AFRL-RY-WP-P-009-307 A MODULAION BASED APPROACH O WIDEBAND- SAP (PREPRIN) Ke Yong Li, Unnirishna S. Pillai, Peter Zulh, and Mihael Callahan C & P ehnologies, In. OCOBER 007 Approved for publi release; distribution unlimited. See additional restritions desribed on inside pages SINFO COPY AIR FORCE RESEARCH LABORAORY SENSORS DIRECORAE WRIGH-PAERSON AIR FORCE BASE, OH 45433-730 AIR FORCE MAERIEL COMMAND UNIED SAES AIR FORCE
REPOR DOCUMENAION PAGE Form Approved OMB No. 0704-088 he publi reporting burden for this olletion of information is estimated to average hour per response, inluding the time for reviewing instrutions, searhing existing data soures, gathering and maintaining the data needed, and ompleting and reviewing the olletion of information. Send omments regarding this burden estimate or any other aspet of this olletion of information, inluding suggestions for reduing this burden, to Department of Defense, Washington Headquarters Servies, Diretorate for Information Operations and Reports (0704-088), 5 Jefferson Davis Highway, Suite 04, Arlington, VA 0-430. Respondents should be aware that notwithstanding any other provision of law, no person shall be subjet to any penalty for failing to omply with a olletion of information if it does not display a urrently valid OMB ontrol number. PLEASE DO NO REURN YOUR FORM O HE ABOVE ADDRESS.. REPOR DAE (DD-MM-YY). REPOR YPE 3. DAES COVERED (From - o) Otober 007 Conferene Paper Preprint 5 May 006 9 Otober 007 4. ILE AND SUBILE A MODULAION BASED APPROACH O WIDEBAND-SAP (PREPRIN) 6. AUHOR(S) Ke Yong Li (C & P ehnologies, In.) Unnirishna S. Pillai (Polytehni University) Peter Zulh (AFRL/RIEC) Mihael Callahan (AFRL/RYR) 5a. CONRAC NUMBER FA8750-06-C-07 5b. GRAN NUMBER 5. PROGRAM ELEMEN NUMBER 604F 5d. PROJEC NUMBER 507 5e. ASK NUMBER RL 5f. WORK UNI NUMBER 57R5 7. PERFORMING ORGANIZAION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZAION REPOR NUMBER C & P ehnologies, In. 37 Harrington Avenue Suites 9 & 0 Closter, NJ 0764-9 ---------------------------------- Polytehni University Broolyn, NY 0 Communiations Exploitation Branh (AFRL/RIEC) Information and Intelligene Exploitation Division Air Fore Researh Laboratory 55 Broos Road, Rome, NY 344-4505 United States Air Fore -------------------------------------------------------------------------------------- Radar Signal Proessing Branh (AFRL/RYR) RF Sensor ehnology Division Air Fore Researh Laboratory, Sensors Diretorate Wright-Patterson Air Fore Base, OH 45433-730 Air Fore Materiel Command, United States Air Fore 9. SPONSORING/MONIORING AGENCY NAME(S) AND ADDRESS(ES) Air Fore Researh Laboratory Sensors Diretorate Wright-Patterson Air Fore Base, OH 45433-730 Air Fore Materiel Command United States Air Fore. DISRIBUION/AVAILABILIY SAEMEN Approved for publi release; distribution unlimited. 0. SPONSORING/MONIORING AGENCY ACRONYM(S) AFRL/RYR. SPONSORING/MONIORING AGENCY REPOR NUMBER(S) AFRL-RY-WP-P-009-307 3. SUPPLEMENARY NOES Conferene presentation to be published in the Proeedings of the 4st Annual Asilomar Conferene on Signals, Systems, and Computers, held November 04-07, 007 at the Asilomar Hotel and Conferene Grounds, Paifi Grove, CA. PAO Case Number: WPAFB 07-038; Clearane date: 0 Nov 007. Briefing ontains olor. See also, AFRL-RY-WP-P-009-306 for a briefing hart version, and AFRL-RY-WP-P-009-308 for a postprint version. he U.S. Government is joint author of this wor and has the right to use, modify, reprodue, release, perform, display, or dislose the wor. Paper ontains olor. 4. ABSRAC In this paper, a new method for proessing wideband radar data is presented. o perform the full degree of freedom wideband proessing, 3-D spae-time adaptive proessing (SAP) needs to be implemented, whih involves intense omputational burden. One approah in this ase is to do subband SAP proessing and ombine these outputs. In this paper, instead of traditional subband proessing, the inoming wideband data signal is modulated by multiple arriers, ombined, and filtered prior to proessing using narrowband SAP. his method offers a signifiant derease in omputation burden ompared to the subband method. 5. SUBJEC ERMS wideband spae-time adaptive proessing 6. SECURIY CLASSIFICAION OF: 7. LIMIAION a. REPOR Unlassified b. ABSRAC Unlassified. HIS PAGE Unlassified OF ABSRAC: SAR 8. NUMBER OF PAGES i 9a. NAME OF RESPONSIBLE PERSON (Monitor) Mihael J. Callahan 9b. ELEPHONE NUMBER (Inlude Area Code) N/A Standard Form 98 (Rev. 8-98) Presribed by ANSI Std. Z39-8
