THE UNIVERSITY OF MICHIGAN 5172-6-Q TARGET SIGNATURE STUDY Interim Report 1 September through 30 November 1963 Contract Nr. DA 36-039 SC-90733 Target Signature Research Department of Army Project Nr. 3A99-23-001 November 1963 OBJECT Conduct a Study and Investigation to Determine an Optimum Method of Identifying Military Targets by Radar 5172-6-Q = RL-2123 Prepared By B. F. Goodrich, B. A. Harrison and 0. G. Ruehr

THE UNIVERSITY OF MICHIGAN 5172-6-Q Qualified requestors may obtain copies of this report from the Defense Documentation Center, Cameron Station, Alexandria, Virginia, 22314. DDC RELEASE TO OTS NOT AUTHORIZED. ii

THE UNIVERSITY OF MICHIGAN 5172-6-Q TABLE OF CONTENTS Section Page 1. Purpose 1 2. Abstract 1 3. Visits and Conferences 1 4. Technical Work (1 September - 30 November 1963) 2 4.1 Introduction 2 4.2 Computer Simulation of Mixed Filter-Target Signature Study 2 4.3 Representation of the Target Signatures 20 4.4 Review of Technical Work 25 5. Program for Next Interval 26 Acknowledgement 26 Distribution List 27 iii

THE UNIVERSITY OF MICHIGAN 5172-6-Q 1. PURPOSE The purpose of this program is to conduct an investigation to determine an optimum method of identifying military targets by radar means. 2. ABSTRACT The mixed filter is analyzed in detail using machine simulations. A quantitative estimate of the resolution as a function of the filter parameter is obtained for a given target. The uniform method of describing targets in terms of their frequency signatures is further developed. Included is a tentative criterion for choosing the representations in terms of translates of a given function. 3. VISITS AND CONFERENCES There were no visits made or conferences held during this reporting period. 1

THE UNIVERSITY OF MICHIGAN 5172-6-Q 4. TECHNICAL WORK - 1 September through 30 November 1963 4. 1 Introduction The technical work for the sixth quarter has been concentrated in two areas. First, we have further studied the mixed filter and by use of simulations found a more or less quantitative relationship between the filter parameter and range resolution; however, we have only found a qualitative relationship between the filter parameter and the appearance of spurious target signals due to noise. Second, we have continued our study of a uniform means of frequency signature representation by means of translates. We have a possible means of finding the optimum function to use in the representation. 4.2 Computer Simulation of Mixed Filter-Target Signature Study. A computer simulation study of the mixed filter for target identification was undertaken during the current reporting period. In general, the results seem to corroborate the expectation that a mixed filter is an effective compromise between a matched filter (noise suppression and identification) and an inverse filter (resolution). Optimum results were obtained for values of the filter parameter over the range m = 1 to m = 10. The targets considered are linear arrays of n elements oriented at an arbitrary angle, 0, relative to the receiver. The signature of the target array is. n ndsinO i Wd(n-l)sin sin c dsin e (1) sin c where d is the spacing between elements and c is the speed of light. The mixed filter corresponding to a target a is 2

THE UNIVERSITY OF MICHIGAN 5172-6-Q s (w) X ( A 2 1 (2),m m2+|s (3 ) Or | Sa(u) |2 do a, m2 + S () 2(3) -r The normalization factor, A is chosen so that a return consisting only of a single target of the type sought will give a peak of unit height at the required distance. The matched filter limit, m -- co, is found from (2) and (3) to be X (w) s (a) r (4) The inverse filter, m -- oo, is 1 Sa (X) Xm 2r W * (5) In = 2r I VW) I Thseveral parameters vary. These include the filter parameputer,, the signal toruns over which several parameters vary. These include the filter parameter, m, the signal to noise ratio, orientation of target, number of elements in the target array, and the number and distance of targets. A summary of these runs is included in tabular form in the following tables, giving both a qualitative and quantitative description of the results. Figure 1 displays the range resolution as a function of the filter parameter. The information is obtained from computer runs by measuring peak widths. Figures 2 through 11 present a representative sample of the computer runs. 3

