Multistatic Measurements in a Controlled Laboratory Environment

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1 Multstatc Measurements n a Controlled Laboratory Envronment Ivan Bradarc *, Gerard. Capraro *, Steven H. Brady +, Mchael A. Savlle + and Mchael C. Wcks^ * Capraro echnologes, Inc., Utca, NY, USA + Department of Electrcal and Computer Engneerng, Ar Force Insttute of echnology, Wrght-Patterson AFB, OH, USA ^ U. S. Ar Force Research Laboratory, Sensors Drectorate, USA Abstract In recent years, a novel mathematcal framework for analyzng and desgnng multstatc radar systems has been proposed. It was argued through numerous smulaton examples that multstatc radar system performances can be sgnfcantly mproved by shapng the multstatc ambguty functon. Based on ths framework, rules for waveform selecton, sensor postonng and adequate weghtng of dfferent recevers have been developed. In ths work, we present multstatc measurements obtaned n a controlled laboratory envronment to support some of these recent fndngs and conclusons. he expermental setup conssts of a Lab-Volt M radar system operatng at X-band, ektronx arbtrary waveform generator and ektronx dgtal osclloscope. Multstatc pont target radar measurements for dfferent system confguratons are analyzed. I. INRODUCION he ambguty functon s a wdely used tool for the analyss of radar systems. In recent years there have been consderable efforts to formulate the ambguty functon for bstatc and multstatc radar systems. In [1], the authors developed the ambguty functon for bstatc radar systems. hs work was extended n [2] to the case of multstatc radar systems. In [3-6], the multstatc ambguty functon was used for assessng waveform selecton, sensor postonng and coherent sgnal processng strateges. It was demonstrated through smulatons that multstatc radar system performances can be mproved by adequately shapng the multstatc ambguty functon. In ths work, we try to substantate some of the fndngs and conclusons presented n the above mentoned papers. o accomplsh ths goal we collect and analyze multstatc measurements obtaned n a controlled laboratory envronment. he expermental setup s desgned to replcate the system assumptons made n the prevous smulatons. he paper s organzed as follows. In Secton II, we brefly outlne the basc mathematcal concepts behnd the multstatc ambguty functon. In Secton III we revew some smulaton examples used to llustrate the sgnfcance of the multstatc ambguty functon. Expermental setup used for collectng the multstatc measurements s descrbed n Secton IV. In Secton V, we analyze the obtaned measurements and nvestgate how they relate to the smulaton results. Fnally, n Secton VI we provde concludng remarks. II. MULISAIC AMBIGUIY FUNCION We consder a sngle transmtter multple recever radar system and assume that a coherent processng nterval conssts of a sngle pulse s () t gven as: { j t} () () c s t = 2E Re f% t e ω, 0 t (1) d where Re{} denotes the real part operator, f% () t s the complex envelope of the transmtted pulse, E and d are the energy and duraton of the pulse, respectvely, and ωc = 2π fc s the carrer frequency. Let the complex envelope of the th recever nput ( = 1, 2,..., N) be denoted by r% () t. Accordng to whether a target s absent (H o ) or present (H 1 ), the two hypotheses are presented as () = () j t () = ( τ ) ω + () H : r% t n% t H r t a s t e n t 0 Da 1 : % % % a % where a% s a complex gan whch accounts for propagaton and scatterng effects along the th path between the transmtter, target and the th recever. τ a and ω Da denote the actual total delay and Doppler shft experenced by the transmtted sgnal along the th path, and n% () t denotes the complex envelope of the addtve nose present at the th recever nput. Assumng addtonally that the envelopes n% () t are complex Gaussan random processes wth zero-mean and whte n quadrature components wth power spectral denstes N 0 2, the sgnal at the output of the matched flter of the th recever becomes (2) /10/$ IEEE