A Modulation Based Approah to Wideband-SAP Ke Yong Li, Unnirishna S. Pillai, Peter Zulh 3, and Mihael Callahan 4 C & P ehnologies, In., Closter, NJ 0764, li@ptnj.om Polytehni University, Broolyn, NY 0, pillai@hora.poly.edu 3 Air Fore Researh Laboratory (AFRL), Rome, NY 344, zulhp@rl.af.mil 4 AFRL, Wright-Patterson AFB, OH 45433, Mihael.Callahan@wpafb.af.mil Abstrat- In this paper, a new method for proessing wideband radar data is presented. o perform the full degree of freedom wideband proessing, 3-D spae-time adaptive proessing (SAP) needs to be implemented, whih involves intense omputational burden. One approah in this ase is to do subband SAP proessing and ombine these outputs. In this paper, instead of traditional subband proessing, inoming wideband data signal is modulated by multiple arriers, ombined, and filtered prior to proessing using narrowband SAP. his method offers a signifiant derease in omputation burden ompared to the subband method. I. INRODUCION One way to understand the wideband data is to onsider it as a olletion of narrowband data senes. Reall that the narrowband data vetor x () t for an N sensor, M pulse array has the form [] x () t A(, ) s(, ) () i, j i, j i, j i j where represents the lutter satter return from the i, j (, i j ) th path in the field of view, A( i, j, ) the array fator at frequeny. Here s( i, j, ) represents the spatio-temporal steering vetor at frequeny given by s(, ) b(, ) a(, ) () i, j i, j i, j where the spatial steering vetor is a(, ) is given by jdsin / j( N) dsin / a(, ), e,, e (3) and the temporal steering vetor b(, ) is given by d jd j ( M) d (, ) d,,,. b e e (4) Here d represents the interelement spaing distane and Doppler is given by d V o r sin. d (5) / In () - (5), refers to the operating wavelength, V o the platform veloity along the line of the array and r represents the pulse repetition interval. With x () t in () representing the th narrowband data, and x() t the desired wideband data, we have K x() t x (). t (6) With t () representing the reeived wideband lutter data and f () t representing the reeived wideband target data, the total reeiver signal in (6) an be written as x() t f() t (). t (7) Assume that the target is moving with a relative veloity V at an arrival angle of (both parameters are unnown), the o MN target signal f () t have the form of f () t f t( i) ( ) (8) i where the spatial delay is given by and the temporal delay is given by Hene the target return has the form d sin o (9) V r sin o. (0) f f, f,, f M () where f th represents the m pulse return given by m
() f f( t( M ) ),, f( t( M ) ( N ) ). m In the wideband ase, the optimum proessor is a whitening filter H ( z) followed by a mathed filter []. his whitening proessing is shown in Fig.. he white noise wt () in Fig. represents the whitened interferene. Fig. Whitening of wideband data. Using (7) - (), in the frequeny domain, the whitening filter output is given by j e a(, ) Y F e w e a(, ) j ( M) e a(, ) bv (, ) a(, ) s(, V, ) ( ) j j ( N) ( ) H( ) e ( ) j j F( ) H( e ) s(, V, ) w( ) g w (3) where g represents the target output and w represents the interferene output. In this ase, the mathed filter is given by g. hus the optimum wideband proessor an be shown as in Fig.. Fig. Optimum wideband proessor. As a first approximation, if we use a narrowband lie whitening filter with a onstant term, then where Whitening x() t Filter y() t g() t w() t H( z) Whitening Filter yt () Y( ) F.. H R (4) / ( z), White noise M. F. Z Y ( ) M. F. g represents the