Target Description 0 n Distance Run m STNR No. Noise Separation Remarks meters Suppression 1 2 3 4 5 6 7 8 9 10 11 13 14 17 18 19 0 10 2 5 5 10 5 10 20 99 20 1 1 5 2 5 o 30 6 1500 OD 30 6 1503 1503 co 30 6 1503 1503 0 300 6 1500 20 30~ 6 150 1503 10 30 6 1500 1500 20 300 6 1503 1503 0 300 6 150 1503 10 300 6 150 1503 5 300 6 1503 1503 5 300 6 1500 1503 o 30 6 1500 20 31500 6 1503 5 300 6 1500 1503 1500 10 300 6 1503 20 300 6 1500 1503 10 300 6 150 00 1503 01 1503 N. A. Excellent N. A. Fair Go od Good Poor Poor Good Good Excellent Good Poor None Fair Fair Fair Poor Good None N. A. Poor Very Poor Good Very Poor Good Good Good Poor N. A. Good I N. A. Poor effects seem to result from noise sample. Peak at 1500 is absent. Left peak is lower than several spurious peaks. Left peak is lower than several spurious peaks. Peak at 1503 is not suppressed. Spurious peak is higher than signal peaks. Peak at 1503 is completely suppressed.

Target Description n Distance Noise meters Suppression Run No. m STNR 0 Separation Remarks 20 2 10 30 6 1500 200 1503 21 5 10 30 6 1500 250 1503 22 2 10 25~ 6 1503 300 1500 23 25 10 350 6 1503 24 5 10 300 6 1500 1503 25 2 10 30~ 6 1500 1503 n0 26 25 10 300 6 1503 1503 27 5 10 300 6 1500 27 5 10 6 350 1503 28 2 10 350 6 1503 350 1503 10 300 6 1500 29 25 10 40 6 1503 350 1500 40 1503 32 5 10 900 6 1503 900 1503 33 2 10 0 6 1503 934 10 1503 34 10 10 310 6 1504 310 1504 Fair Good Very Poor Excellent Excellent Fair Excellent Good Fair Good Poor Fair Fair Poor N. A. N. A. N. A. N. A. Peak at 1503 is completely suppressed. Desired peak (1500) is displaced one meter to left. Undesired peak (1503) is suppressed. Poor noise conditions outweigh target discrimination evaluation. Undesired peak (1503) is suppressed. Excellent Good None N. A. N. A. N. A. N. A. N. A. N A. N. A. Spurious peaks. Undesired peak is suppressed. Undesired peak is suppressed. Spurious peaks. Undesired peak is suppressed. Peak at 1503 is suppressed. Spurious peaks at 1484 and 1506. Undesired peak is suppressed. Peak at 1500 displaced 1.5 meters to right. Peak at 1503 not completely suppressed. Poor noise conditions preclude evaluation. Peak at 1500 is 1.1. Peak at 1504 is. 8. Good N. A.

Target Description n Distance Noise meters Suppression Run No. m STNR 9 Separation Remarks 35 10 10 320 320 36 10 10 330 33o 37 10 10 34o 340 38 10 10 350 435 6 6 6 6 I 39 10 10 30~ 4 300 4 40 10 10 30~ 6 5 41 10 10 30~ 6 7 42 10 10 30 6 8 43 10 10 30~ 6 9 44 10 10 300 4, 5 6,7 8,9 45 10 10 30~ 4-9 46 10 10 30~ 4-9 1500 1504 1500 1504 1500 1504 1500 1504 1510 1500 1504 1500 1504 1500 1504 1500 1504 1500 1504 1500 1504 1520 1500 1520 1500 1520 8 targets at 4243 Good Good Good Fair Fair Good Good Good Poor Poor Poor Poor N. A. N.A. N. A. N. A. N. A. N. A. N. A. N. A. N. A. N. A. N. A. N. A. Peak at 1500 is 1. 3 Peak at 1504 is. 8. Peak at 1500 is 1.1 Peak at 1504 is. 6. Peak at 1500 is 1.1 Peak at 1504 is.5. Undesired peaks are suppressed. Peak at 1500 is 1. 1. Peak at 1504 is.5. Peak at 1500 is 1.0 Peak at 1504 is.5. Peak at 1500 is. 9 Peak at 1504is 1.2. Peak at 1500 is. 9 Peak at 1504 is 1.4. Peak at 1500 is. 7 Peak at 1504 is 1.8. No peaks above.25 Possible cancellation effects. No peaks above.25 Possible cancellation effects. No peaks above.25 Possible cancellation effects. 6 47 1.25 10 30~ Fair N. A

