DETECTION AND FALSE ALARM PERFORMANCE OF A PHASE-CODED RADAR WITH POST-MTI LIMITING

Transcription

1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY LINCOLN LABORATORY DETECTION AND FALSE ALARM PERFORMANCE OF A PHASE-CODED RADAR WITH POST-MTI LIMITING R. M. O'DONNELL Grup 43 TECHNICAL NOTE NOVEMBER 1975 Apprved fr public release; distributin unlimited. LEXINGTON MASSACHUSETTS

2 ABSTRACT This reprt studies the detectin and false alarm perfrmance f the generic type f radar which emplys a phase-cded pulse cmpressin and an MTI system fllwed by limiting. This technique has been referred t as CPACS (Cded Pulse Anti-Clutter System). One specific implementatin f the technique was studied in detail. Since the prcessr emplys nnlinear peratins, Mnte Carl simulatin techniques were used rather than analytical techniques. The results shw that fr the system simulated there is very pr detectin perfrmance in clutter areas with clutter-t-nise C/N greater than 20 db. Fr values f C/N greater than 30 db there is zer detectability f signal, nise r clutter because f limiting in the A/D cnverters and the limiter after the three-pulse MTI canceller. This is a manifestatin f the s-called "black hle effect". Even in a very lw C/N envirnment the prcessr is 7 db less than the ptimum receiver. iii

3 I. Intrductin It is the purpse f this reprt t study the detectin and false alarm perfrmance f the generic type f MTI radar system in Figure 1. In this radar system the transmitted pulse is staggered frm pulse-t-pulse and is phase cded with a thirteen-bit Barker Cde. The transmitted pulses are staggered in time t increase the unambiguus radial velcity interval and are phase cded t cmpress the pulse s that backscatter frm the grund clutter will be reduced due t the smaller range reslutin cell size. Only ne channel f the received signal is prcessed. This signal is sent thrugh a 9-bit A/D cnverter, a three-pulse canceller, a limiter, a Barker decder and a detectr whereupn the resulting signals are sent thrugh a threshld which is the same fr all range-azimuth cells. Because f the nn-linear elements in the prcessr, a Mnte Carl simu- latin technique was used t evaluate this type f prcessr. It was felt that analytical techniques wuld nt be useful because f the nn-linear elements in the system. When simulating the clutter, care was taken t include the effects f antenna mtin which decrrelates the backscattered clutter frm n [1] pulse-t-pulse. II. Prcessr Structure A. A/D Cnverters It is assumed that the A/D cnverters are 9 bits and that if the signal input t the A/D's is greater than 256=2, the utput value is +256 and that if the signal input t the A/D's is less than -256, then -256 is utput.

4 u 09 cu u u a. 03 C 60 M cd X) M H CE UJ UJ UJ -J UJ CO -1 (T _i id I z> h- CL Z, < c I \ <

5 B. Three-Pulse Canceller It is assumed that the three-pulse canceller may r may nt have a feed- back mde. The difference equatin fr the three-pulse canceller withut feedback is Y.(n) = X.(n-2) - 2 X.(n-l) + X.(n) (1) where Y.(n) is the utput fr the nth pulse and the ith subpulse* and X.(n) is the input t the canceller fr the nth pulse and ith subpulse. The dif- ference equatin fr the three-pulse canceller with feedback is given: Y.(n) = e.(n) - 2 e.(n-l) + e.(n-2) (2) e.(n) = X.(n) - 1/4 e. (n-1) - 1/4 e.(n-2) (3) where X.(n) and Y. (n) are defined as in Equatin 1. In actual peratin f the radar, the feedback ptin in the three- pulse canceller is rarely used. Because f this, the feedback ptin in the MTI circuit was nt used when the radar was simulated in this study. C. Limiter Next, the pulse passes thrugh a limiter whse prperties are Y.(n) = +1 fr X.(n) > 0 Y.(n) = 0 fr X.(n) = 0 Y.(n) = -1 fr X.(n) < 0 *Each pulse is divided up int 13 subpulses by the Barker Cde.