interferene/lutter ovariane matrix. In that ase, the output of the optimum wideband proessor is given by Z g Y( ) / s (, V, ) R / R X( ) s V X W X (,, ) R ( ) ( ) ( ) (6) where W ( ) represents the optimum wideband SAP proessor and it is given by W R s V (7) ( ) (,, ). Notie that the optimum wideband SAP proessor in (7) has the same form as in the narrowband ase. However, it is a frequeny sensitive proessor and it is diffiult to implement at all frequenies simultaneously. When the whitening filter H ( z) involves delay-lines, the struture in (7) beomes more omplex. In summary, the phase delays in wideband SAP proessor beome frequeny sensitive filters. he optimum wideband proessor must be ompensated at all frequenies simultaneously. In pratie, subband shemes an be used for wideband proessing. However, this sheme is suboptimal sine narrowband proessing is done on eah subband. II. SUBBAND APPROACH In the subband method, the reeived wideband data is expressed as sum of multiple narrowband signals as in (6). A ban of band-pass filters spanning the total signal bandwidth is used to divide the signal into sub-bands. If the bandwidth of the ban s filters is small enough then the subbands approximate narrowband signals and an be proessed using narrowband SAP. A typial filter ban is shown in Fig. 3 whih uses least square approximate FIR low pass filters modulated to the enter frequeny of eah frequeny band. By modulating a low pass filter to a desired frequeny, the passband of the filter inludes desired frequenies. he sampling frequeny for the filter shown in Fig. 3 is 635MHz with 5 taps for eah filter. A total of 0 filters within the filter ban spans 80MHz bandwidth is used. Eah filter has a 3dB bandwidth of 8MHz. he enter operating frequeny of the array onsidered here is at 435MHz and 80MHz bandwidth orresponds to 8.4% Fig. 4 shows the struture of the subband method that use K beamformers. R Et { ( ) ( t)} 0 (5)
Fig. 6 shows the average of the 0 subbands. A uniform array with 4 sensors and 6 pulses is onsidered here. he array interelement spaing is seleted to be half wavelength at enter frequeny. he lutter to noise ratio and target to noise ratio are set at 40 db and 0 db respetively. Fig. 3 wenty sub-band least squares FIR filter ban ranging from 395MHz to 475MHz. Input Spetrum subband Multiple Beamformers (a) op View (b) Side View Fig. 6 Average Power Spetrum for 0 sub-bands proessed with sample matrix inversion with diagonal loading and subarray/subpulse smoothing (SMIDLSASPFB). K III. MODULAION-SUM-FILER APPROACH x( ) Subband Channel Subband Channel Subband Channel K K Beamformer Beamformer Beamformer K z ( ) his modulation-sum-filter method presented here for ombining wideband data is in a sense equivalent to the fousing approah, although unlie the fousing method, there is no need to estimate the fousing matries [ 4 ]. Instead, the multiple modulations are used to fous the wideband data into a narrow band region where they are summed and proessed using narrowband SAP. his proedure is illustrated in Fig. 7 below. Fig. 4 Subband approah. Fig. 5 shows the 4 frequeny band outputs of the subband approah when 0 subbands are used. he sample matrix inversion with diagonal loading and subarray/subpulse smoothing (SMIDLSASPFB) tehnique is used here [3]. Fig. 7 Illustration of subbands being modulated to a ommon enter frequeny (a) Subband, Freq. = 395 MHz (b) Subband 4, Freq. = 49 MHz By aligning the signals being added prior to band pass filtering, only one band pass filter is required. he signals are aligned by modulating eah subband to the enter frequeny as shown in Fig. 8 where X is the Fourier X is the Fourier ransform of transform of x t, j o t x t modulated by e, and H BF represents the bandpass filter. he sum of the modulated signals an be expressed as the signal multiplied by a sum of modulating funtions shifting eah subband to the ommon enter () Subband 7, Freq. = 443 MHz (d) Subband 0, Freq. = 467 MHz Fig. 5 Angle-Doppler output for different subbands. jont o n. (8) y t x t e X Y n n 3