Target Description Run m STNR 6 n Distance No. meters 48.01 co 30~ 6 1500 49.50 ao 30~ 6 1500 50 1.00 oo 30~ 6 1500 51 5 co 30~ 6 1500 52 10 ao 30~ 6 1500 53 20 oo 30~ 6 1500 54 50 oo 30~ 6 1500 55 100 co 30~ 6 1500 56 15 00 300 6 2targ 57 15 300 6 2targets at 2121 1500 58.01 co 300 6 10 1504 15:20 59 5 20 300 6 1500 1504 1520 Noise Suppression N. A. Separation Remarks N. A. Runs 48 through 55 inclusive were made to measure peak width (resolution)as a function of m. N. N. N. N. N. N. N. N. A. A. A. A. A. A. A. A. N. N. N. N. N. N. N. N. A. A. A. A. A. A. A. A. N. A. N. A. Good N A. N. A. Excellent Good N. A. Peaks: 1.1,.8,.6, 1.2, 1.1,.5. Interference appears to give spurious peaks. 60.01 co 30~ 4-9 1500 1504 1520

Target Description n Distance Noise meters Suppression Run m No. 61.01 STNR 0 Separation Remarks 64 65 66 1000 10,000 5 1500 co 30~ 4-9 1500 1503.5 1517.5 oo 30~ 6 1500 oo 30~ 6 1500 30 4 1475 6 1500 9 1525 N. A. N. A. N.A. N. A. N. A. N. A. N. A. Good Interference appears to give spurious peaks. Runs 64 and 65 were made to measure peak width as a function of m. Peaks:.7, 1.0, 1.2.

THE UNIVERSITY OF 5172-6-Q MICHIGAN 10,.1000. I I I I I 1,0 000. 100. I I / / / -90 I~ d11 a- - - - -I 6 db p 4) -4 —b (1) Cd 04 p i.r-j %.Op 1-1 '-p, 10. 1.'( / / / / / I I I 'T I I I I I.01. 2. 4. 6. 8 1. 0 1. 2 FIG. 1: Range Resolution (peak width/incident pulse length). 9

.aa***** GRAPH OF DISCRIMINATION FUNCTION ***aa 2.000 + --- —+ --- —--— + --- —-— + --- —--- -- ----- ---------— + --- —I I I I I - I FIG. 2:- R No.3 I I I I I I I I ~ m I2TN=2 0I ]I__O - = 2; 3T~; = 20 0 0; A I I I ' I - I I Distanes: 1500and 1503 mtrs I B I I I I I___ I I — I 13 Ix 1 I.. I..........-......... -...I, i --- —--— i i1 —1 ---- ii ---- i --- —-— i --- I ---S I I I I I I I I I I I O I I I I I I I _ I I I I L 1.600 +. —.-.+ --- —--------..... --- —--.. --- ——.. —...-..+ ---+ I I I I I I I I I I I L 1.400 + --- —--— + --- —------------------------------------------ Q I I I' I I I I I I I U I I I II I I I I I I I A I I I I I I I I I I R I I I_ I I I I I I I I E 1.200 + ---- ----— +- - --- --------. --- --- I I I 0I I I I I I I I O I I I I I * I I I I I I F I I I * I I I I I I I I I I I I I I I I I I D 1.000 + --- —--—. --- —--— + +. ---. —4 ----+ + +4 + + I I I I I I * I I. I I I I S I I I I I I I I I I I C I I I ' I I I I I I I I R I I I' I I I I I I I I 0.800 + --- —------------------------— + --- —— + --- —— + --- --------— + --- —-— +-. --- —— + M I I I I______ I I I I I I I I I I I I I * I I I 1 N I I II I I I I I I I A I I I I I, I I I I I I r 0.600 ---------— + ------- -------------------- --------- --------- ------- I I I I jI I I I I I I I O I I I I I -I I I I i I N I. i I aI I I I I I I I I I I I I I I I I F 0.400 4 + + -— + + ----- ---—.-. ---. +. ---+ — - —. ---.+ U I I. I I I I I I I I I C I Ia I I a I I I I I I, T I I I I I I I I I I I 0.200 +- + ---- + — --—, + --- ——.+ --- — -.+ —.+......... ---+ --- —-—.+ N * I I * * I I I ** I I I I *a a 1 I a I I 'I ' I I I a' _ I I I I I * a* ** * I * I I.000 ----------------- ---— **** --- —------------- ---— + --- —---. ---+ — ---------------------—. — 0.000 -------- --------------- - --— ~ — ----- -----—. — ----- 1494.00C 1496.000 1498.000 1500.000 1502.000 1504.000 1506.000 1508.000 1510.000 1512.000 1514.000 R A NG E I N T E R S 0