2 Report Documentaton Page Form Approved OMB No Publc reportng burden for the collecton of nformaton s estmated to average 1 hour per response, ncludng the tme for revewng nstructons, searchng exstng data sources, gatherng and mantanng the data needed, and completng and revewng the collecton of nformaton. Send comments regardng ths burden estmate or any other aspect of ths collecton of nformaton, ncludng suggestons for reducng ths burden, to Washngton Headquarters Servces, Drectorate for Informaton Operatons and Reports, 1215 Jefferson Davs Hghway, Sute 1204, Arlngton VA Respondents should be aware that notwthstandng any other provson of law, no person shall be subject to a penalty for falng to comply wth a collecton of nformaton f t does not dsplay a currently vald OMB control number. 1. REPOR DAE MAY REPOR YPE 3. DAES COVERED to ILE AND SUBILE Multstatc Measurements n a Controlled Laboratory Envronment 5a. CONRAC NUMBER 5b. GRAN NUMBER 5c. PROGRAM ELEMEN NUMBER 6. AUHOR(S) 5d. PROJEC NUMBER 5e. ASK NUMBER 5f. WORK UNI NUMBER 7. PERFORMING ORGANIZAION NAME(S) AND ADDRESS(ES) Ar Force Insttute of echnology,department of Electrcal and Computer Engneerng,Wrght-Patterson AFB,OH, PERFORMING ORGANIZAION REPOR NUMBER 9. SPONSORING/MONIORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONIOR S ACRONYM(S) 12. DISRIBUION/AVAILABILIY SAEMEN Approved for publc release; dstrbuton unlmted 11. SPONSOR/MONIOR S REPOR NUMBER(S) 13. SUPPLEMENARY NOES See also ADM Presented at the 2010 IEEE Internatonal Radar Conference (9th) Held n Arlngton, Vrgna on May Sponsored n part by the Navy. 14. ABSRAC In recent years, a novel mathematcal framework for analyzng and desgnng multstatc radar systems has been proposed. It was argued through numerous smulaton examples that multstatc radar system performances can be sgnfcantly mproved by shapng the multstatc ambguty functon. Based on ths framework, rules for waveform selecton, sensor postonng and adequate weghtng of dfferent recevers have been developed. In ths work, we present multstatc measurements obtaned n a controlled laboratory envronment to support some of these recent fndngs and conclusons. he expermental setup conssts of a Lab-VoltM radar system operatng at X-band, ektronx arbtrary waveform generator and ektronx dgtal osclloscope. Multstatc pont target radar measurements for dfferent system confguratons are analyzed. 15. SUBJEC ERMS 16. SECURIY CLASSIFICAION OF: 17. LIMIAION OF ABSRAC a. REPOR unclassfed b. ABSRAC unclassfed c. HIS PAGE unclassfed Same as Report (SAR) 18. NUMBER OF PAGES 5 19a. NAME OF RESPONSIBLE PERSON Standard Form 298 (Rev. 8-98) Prescrbed by ANSI Std Z39-18

d ~ r () t N 0 ~ ( t τ ) * jω t = f H e DH dt * where f % () t denotes complex conjugate of f % () t, and τ H and ω DH denote the hypothetcal total delay and Doppler shft experenced by the transmtted

he ambguty functon for the th recever becomes [2] ( τ, τ, ω, ω ) Θ = H a DH Da 2 * j( Da DH ) t f% ω ω ( t τa ) f% ( t τ H ) e dt = (3).

