JIN, BIYING LU, JUN HU, ZHIMIN ZHOU, AN EXTENDED VIRTUAL APERTURE IMAGING MODEL nd wall have suffeed diffeent degees of fault. Then, the ange position of the nd wall font suface unde the wallcoodinate-syste should be 4.6 fo Fig. 6. Howeve, it is appoxiately 5.0 in Fig.. That is to say, the nd wall font suface lags 0.38 because of the st wall. The st wall thickness is 0.8 ; thus, the deduced dielectic constant is This value can be used as a efeence value to assess the final estiation esult. When estiating the echo tie delay of the st wall ea suface, we have to conside the dispesion effect caused by the wall. Dispesion educes the coelation between the echo and tansitting signal geatly, and this eans that we cannot obtain an effective estiation of the st wall ea suface echo tie delay fo the taditional atched-filteing echo [8]. Potiva et al. poposed that the echo tie-delay can be estiated by subspace decoposition on the deconvoluted echo data [9]. Based on this idea and efeencing the fequency doain deconvolution ethods, which ae widely used in ultasonic detection [30], we adopt the fequency doain Wiene invese filte to coplete deconvolution of the oiginal echo data. Then, the axiu entopy (ME) powe spectu [3] is used to estiate the echo tie delay of the st wall ea suface. Fig. 3. Copensation BP iaging esult. The iage entopy is coonly used to evaluate the iage quality [3], and its definition is as follows: ( x y H 4 x y I( x, y) ) I( x, y). (4) Usually, the salle H is, the bette the iage quality is. Then, we use iage entopy to evaluate the iage with/without copensation, and the esults ae shown in Tab. 4. Noalized Aplitude Iage without Iage with copensation copensation Iage entopy Tab. 4. The copaison of the iage entopy in the iage with/without copensation. Cobining Fig. 3 and Tab. 4, we find that by the copensation of envionental paaetes, the position deviation of the scene behind the oute wall has been effectively coected, and the iage quality has also ipoved. Fig.. Tie delay estiation. Fig. shows the esults of tie delay estiation. With the help of deconvolution, the st wall ea suface echo becoes easy to identify in the ME powe spectu. Then, fo Section 3., the wall thickness and dielectic constant can be estiated. The whole envionental estiation esults ae shown in Tab. 3. R () ( ) d () Estiates Tue value Relative eo -0.68% 9.97% 3.00% -5.9% Tab. 3. Estiation esults of the envionental paaetes. Finally, we use these envionental paaetes to obtain the copensation BP iaging fo the echo data: 7. Conclusion In this pape, an extended though-the-wall iaging odel and its associated envionental paaetes estiation algoith ae pesented fo the vitual apetue ada syste. Because it has no special equieents fo the aay attitude, this iaging odel is oe suitable fo the actual situation. Siultaneously, without any exta easueents o behind-the-wall doinant scattees to assist, the envionental paaetes estiation algoith is of low coputational coplexity and easy to ipleent. The pocessing esults of the easued data show the ipoveents to the though-the-wall iaging. Futheoe, the envionental paaetes estiation algoith is tested on a single wall. In fact, it has the potential to estiate the paaetes of ulti walls, and this will be ou futue wok.

8 RADIOENGINEERING, VOL. 3, NO. 3, SEPTEMBER Acknowledgeents This wok is suppoted in pat by the National Natual Science Foundation of China unde Gant 6744 and 6376, and the eseach poject of National Univesity of Defense Technology unde Gant CJ Appendix We entioned in Section that the eleent pai AB, which inclines the wall, can be equivalent to a vitual eleent pai A ' B', which paallels the wall. Hee, we will pove this. Befoe poving, we eaffi the elevant definitions and assuptions: th Tx is located at A, and its distance to the wall is n th Rx is located at B, and the length of AB is L n. R. To siplify the poving pocess, we define that n when th Tx is futhe than n th Rx fo the wall. Othewise, n. Fig. 4. The font suface echo path. Fig. 4 shows the echo path of the font suface AK, and BH is paallel to the wall. K is the intesection of CB s extension line and AK. I is the intesection of BH and AC. P is the