6 where X.(n) is the digital vltage input t the limiter fr the ith subpulse and the nth pulse, and Y.(n) is the vltage utput frm the limiter fr the ith subpulse and nth pulse. D. Decder A standard Barker decder is emplyed t measure which subpulse the target is in. A blck diagram f the decder is given in Figure 2. With this decder, the vltages frm 13 cntiguus subpulse samples are added tgether after weighting by the Barker cdes. E. Detectr It is assumed that the radar has an envelpe detectr which extracts the mdulatin frm the carrier frequency. F. Threshlding The utput f the detectr is displayed n PPI after passage thrugh a fixed threshld fr all range-azimuth cells. III. Simulatin A. Generatin f Targets, Clutter and Nise The target vltage at the radar receiver IF is given by V (t) = a. V cs 2TT fjt s is d

7 u 0) T3 O u cu T3 U <U A! M re P5 I en 3 6 re u M re u H

8 where V = peak signal vltage 2V f = r d = Dppler frequency f target a. = 13-bit Barker cde, +1, +1, +1, +1, +1, -1, -1, +1, +1, -1, +1, -1, +1 V = target radial velcity Y = wavelength f target t = time Nte that the radar des nt have an I and Q channel. Because the radar has nly ne channel, it is subject t the "blind phase" prblem which decreases significantly the average detectability f radar. In this simulatin the target phase was chsen t be the ptimal ne. Because f this effect, actual radar will have perfrmance smewhat less than that simulated here. The target vltage is sampled at the intervals given by ne f the tw nine-pulse staggers used in the evaluatin. The nine-pulse stagger intervals are given in Table 1. The pulse width is assumed t be 6 ysec and thus the pulse width f the subpulses is.46 ysec. Clutter is generated using a prgram develped at the Labratry by M. Labitt. The prgram generates clutter whse crrelatin prperties frm pulse-t-pulse are determined by the scan rate f the antenna, the aperture f the antenna and the wavelength. In this case, the scan rate was ne revlutin per 12 secnds, an aperture f 14.7 meters and a wavelength f.23 meter(l-band). The clutter return fr a given subpulse was taken t be the sum f the return frm clutter cells illuminated by all 13 cded subpulses whse time delay matched the delay fr the subpulse f interest. The 6

9 Table 1 Time Between Pulses (ysec) Stagger 1 Stagger M< sec ysec

10 clutter was assumed t be independent frm subpulse-t-subpulse, but crrelated partially frm pulse-t-pulse due t the scanning f the antenna. Nise was assumed t be zer mean and Gaussian whse RMS value relative t a least cunt in the A/D cnverters was an input parameter. The RMS clutter vltage and RMS signal vltage were calculated frm the input values f clutter-t-nise rati per subpulse and signal-t-nise rati per subpulse, and the RMS nise value relative t a least cunt in the A/D cnverters. IV. Simulatin & Results The results f false alarm statistics f the simulatin are shwn in Figures 3 thrugh 5. Figures 3 thrugh 5 present the prbability f false alarm vs threshld setting per subpulse fr varius clutter-t-nise ratis, threshld settings and values f RMS nise level relative t the least cunt in the A/D cnverters. The three-pulse canceller was used withut feedback and the first f the tw nine-pulse staggers was used. We see frm Figure 4 that fr very lw clutter-t-nise (C/N) levels a threshld f 12 r greater -3-4 is necessary fr a P A f between 10 and 10. Therefre in the detectin FA results which fllw, we chse a threshld f greater than 11 as a criteria fr detectin. In Figure 6, the prbability f detectin vs signal-t-nise per subpulse is pltted fr varius values f C/N. Ntice that detectin per- frmance degrades significantly fr C/N > 20 db. Als fr lw values f C/N, a signal-t-nise rati f abut 1 db per subpulse is necessary fr detect- ability. Fr values f C/N greater than 30 db, there is almst zer detect- ability because f the limiting in the A/D's and the limiter after the three- pulse canceller. 8

11 1.0 5 < UJ in V 00 < CD cc a THRESHOLD SETTING Fig. 3. cunt. Prbability f false alarm vs threshld setting RMS nise =1 least

12 T RMS NOISE LEVEL = 0.5 LEAST COUNT O C/N = -20dB C/N = A C/N = OdB 20dB D C/N = 40dB 5 X < 0.1 CO -J < CD < DD O Od Q THRESHOLD SETTING Fig. 4. Prbability f false alarm vs threshld setting RMS nise level 0.5 least cunt