____________________________***** GRAPH OF IDISCRIMINATION FUNCTION ***** 2.000 + --- —-— + --- —— + -------— + + ---+ --- —— + —.-+ --- —------- ------- I I I I I I I I I I I I I I I I I I FIG.3: RunmNo. 5 I _____ I I I I I _ I I I I ~ I I I I - I -. —. - - m = 5; STNR = 10; 0 = 30~; I A B S 0 L T I E S U A R 0 F "I" 0 S C R N I M I N A I u.-N^.-... F U N C r I N 1.800 +- - ---— + ---.. -—. ----------- I _i..... - I'-^- - ^ -- - _-....... -- - n = 6; Distances 1500 and 1503 meters " I I I I I I ______I I __I I I IIII I I I I I - I I I __ I I I.I I I _ I __ I _ I 1 -.-...-....... _ _...... _..._.. ~.... _.. _. ~... _. _ _ _. -. _ __ _ ____.. -.. 1.600 --------- ----------------— + --- —-----------— + --- —--— 4+ ---+ --- —--------------—. --- —-- -.0 ------- -------— > --- —---— ^ --- — -— > --- —---— ^ --- —-7 - ----- *~ ---- -77 ------- -----------------... I -..... I __* -I I I I I ___......I. I I I I I I I I I I I I I I I _ I I I I I I_ I I I I I I I I ** I I I I I I 1.400 +- - +- - + - +- - — +- - +- - -+- — 0+- - +- - -+... I-......[...-..........- - - - - - - -. -..........-......... I I....I ' - I I.I _ I... I...* I_ I I _ __I I I I I I I I I I i-.............. I I I I I I I I I __ _ I I I I I 1 *2.0 +- - +- - - +-.........+- - -+- - +- - +- - -4- - - - - I I I I I I I I I * 1 I * *II I I I I I I I I _ I I I I I I I I I I * I I I I I I I 1.000 + ----+ ---~- -.... ---+. ---..... ---+ ---. ---+ I. I I I......... I I I..........I I I I I I I I I I I I I I I I I I * i. * I I I I I I I I 1 I * I -I ____.I I I I I C. 800 + --- —-+ --- —---— 4 ----— + ----— + --------— + ----* ---+ ---+ -- --— 4 ---4 I I... I........I I I I I I I I ~I'I I.... I...........'-........... I I I _ _ I ___________ I* I I I I I I I i _. I..i- _-' I______ I. I 0.600 + +. ---+-...... —+-. ---*~ ---4 ---+ — -— + --------- I I I I...... I........I I I I I I I I I I I I I I I I I i ' I. * I I I --- —----—. I.. I......... I I I I I I _ I * I I __I I I I_ I I I 0.400 +.. ---.. —.- -----—... ---+- — +-+.. —+ ---.+ ---. ---. + ---4~ I I I I -I I I I I I I I I I I * ~*** I I-* I - I i I I I..**. I I I* I _I__I I, #* I _ I I """ ~ ~j, - r. — -T - i i" * r- "~ i 0p_200 + --- —-4-* ---- --------— i ---+ --- —4* ---+ ---* ----~ ---4 --- —* —4-4 --- —-4-~ I * I I I I **I - I - - I I I I * I * 1* I I I i * I *.__I_ I I I * I I * I I I *I I....... I I I I**** I ***** I I I I *** ** I I I 0.00 +- ----— + —+ -+ --- -+ ---------------------- ------------— + 14-94.-0C 1496.000 1498.C0 150C.CC0 1502.0oo00 1504.000 1506.000 1508.000 1o10.000ooo 1512.000 1514.000 _ A GRANGE I N METERS