3 d ~ r () t N 0 ~ ( t τ ) * jω t = f H e DH dt * where f % () t denotes complex conjugate of f % () t, and τ H and ω DH denote the hypothetcal total delay and Doppler shft experenced by the transmtted sgnal assumng a target present n the radar cell under test. Sgnals d, = 1, 2,..., N, represent local statstcs obtaned at each recever. he ambguty functon for the th recever becomes [2] ( τ, τ, ω, ω ) Θ = H a DH Da 2 * j( Da DH ) t f% ω ω ( t τa ) f% ( t τ H ) e dt = (3). (4) he global ambguty functon s then gven as a weghted sum of the bstatc ambguty functons: concentrate on target poston only. hus, the multstatc ambguty functon wll be presented as a functon of x and y coordnates only. III. SIMULAION RESULS We wll now llustrate the multstatc ambguty functon usng the example borrowed from [5]. Let us consder a 2-D multstatc system confguraton wth 4 recevers and one transmtter as shown n Fgure 1. N Θ τ, τ, ω, ω = Θ,,, (5) ( ) c ( τ τ ω ω ) where H a DH Da H a DH Da = 1 [ τ 1, τ 2,, τ ] = [ τ 1, τ 2,, τ ] [ ω 1, ω 2,, ω ] [ ω, ω,, ω ] τ = K, H H H HN τ K, a a a an ω = K, DH DH DH DHN ω = K Da Da1 Da2 DaN and c, = 1,..., N are the weghtng coeffcents that satsfy the relatonshp c = 1. N = 1 he ambguty functon (,,, ) Θ τ τ ω ω for a H a DH Da gven target (fxed τ a and ω Da ) s a 2N - dmensonal functon. Snce we are ultmately nterested n target poston (defned by ts coordnates, e.g. x, y and z ) and ts velocty vector (defned by ts components, e.g. x&, y& and z& ) t s more practcal to express the ambguty functon as a functon of these quanttes. he hghly nonlnear nature of mappng between the delays and Doppler shfts on one hand, and target coordnates and ts velocty vector components on the other, makes the analyss of multstatc radar systems especally challengng and the system geometry very mportant. It should be ponted out that ths nonlnearty does not exst n monostatc radar systems. hus, to smplfy the analyss, but more mportantly, to account for the system geometry when formulatng the multstatc ambguty functon, we algn all recevers wth respect to the target poston and velocty. In addton, n order to vsualze the problem we usually select two fxed dmensons to present the multstatc ambguty functon. In ths paper, we wll consder 2-D system geometres and Fgure 1. Multstatc system geometry Wthout the loss of generalty, the target s placed at the orgn (labeled gt), four recevers are shown as R, = 1, 2, 3, 4 and the transmtter s shown as. he dstance between the target and all the sensors (transmtter and recevers) s assumed to be 10 km. Assume that we are nterrogatng a relatvely small area (100m x 100m) as compared to dstances between the sensors and that range resoluton s our prmary concern. In ths example the transmtted waveform s a sngle pulse Barker 13 waveform wth the pulse wdth of 44 ns. We wll also assume that all recevers are weghted equally (a reasonable assumpton snce all dstances are the same). he multstatc ambguty functon (presented n x-y plane) s shown n Fgure 2, whle the correspondng 3-dB man lobe contour plot s shown n Fgure 3. Fgure 2. Multstatc ambguty functon /10/$ IEEE

Fgure 3. Multstatc ambguty functon (3-dB contour plot) he area of the 3-dB man lobe contour n ths example s 0.7886 m 2.

4 Fgure 3. Multstatc ambguty functon (3-dB contour plot) he area of the 3-dB man lobe contour n ths example s m 2. Note that a 3-dB area of the multstatc ambguty functon s closely related to the resoluton of the correspondng multstatc radar system. Let us now consder a scenaro where postons of all recevers are fxed, whle the poston of the transmtter can change as long as the dstance from the orgn remans the same (10 km). In partcular, let us move the transmtter along the arc shown n Fgure 4. Fgure 4. Multstatc system geometry (movng transmtter) Fgure 5 shows the 3-dB man lobe contour area results for dfferent transmtter postons (angle α was vared between 0 and π/2 (see Fgure 4)). As can be seen n Fgure 5, n order to acheve the best range resoluton, the transmtter should be placed rght n the mddle between recevers R 1 and R 2. As the transmtter moves closer to one of the recevers, the range resoluton deterorates (note that α = 0.05π n Fgure 3). hs s a somewhat expected result that we wll try to verfy and substantate wth real measurements. Fgure 5. 3-dB man lobe area results (movng transmtter) IV. EXPERIMENAL SEUP Our measurement equpment conssts of a Lab-Volt M radar system operatng at X-band, ektronx arbtrary waveform generator (AWG) and a ektronx dgtal osclloscope. he Lab-Volt M s descrbed n detal n [7], and provdes many of the basc components needed for tmng and synchronzaton of the Sngle Input Multple Output (SIMO) system that s of nterest here. ektronx arbtrary waveform generator creates the phase coded baseband sgnals, the Lab- Volt X-band source, antennas, synchronzer, and target postoner are combned wth addtonal mxers and flters to form the radar front end, and the ektronx dgtal osclloscope serves as the dgtal recever. he complete system s presented n a companon paper [8]. he hgh-speed samplng capablty allows data capture at rado frequences (RF) and baseband converson s performed dgtally n MALAB. As the bstatc recever s repostoned around the crcle, the transmt waveform s rebroadcast so that subsequent measurements can be assembled as f N recevers were smultaneously operated. hs approach essentally smulates a sngle transmtter multple recever operaton and the data can be used to support varous SIMO sgnal processng algorthms. he measurement equpment s shown n Fgure 6. o meet our goal of closely matchng the smulaton assumptons made n [5] the system s confgured as shown n Fgure 7. At the center of the crcle n Fg. 7 s a pont target (1-n metal sphere). he prmary recever s co-located wth the transmtter n a monostatc confguraton and the remanng recevers are postoned at multple locatons around the crcle. As depcted n Fg. 7, the partcular set up only supports two smultaneously operated receve channels. However, by keepng the transmt path and waveform exactly the same (a dstnct advantage of usng the AWG), we can reposton the secondary recever and repeat the experment to obtan N dfferent receve locatons. hs process smulates N smultaneously operated recevers and serves as a way to scale the measurement for the laboratory envronment that may otherwse suffer mutual couplng effects between the varous receve antennas when operated n close proxmty /10/$ IEEE