idpoint of AH, and B is the idpoint of BK. BJ AK. A is the intesection of B P and AI, and Q is the intesection of B P and BJ. CO B P. eflection law AC = KC & IC BC AI KB P & B ae the idpoints of AH & BK, espectively. PB // AK // BH A & Q ae the idpoints of AI & BJ, espectively. AA BB Then, we have: AC BC AC BC (4) Theefoe, AB is equivalent to A B fo the length of the ea suface echo path. Futheoe: APA BQB. (43) Then, fo the isosceles A CB AB PQ L cos, (44) R P A' n OC R 0.5 L sin. (45) n n C ' O' Fig. 5. The ea suface echo path. Fig. 5 shows the echo path of the ea suface. AK ' & BH ae paallel to the wall. K ' is the intesection of AK and the extension line of FB. G is the intesection of BH and AE. BJ ' AK, P& B ' ae the idpoints of AH & BK ', espectively. A ' is the intesection of BP ' and AG, and Q ' is the intesection of BPand ' BJ '. D is the eflection point on the ea suface, DO ' BH, and C ' is the intesection point of DO ' and the font suface. eflection law & efaction law AE K' F & GE BF AG BK' P & B ae the idpoints of AH & PB ' // A' K // BH Q ' J' B' K ' BK ', espectively. A ' & Q ' ae the idpoints of AG & BJ ', espectively. AA' BB' Then, we have: AE ED FD BF A' E ED FD B ' F (46) Theefoe, AB is equivalent to A B fo the length of the ea suface echo path. Futheoe: Then, fo the isosceles ACB : APA BQB. (47) AB ' ' PQ' L cos, (48) n OC ' ' R 0.5 L sin. (49) n n Accoding to (44) and (45), we get:

9 850 YONGPING SONG, TIAN JIN, BIYING LU, JUN HU, ZHIMIN ZHOU, AN EXTENDED VIRTUAL APERTURE IMAGING MODEL Consequently: ACB A CB. (50) AC BC AC BC A' C' B' C'. (5) So, AB is equivalent to A' B ' fo the length of the font suface echo path. In suay, fo the path length of the echo fo font and ea suface, th Tx and n th Rx, whose connection AB inclines the wall, can be equivalent to a vitual eleent pai A' B ', which paallels the wall. The equivalent spacing is Ln cos, and the equivalent distance to the wall is R 0.5 nlnsin while n when th Tx is futhe than n th Rx away fo the wall. Othewise, n. Refeences [] CHETTY, K., SMITH, G. E., WOODBRIDGE, K. Though-thewall sensing of pesonnel using passive bistatic wifi ada at standoff distances. IEEE Tansactions on Geoscience and Reote Sensing, 0, vol. 50, no. 4, p [] SU, Y. J. The eseach on eceive technology of the though-thewall suveillance ada. Jounal of China Acadey of Electonics and Infoation Technology, 0, vol. 6, no. 6, p [3] LI, J., ZENG Z., SUN, J., LIU, F. Though-wall detection of huan being's oveent by UWB ada. IEEE Geoscience and Reote Sensing Lettes, 0, vol. 9, no. 6, p [4] AFTANAS, M., DRUTAROVSKY, M. Iaging of the building contous with though the wall UWB ada syste. Radioengineeing, 009, vol. 8, no. 3, p [5] CHANG, P. C. Physics-based invese pocessing and ulti-path exploitation fo though-wall ada iaging. Docto of Philosophy Thesis. USA, Ohio State Univesity, 0. [6] BARANOSKI, E. J. Though-wall iaging histoical pespective and futue diections. In Poceedings of the IEEE Intenational Confeence on Acoustics, Speech and Signal Pocessing. Las Vegas (USA), 008, p [7] SISMA, O., GAUGUE, A., LIEBE, CH., OGIER, J. M. UWB ada: vision though the wall. Telecoun. Syst., 008, vol. 38, no. -, p [8] SONG, L. P., YU, C., LIU, Q. H. Though wall iaging (TWI) by ada: -D too gaphic esults and analyses. IEEE Tansactions on Geoscience and Reote Sensing, 005, vol. 43, no., p [9] DEBES, C., AMIN, M. G., ZOUBIR, A. M. Taget detection in single- and ultiple-view though-the-wall ada iaging. IEEE Tansactions on Geoscience and Reote Sensing, 009, vol. 47, no. 5, p [0] SHOUHEI, K., TAKUYA S., TORU, S. High esolution 3-D iaging algoith with an envelope of odified sphees fo UWB though-the-wall adas. IEEE Tansactions on Antennas and Popagation, 009, vol. 57, no., p [] BROWNE, K. E., BURKHOLDER, R. J., VOLAKIS, J. L. Fast optiization of though-wall ada iages via the ethod of Lagange ultiplies. IEEE Tansactions on Antennas and Popagation, 03, vol. 6, no., p [] CHEN, P. H., NARAYANAN, R. M. Shifted pixel ethod fo though-wall ada iaging. IEEE Tansactions on Antennas and Popagation, 0, vol. 60, no. 8, p [3] WANG, Y., FATHY, A. E. Advanced syste level siulation platfo fo thee-diensional UWB though-wall