__ ___GRAPH CF DISCRIMINATION FUNCTION ***** 2.000 + --- —-----------— + --- —---------------------------------------------— + --- — I I I I I I I I I I I I I I I I I I FIG. 4: Run No. 6 I I___ I I_ I I I I I I I I I I I I m= 10; STNR = 10; 0=300; 1.8CO + --- —-— + --- —----------------------------------------- A- I -- n = 6 Distances: 1500 and 1503 meters I I I II I I I I I I I I S I I I I I I I I I I I O I_ I I I I _ _ I ** I I I I I I L 1.600 + --- —------ --------- --- -- ------------- ------ ----- U I I I I _ __ I * I I I I I I T I I I * I* I I I I E I I I *I 1 I I I I I I I I I I I I I I I I S 1.400 +.. ---+ — + *-+-* --- —— + ---- -— + --- —--- (-J rh U A R 0 F C; -7 -I I M I N A! I 0 N F....f ---N I I I I I* *1 I I I I I I I I I I I I I I I I I I I I I I. I- I I I I I I I I I I I I I I... i'.2O. '+...,..+.......I........~......_~..~...~'':.. _.. __ ~.. __ L.-.- +.........I '~+ 1.200 + --- —--— + --- —--— + --- —--— + --- —---- - --- +- - -— + --- + I I I. I. _ I I I I I I I I I I I * I I I I I I I I I _ I I I I I I I I I I I I * I* I I I I I 1.00 + --- —-- -- + --- —-+ --- —----— * — -----— + ---- -- + --- ---— + --- —- -— + I........1 *. i............... I I I I I I I I I * I I I I I I I I I I I I I I I I I I I * I I I I __ I I I I 0 8CO + --- —---------— + --- —---— + ---- -— + —*- 4 --- —+ --- 4 ---+ 0. 6 G0" +" T. " " '" " + 4- + *- ** - ~ - - -........-........- ~ -...,I.-_ +.......... +..I~ ~ ~~~~ I *+ I I -i ---* I F *I I I I I I _. I. I I I _. I I I I I I I I I I I I I I 0.6CO +- — +- — + + — -+- — + --- —- — + --- —-+ --- + ----+ ----+ -...... i'............-I......... -... L..........I I I " I.............. I I I I I I I I I I I I I I I I I I I I I I I I I I I __ * I I I * II I I I 0.0 + ---- -----— + ---+ ----+ — -+ — -+ ---+ ---+ ----+ ___ _ I__ _ I _ i_ ___ I I.1 I I I I I * - I * I I I I I C I 0.200 N I I I I I I I I I I I II ' *1 I I I I — I I I 'I ----— + --- —----------— + --- —-------------- ---------------------------- I I * I I I I ~ -- I I I I ** I I * ** I I*** I I I I I ** ******* I I I I I ******** I I I O.OO0 ** — '- -+ ----- - -- + ----+- — + - -- -+- -z'4. ---..+. -----. 1494.000 14 96.000 1498.0CO 1500.000 1502.000 1504.000 1506.000 1508.000 151C. CCO 1512.CCO 1514.000 R A N G E IN M E T E R S

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***** GRAPH OF DISCRIMINATION FUNCTION ***** 2.000 ++++++ -+ --- —----- ---------------- -— + --- —-— + I I I I I I I I I I I I I I I I FIG. 9: Run No. 36 I I I I I I I I I i I I I I I m 10; STNR =10; 0 = 30~ and33~; I 1.800 ----------------------------- - ---------- — + A I n 6; Distances: 1500 andl 1504 meters B 1 1 I I I I I 1 I I I S I I 1 I 1 I I I I I I 0 I I I I I I I I I I L 1.600 ----------------------------------— + --- —---------------------------------------------------— + U I I I I I I I I I I I T I I I I I I I I I I I E I I I I I I I I I I I I I I I I I I I I I I S 1.400 +++ --- + ---+ --- _ - -------— + --- —---— + Q I I I I i I I I I I I U I I I I I I I I I I I A I I I I I I I I I I I R I I I I I I I I I I I E 1.200 + ---+ — -+ --- —--— + ----+ ---__ ---++ --- —--— _ —_____ -------— + --- —--— + --- —+ I I I I I I I I I I I 0 I I I **I I I I I I I I F I I J I I I I I I I I I I * I II I I I D 1.000 + --- —-- -------— + ---* —+ - -+ ----+ --- _-+ --- —--— + --- —— +-_ —+ --- —--— + I I I I I I I I I I I I S I I I I I I I [ I I I C I I I I I I I I 1 I I R I I I * I I I I I I I I 0.800 + ------- -- - -- -+- — ++- -._-_ - -+ --- —--— _______-_________ — _________ — M I I I I I I I I I I I I I I I I * I I I I I I I N I I I * I [ * I I I I I I A I I I I * I ***** I I I I I r 0.600 ------- -+ — -+ — -+ ----* ----+ ---* ----+** --- —4-,- -— _ --- —---— __+-+-~_ ---___+ I I I I * I I * 1 *. I I I I I 0 I I I I * 1* 1 * I I I I I N I I I I * 1 1 * I I I I I I I I * I I * I I I I F 0.400 + — -+ — -+ ---+ —_ ---*+ ---_-.-+______- — +-_ ----_ —+- — + ---+ U I I I* 1 1 I *I 1 1 I I N I I I I I I I I I I C 1 1 I 1 1 1 I** I I I I r I I I I I 0.200 + --- *** -- -— + --- —— + --- —+-+ --— _+ ---* ---- -— + --- —— _-+ --- —— _-+ O 1 *1 ** 1 1 I I I * I I I I N I *. I *.I I I I I * I I I I I *** I I I I I I * I I I I I * I I I I I I *.* I I I 0.000 + --- + + --- —— + --- + --- —-— + ---4 -— + --- +-**** ---+ — — + ---_ -- -+ 1494.000 1496.000 1498.000 1500.000 1502.000 1504.000 1506.000 1508.000 1510.000 1512.000 1514.000 R A N G t I N M E T E R S