450 400 350 300 250 d 1 200 150 100 50 0 0 5 10 15 20 25 30 35 40 45 50 tme [ns] Fgure 6. Measurement equpment Fgure 8.

Next we algn and combne the obtaned results to create the correspondng data cube plots that should represent the shape of the multstatc ambguty functon.

5 d tme [ns] Fgure 6. Measurement equpment Fgure 8. Output of the matched flter correlator Smlar results are obtaned for the remanng three recevers. Next we algn and combne the obtaned results to create the correspondng data cube plots that should represent the shape of the multstatc ambguty functon. We assume that the nterrogaton area s a square 2m x 2m wth the target placed at the orgn and orented the same way as the laboratory setup shown n Fgure 7. Fgure 9 shows the correspondng normalzed bstatc data cube (Recever 1) 2 where global statstcs s formed as D = d 1. Fgure 7. Laboratory setup V. MEASUREMEN RESULS Our measured data were obtaned usng a carrer frequency of approxmately f c = 10 GHz, 4-element Barker code transmttng waveform (phase sequence: 0, 0, 0, π, wth 0.5 ns chp wdth) and measurement radus R o = 1.02 m (see Fg. 7). In order to relate our measurements wth the smulaton results presented n Secton III let us frst consder the smulated confguraton wth four recevers and the transmtter located at α = π 4 (see Fgure 4). Recall that ths was the confguraton that had the best resoluton as measured by the 3-dB man lobe contour area. In order to create the same confguraton we postoned four bstatc recevers at φ1 = π 4, φ2 = 7π 4, φ3 = 5π 4 and φ 4 = 3π 4 (see Fgure 7). Let us process the sgnal measured at the frst recever ( φ 1 = π 4 ) and converted to baseband. he correspondng output of the matched flter correlator s shown n Fgure 8. Note that ths sgnal represents the local statstcs as defned by Eq. (3) and ntegrated over 100 pulses. Fgure 9. Normalzed bstatc data cube Fgure 10 shows the correspondng normalzed multstatc data cube where the global statstc s formed as: D = wd + w d + w d + w d (6) where w 1, w 2, w 3 and w 4 are the weghts assocated wth each recever. In ths example sgnals from all recevers are frst normalzed and then weghted equally. hs was done n order to relate obtaned measurements wth the smulaton results where potentally dfferent sgnal to nose levels were not modeled. hus, we normalzed our dfferent bstatc measurements so that they have the same energy. hs, however, mght not be the case n practce as dfferent bstatc recevers mght capture dfferent levels of returned energy /10/$ IEEE

even n the case of an deal sphercal target. As a result, both the probablty of detecton and resoluton mght be affected. hs ssue wll be studed n future work. Fgure 10.