his ombined signal is finally bandpass filtered, effetively resulting in a single subband ontaining the averaged information of various subbands. hus Z( ) H ( ) Y( ) (9) BF represents the filtered output. In the final step, traditional narrowband SAP proessing an be applied to the filtered final output in (9). bandpass filter with 8MHz bandwidth. he sample matrix inversion with diagonal loading and subarray/subpulse smoothing tehnique using 0 samples is shown here. Observe that the wideband target is learly identified. However, the Angle-Doppler spread ours as shown here where a single target with veloity = 40m/s appears as an extended target with different veloities. Doppler spread (a) op View (b) Side View Fig. 9 Angle-Doppler spreading. Data is modulated by 0 arriers to 435MHz. Combined data is filtered with a bandpass filter with 8MHz bandwidth. Fig. 8 Illustration of modulated versions of the same signal. In pratie, the total number of arrier frequenies being used and the bandwidth of the bandpass filter are free design parameters. In what follows, a set of simulation results are presented to exhibit the effets of these two parameters. Fig. 0 shows the Angle-Doppler output using the Modulation-Sum-Filter approah using 0 modulations. he ombined data is filtered using a bandpass filter with 4MHz bandwidth. One again, the target is learly identified and the Doppler spread present there is visible. On omparing Fig. 0 with Fig. 9, the sidelobe level using 0 modulations is lower than that using 0 modulations. hus the performane of the proessing output using 0 modulations is superior to that using 0 modulations. In pratie, the total number of arrier frequenies being used and the bandwidth of the bandpass filter need to be seleted arefully to obtain optimum performane. Doppler spread IV. SIMULAION RESULS Using the Modulation-Sum-Filter approah, a single target at in the filtered data generates multiple target vetors orresponding to frequeny,,,. Or L equivalently, proessing the data at o generates multiple targets at,,, where L sin sin,, 3,,. (0) o L As a result, Angle-Doppler spread ours in SAP output spetrum proessed at a single frequeny. Fig. 9 shows the Angle-Doppler output using the Modulation-Sum-Filter approah. In Fig. 9, ten arriers are used for modulating the data to the enter frequeny 435 MHz. he ombined data is then filtered with a single (a) op View Fig. 0 Angle-Doppler spreading. Data is modulated by 0 arriers to 435MHz. Combined data is filtered with a bandpass filter with 4MHz bandwidth. V. CONCLUSIONS (b) Side View his paper presents a new method for proessing wideband radar data. Instead of traditional subband proessing, inoming wideband data signal is modulated by multiple arriers, ombined, and filtered prior to proessing using narrowband SAP. his method offers a signifiant 4
derease in omputations ompared to the subband method. he detetion performane is affeted by free parameters suh as the number of modulations used and the bandwidth of the filter. Using the Modulation-Sum-Filter approah, a single target in the filtered data generates multiple targets orresponding to different frequenies. As a result, Angle- Doppler spread ours in SAP output spetrum proessed at a single frequeny. Methods to align the angle-doppler spetrum need further study. AKNOWLEDGMEN he researh desribed herein is supported by the Air Fore Researh Laboratory (AFRL) Sensors Diretorate, Radar Signal Proessing Branh under USAF Contrat FA8750-06-C-07. REFERENCES [].C. Cheston and J. Fran, Phase Array Radar Antenna, Radar Handboo, Chapter 7, MGraw Hill, New Yor 990. [] J. R. Gueri, Spae-ime Adaptive Proessing for Radar, Arteh House, Boston, 003 [3] S. U. Pillai, K. Y. Li, B. Himed, Spae Based Radar heory & Appliations, MGraw Hill, NY, o be Published in De. 007. [4] H. Hung, M. Kaveh. Fousing Matries for Coherent Signal- Subspae Proessing. IEEE ransations on Aoustis, Speeh, and Signal Proessing. Vol. 36, No. 8, August 988. 5