iaging SAR using tie-doain appoach. IEEE Tansactions on Geoscience and Reote Sensing, 0, vol. 50, no. 5, p [4] LIU, X., LEUNG, H., LAMPROPOULOS, G. A. Effect of wall paaetes on ulta-wideband synthetic apetue though-the-wall ada iaging. IEEE Tansactions on Aeospace and Electonic Systes, 0, vol. 48, no. 4, p [5] LI, L., ZHANG, W., LI, F. A novel autofocusing appoach fo eal-tie though-wall iaging unde unknown wall chaacteistics. IEEE Tansactions on Geoscience and Reote Sensing, 00, vol. 48, no., p [6] JIN, T., CHEN, B., ZHOU, Z. Iage-doain estiation of wall paaetes fo autofocusing of though-the-wall SAR iagey. IEEE Tansactions on Geoscience and Reote Sensing, 03, vol. 5, no. 3, p [7] WANG, G. Y., AMIN, M. G. ZHANG, Y. M. New appoach fo taget locations in the pesence of wall abiguities. IEEE Tansactions on Aeospace and Electonic Syste, 006, vol. 4, no., p [8] WANG, G. Y., AMIN, M. G. Iaging though unknown walls using diffeent standoff distances. IEEE Tansactions on Signal Pocessing, 006, vol. 54, no. 0, p [9] SAGNARD, F., ZEIN, G. E. In situ chaacteization of building ateials fo popagation odeling: fequency and tie esponses. IEEE Tansactions on Antennas and Popagation, 005, vol. 53, no. 0, p [0] LI, X., HUANG, X., JIN, T. Estiation of wall paaetes by exploiting coelation of echoes in tie doain. Electonics Lettes, 00, vol. 46, no. 3, p [] AFTANAS, M., SACHS, J., DRUTAROVSKY, M., KOCUR, D. Efficient and fast ethod of wall paaete estiation by using UWB ada syste. Fequenz Jounal, 009, vol. 63, no. -, p [] PROTIVA, P., MRKVICA, J., MACHAC, J. Estiation of wall paaetes fo tie-delay-only though-wall ada easueents. IEEE Tansactions on Antennas and Popagation, 0, vol. 59, no., p [3] JIN, T., CHEN, B., ZHOU, Z. Estiation of wall paaetes fo cognitive iaging in though-the-wall ada. In Poceedings of the 0 IEEE th Intenational Confeence on Signal Pocessing. Beijing (China), 0, p [4] MCCORKLE, J. W. Focusing of synthetic apetue ulta wideband data. In Poceedings of the IEEE Intenational Confeence on Systes Engineeing. Dayton (USA), 99, p. 5. [5] WANG, H. J., HUANG, C. L., LU, M., SU, Y. Back pojection iaging algoith fo MIMO ada. Systes Engineeing and Electonics (China), 00, vol. 3, no. 8, p [6] AHMAD, F., AMIN, M. G., KASSAM, S. A. Synthetic apetue beafoe fo iaging though a dielectic wall. IEEE Tansactions on Aeospace and Electonic Systes, 005, vol. 4, no., p [7] JIA, Y., KONG, L., YANG, X. Ipoved coss-coelated backpojection algoith fo though-wall-ada iaging. In Poceedings of the 03 IEEE Rada Confeence. Ottawa (Canada), 03, p. 3. [8] WEISS, L. G. Wavelets and wideband coelation pocessing. IEEE Signal Pocessing Magazine, 994, vol., no., p [9] PROTIVA, P., MRKVICA, J., MACHAC, J. Tie delay estiation of UWB ada signals backscatteed fo a wall. Micowave & Optical Technology Lett., 0, vol. 53, no. 6, p. 444 to 450. [30] ALI, M. G. S., ELSAYED, N. Z., EBEID, M. R. Signal pocessing of ultasonic data by fequency doain deconvolution. Walailak

10 RADIOENGINEERING, VOL. 3, NO. 3, SEPTEMBER Jounal of Science and Technology, 03, vol. 0, no. 3, p. 97 to 304. [3] QIU, T. S., WANG, H. Y. A high tie delay estiation based on the axiu entopy powe spectu estiation. Jounal of Electonics (China), 997, vol. 4, no. 3, p [3] LI, L., ZHANG, W., LI, F. A novel autofocusing appoach fo eal-tie though-wall iaging unde unknown wall chaacteistics. IEEE Tansactions on Geoscience and Reote Sensing, 00, vol. 48, no., p About Authos... YONGPING SONG eceived his B.S. degee in Electonic Engineeing fo the National Univesity of Defense Tech- nology, Changsha, China in 0, and now he is studying fo the M.S. degee in Infoation and Counication Engineeing. His eseach inteests include ada iaging and autoatic taget detection. TIAN JIN eceived B.S., M.S. and Ph.D. degees in Infoation and Counication Engineeing fo the National Univesity of Defense Technology, Changsha, China, in 00, 003, and 007, espectively. He is cuently an associate pofesso of the National Univesity of Defense Technology. His Ph.D. dissetation was awaded as the National Excellent Doctoal dissetation of China in 009. His fields of inteest include ada iaging, autoatic taget detection, and achine leaning.