0 0 0 n I LO - I - - I I I - -I --- + + if I - +......... I I I I I I I I I I I 10 I II I I I I I I II I I I 9 9 Ln 7 L 0! I 0 I I! I I *,I I 0 ~ ~~ II i II LL uj * II Z I II I 09 9O I I 0 4/ -CI * + - I I 9 *9 9 0 CN 0 II ZI IC 9 I I 9 * 99 '1 eO '-'.9~~~~4 9 9 9I I * 9 9 9 I' 9I 9 I 9 I *9 9 Z/9 9 I *- 9 9 0 * 0 9 9 I 9 I 9 *9 9t ' 19 9 I 9 9 9 w z iI I99 I I 9 9 * 9 9 1 99 * 9 9 I I I I -3 I I I * I I U + i I * I I 0 9 I99 I 9 I 99 I 9 9 I9I9I * 9 I 9 9 I I 99I I 9 9 9 9 9 I I I 9 0 Y I~~ ~ ~ 9 I I I 0 00 ~~*I I 9 9 9 * 9 - 03 II 9 I I99 * I 99I I I 9Y ~ + ~y+ yy 9 9+ 9 I 9 c I 9 cw I 9 *9 0c+wwI 0 0 0 9 I* I o 9 I 0 0 0 0 0 0 0 0 0 0 0 0'0 0 0 00 0 0 00 - 0 03 0 -tN 0 0 '0 ~ N 0 * * 00 * -~ - ~ -' 0 0 0 a O n 3c.;~3QuJ C~-0 O u -~L -Z Lu3 Z U Oc —0 7

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THE UNIVERSITY OF MICHIGAN 5172-6-Q 4. 3 Representation of the Target Signatures We continue with our analysis of the use of Wiener's theorem on translates for the representation of target signatures. Briefly, we summarize the problem of target signature representation as follows. Given a set of signature functions S(w), where a designates the awth target, we wish to find a representation in terms of translates of a function S (w) in the sense Ski))a A S(W + W) kk where we leave the question of convergence for later. We have from the Wiener theorem that for a sufficiently broad class of functions the approximation is possible. What we need to find is; 1) a constructive method of realizing the expansion, and 2) a criterion for choosing the best S for our filter scheme. On obtaining the representations for a given set of targets we can define a set of translates which can be used for any of the targets by simply forming the union of the translates for each of them. The coefficients A: now can be used to characterize the target signatures; S (W) *-*. (6) To form a filter which can detect target a and discriminate against target IB we need to modify S (w) so that the overlap between S and S is as small as possible. If we look for T 1Va hr S i(7) where S (w) is formed by putting a 20

THE UNIVERSITY OF MICHIGAN 5172-6-Q Ak ~S^w)=L1A^S(~y+), (8) in order that \Gr ~t < ~ and (9) Ova 2 where e and M are positive numbers. Then a filter constructed from S (o) should in some sense satisfy the discrimination requirements. We still need a criterion for choosing S. For a given set of targets and for a given S we define a set of translations and we need put some limitation on IS*S(AW) < 't where Au is the smallest interval between translations. We have made some progress in this wise. We, for convenience, have represented the signature functions in terms of convolutions rather than translations. Let there be given a set of spectra S1 (U), S2 (o),..., Sn(L). We wish to find a function (spectrum) S(u) such that in the representation S (w) = 0 (rl)S(w-ri) drn a 21