Frst we observe the ablty of the multstatc system to localze the target n space as was already suggested n our smulatons (see Fgure 2).

6 even n the case of an deal sphercal target. As a result, both the probablty of detecton and resoluton mght be affected. hs ssue wll be studed n future work. Fgure 10. Normalzed multstatc data cube (frst confguraton) Let us comment on the shape of the normalzed multstatc data cube shown n Fgure 10. Frst we observe the ablty of the multstatc system to localze the target n space as was already suggested n our smulatons (see Fgure 2). In our comparsons wth smulatons we are prmarly nterested n the man lobe 3-dB area. For the measured system confguraton t equals m 2 as can be computed form the date cube. One can also notce certan patterns outsde the man lobe that we do not see n our prevous smulatons (see, for example, Fgure 2). hs s due to the relatve sze of the nterrogaton area. Whle n the case of our smulatons, dstances among the transmtter, recevers and the target were much greater (~ 10 km) than the sze of the nterrogaton area (100m x 100m), n the case of measurements they were at the same order of magntude. Fgure 11. Normalzed multstatc data cube (second confguraton) Next we changed the multstatc system confguraton and postoned the four bstatc recevers at φ1 = π 12, φ2 = 19π 12, φ3 = 13π 12 and φ 4 = 7π 12. hs s the same confguraton as the one n Fgure 4 for the transmtter located at α = π 12. he correspondng normalzed multstatc data cube s shown n Fgure 11. hs tme the measured man lobe 3-dB area equals m 2. hus, we experenced degradaton n resoluton whch s consstent wth our smulaton results (see Fgure 5). VI. CONCLUSIONS In ths paper we presented multstatc measurements obtaned n a controlled laboratory envronment. Dfferent multstatc system geometres were consdered. We were able to verfy the theoretcal fndngs regardng the sensor placement that were based on the multstatc ambguty functon. he measured man lobe 3-dB area results closely match the results obtaned n smulatons (speakng n relatve terms snce the waveform used and relatve dstances were dfferent). Future work s needed to nvestgate n measurements the role of waveform selecton and weghtng of dfferent recevers play n multstatc radar systems and compare results wth the theoretcal fndngs. he vews expressed n ths artcle are those of the authors and do not reflect the offcal polcy or poston of the Unted States and Royal Australan Ar Forces, the respectve Departments of Defense, or the U.S. and Australan Governments. REFERENCES [1]. sao, M. Slaman, P.K. Varshney, D.D. Wener, and H. Schwarzlander, Ambguty Functon for a Bstatc Radar, IEEE ransactons on Aerospace and Electronc Systems, Vol. 33, No. 3, July [2] D.D. Wener, M.C. Wcks, and G.. Capraro, Waveform Dversty and Sensors as Robots n Advanced Mltary Systems, 1 st Internatonal Waveform Dversty and Desgn Conference, Ednburgh, UK, November [3] I. Bradarc, G.. Capraro, D.D. Wener, and M.C. Wcks, Multstatc Radar Systems Sgnal Processng, IEEE Conference on Radar, Verona, New York, USA, Aprl, [4] I. Bradarc, G.. Capraro and P. Zulch, Sgnal Processng and Waveform Selecton Strateges n Multstatc Radar Systems, Internatonal Waveform Dversty and Desgn Conference, Psa, Italy, June 2007, nvted paper. [5] I. Bradarc, G.. Capraro, and M. C. Wcks, Waveform Dversty for Dfferent Multstatc Radar Confguratons, Aslomar Conference on Sgnals, Systems, and Computers, November [6] I. Bradarc, G.. Capraro, and M.C. Wcks, Sensor Placement for Improved arget Resoluton n Dstrbuted Radar Systems, IEEE Radar Conference, Rome, Italy, May [7] Lab-Volt Ltd, Prncples of RADAR Systems, 2nd ed. Quebec, Canada: Lab-Volt Ltd, September [8] S. Brady and M. Savlle, Scalng Radar Measurements for Advanced Algorthms, IEEE Internatonal Radar Conference, Washngton DC, USA, May /10/$ IEEE

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