13 r < UJ tn O > CO < CO RMS NOISE LEVEL O 0.5 LEAST COUNT A 10 LEAST COUNT 1.5 LEAST COUNT CLUTTER-TO-NOISE LEVEL 30dB THRESHOLD SETTING Fig. 5. Prbability f false alarm vs threshld setting clutter-t-nise level (C/N) = 30 db. 11

14 0.8 - LLJ Q O < CD O <T Q_ SIGNAL-TO-NOISE RATIO(dB) Fig. 6. Prbability f detectin vs signal-t-nise rati fr ptimum prcessr and simulated MTT radar at varius clutter-t-nise ratis. 12

15 Thus we see that in the presence f heavy clutter, there is a "black hle effect," that is threshld crssings due targets, clutter, r nise are cm- pletely inhibited. In Figure 6, we have als presented the detectin statistics fr the -4 ptimum prcessr. This curve is the single pulse P^ vs S/N at P_,, = 10 D FA fr a steady target in Gaussian nise. This curve has been ffset by db, 11.1 db due t the gain f the 13-bit Barker cde and 4.25 db due t inte- gratin gain f the three-pulse canceller. It is evident that even fr a very lw clutter-t-nise level envirnment this prcessr is at least 4 db wrse than the ptimum receiver. Als, when the signal was generated the phase f the signal vltage was set equal t zer and the in-phase cmpnent (I channel) used. The assumptin neglected the effects f blind phases f the target. This lss is abut 3 db. Thus, we see that verall, this type f MTI prcessr has abut 7 db less perfrmance than the ptimum prcessr. In Figure 7, the prbability f detectin vs signal-t-nise rati fr C/N = 30 db is presented fr three values f RMS nise vltage relative t a least cunt in the A/D cnverters. It is apparent that the higher the RMS nise vltage, the lwer the perfrmance f the system. In Figure 8, detectin statistics are presented fr three values f target radial velcity. The tw values f target speed which bracket the 35-knt value shw degraded per- frmance as expected. The 35-knt speed crrespnds t the 1/2 the first blind speed in a cnstant PRF system with pulse interval f abut 3 msec, while 69 knts is at the first blind speed. Althugh the detectin perfrmance 13

16 1.0 RMS 1 NOISE A = 0.5 D = 1.0 «1.5 1 (lest cunt s) A A A K A. _ a _ F DETECTION in O >- 1- _l m < m r ^0.4 D / / / / TARGET VELOCITY = 35kts THRESHOLD V >12 CLUTTER - TO- NOISE RATIO = 30dB SIGNAL-TO-NOISE RATIO(dB) Fig. 7. Prbability f detectin vs signal-t-nise rati fr varius RMS nise levels. 14

17 is degraded significantly at the "blind speed", since we are using a staggered PRF, perfrmance is nt reduced t zer. Lastly, an attempt was made t study the effect f changes in the limiter fllwing the three-pulse canceller. The limiter was mdified t have the fllwing prperties. Y.(n) = +1 fr X (n) > 2 Y.(n) = 0 fr x (n) < 2 Y.(n) = -1 fr X.(n) < -2 A graph f false alarm prbability vs threshld setting fr an RMS nise value f 1 least cunt is presented in Figure 9 fr several values f C/N. Fr this type f limiting, the false alarms are bunched dwn at the lwer ends f threshld values fr lw values f C/N mre s than with the nrmal limiter. Figure 10 presents the detectin statistics fr this limiter with a threshlding criteria f the vltage greater than 11 t declare a target. These results shw slightly prer detectability fr this limiter than with the nrmal ne. V. Summary The detectin perfrmance f the radar is gd fr clutter-t-nise (C/N) ratis less than 20 db, and a signal-t-nise rati f 1 db per subpulse is necessary fr gd detectability. Fr C/N greater than 20 db, there is serius degradatin in detectin perfrmance. Fr values f C/N greater than 30 db, there is almst zer detectability f targets, clutter, r nise because f the limiting in the A/D cnverters and in the limiter after the three-pulse 15

18 VELOCITY OF TARGETS (Ms) A 15.0 D Ui h 0.6 >- CD < CD O ce THRESHOLD V > 12 RMS NOISE LEVEL=1 LEAST COUNT CLUTTER-TO-NOISE RATIO I =30dB SIGNAL-TO-NOISE RATIO (db) Fig. 8. Prbability f detectin vs signal-t-nise rati fr varius target velcities. 16