THE UNIVERSITY OF MICHIGAN 5172-6-Q the functions 0 are "as different as possible". To obtain a criterion of difference (discrimination) we let P 2 c2 =J I0I; a \\ then the set czl is correspondingly different, according as the sum c c is large. Thus we want to find an S Now I 02 f [ 0 a J w t m he sa u and we want to minimize the sum RI Y r^ = c c~" to maximize this sum. - ff -- =2-2R RI a c J ca c c c 3 Denoting Fourier transforms by ^, we have a 1 -iLr 4T c 2r e aJ Zc S (x) a a dx S(x) 22

THE UNIVERSITY OF 5172-6-Q MICHIGAN 2 a '_ 47r -i wx+i y a e S(x) S(x) 4 iS( -dx dy S(x) Hence 20 2 jLIT;\j=i a 7 J 2 7 S 1-S ( 2x) a dx 1S (X) I and we want to minimize this last expression on S, subject, say, to 1 S(x)) I = 1 We set 1 1 C = - 2 7r eica Pcix then by Schwartz inequality c = - 12s x)1 27r |z c aa 1 2.r~ (X) I S(x) 1 dx 1 \ I, a ' — c s (x) 1 27 a 2r J s(x) l2 2 dx s(x) I dx v dx 23

THE UNIVERSITY OF MICHIGAN 5172-6-Q Hence the minimum value of the integral is c, and can be achieved by setting — c- -- L -- - = 2 7X c |s(x)| S (x) or 27re sx 1 = j- s x(X As soon as the c are known, this gives S(x) as any function whose modulus satisfies the above. To determine the c we have a C 1) I' 12 a la 2 S2(x) 1r 1 1 Ir (l"2 c- = Ic — a(X)I C2 -C a This gives n equations in the n unknowns cl, c2,..., c to solve The extension of this criterion to the representation in terms of translations is immediate on nothing that 21 Akf(W + )= a () f(w+ 7)d7 where a(r) = Ak (r1+ k) 24

THE UNIVERSITY OF MICHIGAN 5172-6-Q 4.4 Review of Technical Work We divide the technical work into three topics: 1. The development of the mixed filter concept so as to be able to affect a compromise between best discrimination (matched filter) and best resolution (inverse filter). 2. The test of the scheme using a complex target. We are now prepared to use a vehicle as the target in our simulation experiments. 3. The development of a representation of the target frequency signatures in terms of translates of a suitably chosen function so as to facilitate the construction of filters and so as to be able to decide whether two given targets can be discriminated one from the other. At this point we can make a somewhat quantitative evaluation of the mixed filter in that we can suggest a range of the filter parameter for suppressing a certain noise level or for a certain range resolution. Since we have developed our analysis on the basis of essentially one target we would wait for a more extensive target analysis before we make any more definite predictions as to resolution and discrimination criteria as a function of the filter parameter. We should be able to make a sharper statement after the vehicle simulation. The preliminaries to the vehicle simulation are complete. We have waited with the actual run until we obtained a better understanding of the mixed filter. The vehicle simulation is the next task in our program. In the future other complex targets will also be simulated. The development of a means of representing the frequency signatures in terms of the translates of a given function is the most difficult and, we believe, the most important of our problems. Such representations exist and we need a systematic way of realizing them and a means of choosing the best given function. We have a tentative method of choosing the function but as yet no systematic way of realizing the representations. 25

THE UNIVERSITY OF MICHIGAN 5172-6-Q We attach such importance to the representation of the signature since these representations will permit a systematic way of constructing the best possible filters for discriminating a group of targets one from another. 5. PROGRAM FOR NEXT INTERVAL Due to the amount of effort devoted to the analysis of the mixed filter the planned simulation of a vehicle was not completed. This is, however, a main task for the next period. The analysis if the uniform representation will be continued. The goal is a constructive method of obtaining the representation and a sharp criterion for choosing the expansion function. ACKNOWLEDGEMENTS The authors wish to acknowledge the contributions of Dr. Ziya Akcasu, Mr. John Ducmanis and Mr. Leon Zukowski to this research. 26