19 1.0 - *\J, ' MODIFIED LIMITER \ RMS NOISE = 1 LEAST COUNT V\ O C/N = -20 db L\\ C/N = OdB \\\ A C/N = 20dB \\\ D C / N = 40dB I \ \ \ i i t j > t i i t i > r \ \ \ 1 \ T \n \ \ «\ \ D JL_Vi_rL_^ THRESHOLD SETTING Fig. 9. Prbability f false alarm vs threshld setting fr MTI radar with mdified limiter. 17

20 SIGNAL-TO-NOISE RATIO (db) Fig. 10. Prbability f detectin vs signal-t-nise rati fr varius clutter-t-nise ratis. 18

21 canceller. Even in a very lw clutter-t-nise level envirnment, this radar prcessr is at least 7 db wrse than the ptimum receiver. 19

22 References 1. M. Labitt, "The Generatin f Scanning Clutter," private cmmunicatin. 2. F. Nathansn, Radar Design Principles (McGraw-Hill, New Yrk, 1969) 20

23 UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) 1. REPORT NUMBER ESD-TR REPORT DOCUMENTATION PAGE READ INSTRUCTIONS BEFORE COMPLETING FORM 2. GOVT ACCESSION NO. 3. RECIPIENT'S CATALOG NUMBER 4- TITLE (and Subtitle) 7. AUTHORS Detectin and False Alarm Perfrmance f a Phase-Cded Radar with Pst-MTI Limiting O'Dnnell, Rbert M. 5. TYPE OF REPORT & PERIOD COVERED Technical Nte 6. PERFORMING ORG. REPORT NUMBER Technical Nte CONTRACT OR GRANT NUMBERS F C PERFORMING ORGANIZATION NAME AND ADDRESS Lincln Labratry, M.I.T. P.O. Bx 73 Lexingtn, MA CONTROLLING OFFICE NAME AND ADDRESS Air Frce Systems Cmmand, USAF Andrews AFB Washingtn, DC MONITORING AGENCY NAME & ADDRESS (if different frm Cntrlling Office) Electrnic Systems Divisin Hanscm AFB Bedfrd, MA PROGRAM ELEMENT, PROJECT, TASK AREA & WORK UNIT NUMBERS Prgram Element N F Prject N. E REPORT DATE 21 Nvember NUMBER OF PAGES SECURITY CLASS, (f this reprt) Unclassified 15a. DECLASSIFICATION DOWNGRADING SCHEDULE 16. DISTRIBUTION STATEMENT (f this Reprt) Apprved fr public release; distributin unlimited. 17. DISTRIBUTION STATEMENT (f the abstract entered in Blck 20. if different frm Reprt) 18. SUPPLEMENTARY NOTES Nne 19. KEY WORDS (Cntinue n reverse side if necessary and identify by blck number) phase-cded radar MTI radar system Cded Pulse Anti-Clutter System (CPACS) 70. ABSTRACT (Cntinue n reverse side if necessary and identify by blck number) This reprt studies the detectin and false alarm perfrmance f the generic type f radar which emplys a phase-cded pulse cmpressin and an MTI system fllwed by limiting. This technique has been referred t as CPACS (Cded Pulse Anti-Clutter System). One specific implementatin f the technique was studied in detail. DD U AN M EDITION OF 1 NOV 65 IS OBSOLETE UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (Uhen Data Entered/

24 DEPARTMENT OF THE AIR FORCE HEADQUARTERS ELECTRONIC SYSTEMS DIVISION (AFSC) HANSCOM AIR FORCE BASE, MASSACHUSETTS REPLY TO ATTNOF: TML (Lincln Lab) 3 December 1975 SUBJECT E8D-TR , dtd 21 Nv 75, "Detectin arid False Alarm Perfrmance Of a Phase-Cded Radar with Pst-MIT Limiting" TO: DDC/Air Frce Liaisn Representative Camern Statin Alexandria, VA 2231^ 1. I certify that the subject TR has been reviewed and apprved fr public release by the cntrlling ffice and the infrmatin ffice in accrdance with AFR 80-45/AFSC Sup 1. It may be made available r sld t the general public and freign natinals. 2. Distributin statement A appears n the subject TR and the DD Frm 1473 as required by AFRs and FOR THE COMMANDER A, EUGENE C. RAABE, Lt Clnel, USAF Atch Chief, Lincln Labratry Prject Office ESD-TR (12 cpies)