THE UNIVERSITY OF MICHIGAN 5172-6-Q DISTRIBUTION LIST Address Nr of Copies Copy Nr. OASD (R and E), Rm 3D1065 ATTN: Technical Library The Pentagon Washington 25, D. C. 1 1 Chief of Research and Development, OSC Department of the Army Washington 25, D. C. 1 2 Commanding General, U. S. Army Materiel Command ATTN: R and D Directorate Washington 25, D. C. 1 3 CG, U.S. Army Electronics Command ATTN: AMSEL-CB-B Fort Monmouth, N.J., 07703 1 4 CO, Defense Documentation Center ATTN: TISIA, Building 5 Cameron Station, Alexandria Virginia 22314 10 5-14 CO, U. S. A. Combat Developments Command ATTN: CDCMR-E Fort Belvoir, Virginia 1 15 CO, U. S. A. Combat Developments Command Communications s-Electronics. Agency Fort Huachuca, Arizona 1 16 CO, U. S. A. Electronics Research and Development Activity, ATTN: Technical Library 1 17 Fort Huachuca, Arizona Chief, U. S. Army Security Agency Arlington Hall Station Arlington 12, Virginia 2 18, 19 Deputy Pres. U. S. Army Security Agency Board Arlington Hall Station Arlington 12, Virginia 1 20 Dir. U. S. Naval Research Laboratory Code 2027 Washington, D. C. 20390 1 21 27

THE UNIVERSITY OF MICHIGAN 5172-6-Q CO and Dir. U. S. Navy Electronics Lab San Diego, California 92152 1 22 ASD - ASNXRR Wright-Patterson AFB, Ohio 45433 1 23 AFCRL - CRZC L. G. Hanscom Field Bedford, Mass, 01731 1 24 AFCRL - CRXL-R L. G. Hanscom Field Bedford, Mass 01731 1 25 USAERDL Liaison Office - RAOL Rome Air Development Center Griffiss AFB, New York 13442 1 26 NASA Representative Scientific and Technical Information Facility Box 5700 Bethesda, Maryland 20014 2 27, 28 CO, U. S. Army Research Office Box CM - Duke Station Durham, North Carolina 1 29 CO, U. S. Army Electronics Materiel Support Ag. SELMS-ADJ Fort Monmouth, N.J. 07703 1 30 Dir., Monmouth Office U. S. Army Combat Developments Command Communications-Electronics Agency Fort Monmouth, N.J. 07703 1 31 ESD - ESAT L. G. Hanscom Field Bedford, Mass, 01731 1 32 RADC - RAALD Griffiss AFB, New York 13442 1 33 AFSC Scientific/Technical Liaison Office U. S. Naval Air Development Center Johnsville, Pa, 18974 1 34 CO, USAERDL Attn: Director of Research/Engineering Fort Monmouth, N.J. 07703 1 35 28

THE UNIVERSITY OF MICHIGAN 5172-6-Q CO, Engineer Res. and Dev. Labs Technical Documents Center Fort Belvoir, Va. 1 36 Marine Corps Liaison USAERDL Fort Monmouth, N. J. 07703 1 37 AFSC Sci/Tech Liaison USAERDL Fort Monmouth, N. J. 07703 1 38 CO USAERDL Technical Documents Center Fort Monmouth, N. J. 07703 1 39 U. S. Army Research Liaison Colonel M. F. Bavaro MIT-Lincoln Laboratory Lexington, Mass 02173 1 40 CO, U. S. A. Intelligence Materiel Agency Fort Holabird Baltimore, Md. 21219 1 41 CO USAERDL SELRA/SR(T), Thence to FU Nr. 2 (Record Copy) 1 42 Fort Monmouth, N. J. 07703 C. G. Desert Test Center Fort Douglas, Utah 1 43 CO AFCRL - CRZW 1065 Main Street Waltham, Mass 1 44 President, U. S. Army Arctic Test Board Fort Greely, Alaska 1 45 CG, U. S. Army Test and Evaluation Command AMSTE-EL Aberdeen Proving Ground, Md. 1 46 CG, U. S. Army Test and Evaluation Command AMSTE-BAF Aberdeen Proving Ground, Md. 1 47 CG, U. S. Army Missile Command - AMSMI-RB Redstone Arsenal, Alabama 35809 1 48 29

THE UNIVERSITY OF 5172-6-Q CG, U. S. Army Missile Command - AMSMI-RR Redstone Arsenal, Alabama 35809 CO, USAERDL Logistics Division (For: SRD) Fort Monmouth, N. J. 07703 MICHIGAN 1 11 49 50-60 This contract is supervised by the Advanced Development Branch, Radar Division, Surveillance Department, U. S. Army Electronics Research and Development Laboratories, Fort Monmouth, New Jersey, 07703. Telephone - Eatontown, N.J., Area Code 201, 596-1655. Contracting Officer's Technical Representatives are: Mr. V. L. Friedrich and Mr. J. Maresca. 30