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- 1. PRI Analysis and Deinterleaving Richard G. Wiley, Ph.D. Research Associates of Syracuse, Inc 111 Dart Circle Rome, NY 13441 315-685-3135; dwiley@ras.com 1 Pulse Repetition Intervals (PRIs) are often the key to identifying the signals of many radar systems. The first step is to deinterleave signals from multiple radar systems. This briefing is a a brief introduction to PRI analysis and deinterleaving from the ELINT/EW point of view 2
- 2. PULSE REPETITION INTEVAL (PRI) 3 ELINT Implications of Range Equations and Radar Constraints The effects of the one-way range equation of ELINT and the twoway range equation of radar on signal strength must be understood and explored in order to appreciate the typical situations encountered in ELINT and EW. Similarly, the constraints placed on radar waveforms must be understood in order to correctly interpret the functions and applications of the signals transmitted by radar and also to be aware of the signal characteristics expected to be encountered by ELINT. In many ways, understanding these aspects of ELINT is what separates one who only observes signals from one who both observes and analyzes signals. Reference: ELINT, Chapter 2 4
- 3. Radar and ELINT Range Equations 2 SR PT GT G R 3 4 (4 ) R R LT LR PT GTE G E 2 2 2 (4 ) R E LT LE SE 5 Ratio of ELINT Range to Radar Range A significant aspect of these range equations is that the power level transmitted by pulsed radar transmitters in order to detect targets at long range is very high. This allows ELINT receivers to detect radar signal at very long ranges even when observing the sidelobes of the radar’s transmit antenna. To simplify the discussion, suppose that the ELINT receiver requires a signal level that is a factor times the signal level needed by the radar receiver, that is: SE RE RR RR 4 1 GTE G E LE GT G R LR 6 (S R ) 1/ 2
- 4. 3 1 10 RR 4 GR 100 Ma RangeRatioSL i : am be in 1/ 2 GT =3 E RE/RR ELINT Range/Radar Range RE RR RE RR B 0d RangeRatioMBi be elo Sid 10 : GT =0 E RR 4 GR 1/ 2 dB A 1 sq. m G R 30 dB 100 G E 1 1 10 100 1 Ri Range (km) Figure 2-1 ELINT to Radar Range Ratio 7 2.2 Radar Constraints ELINT signals of interest include radar signals of all types. Sometimes, people concerned about ELINT attribute properties to radar signals that are contrary to the constraints under which radar systems must function. Avoiding this pitfall is an important aspect of ELINT work. Understanding the fundamental limitations faced by radar designers and the associated ELINT implications is important. Consider this statement: “Radars of the future could transmit noise waveforms over GHz bandwidths and be undetectable by ELINT receivers.” Should ELINT equipment be developed to intercept and process this kind of signal? Probably not-because signals like this would not be useful for tracking or search radars in military applications. 8 3 1 10
- 5. Range Resolution related to Bandwidth Range resolution in radar is inversely proportional to the bandwidth of the signal (assuming that it is processed coherently). The fundamental relationship is: c R 2B Here c is the speed of light and B is the bandwidth of the signal during the coherent processing interval; also called its instantaneous bandwidth. For example, to distinguish between two fighters in tight formation 30m apart in range, BW must be about 5MHz. If one postulates a value of B=1 GHz, the radar has a range resolution of 15 cm. This means that the target echoes are resolvable in 15 cm range increments called range cells. The echoes from a 75m target are spread across 500 range cells. 9 Range Resolution (meters) Range Resolution (meters) 1 10 3 100 RngRes bi 10 1 6 1 10 7 1 10 bi Bandwidth (MHz) Bandwidth B (MHz) 1 10 8 Figure 2.2. Range resolution Related to Radar Coherent Bandwidth 10
- 6. This spreading of the echoes across a multiplicity of range cells reduces the apparent radar cross-section (and thus reduces the SNR available) in a single range cell. For this reason, radar designs generally have range resolution appropriate for their function. This leads to choosing coherent bandwidths of 10 MHz or less. (10 MHz corresponds to range resolution of 15 m.) In this sense, there is no such thing as a “spread spectrum” radar— what is transmitted is also received and the resulting range resolution is determined by the bandwidth. What this means for ELINT is that the coherent bandwidth of radar signals is likely to remain the same as it is now provided the radar performs the same task. Range Resolution Required Resolution (m) Bandwidth (MHz) 30 60 5 2.5 2. Detect missile separation at launch 15 10 3. Imaging of Ships, Vehicles and Aircraft .5-1 150-300 4. High Resolution Mapping 0.15 1000 1.Count A/C in attack formation 11 Moving Targets and Integration Time Constraints If a radar is to detect targets moving in a radial direction (toward or away from the radar), the amount of time the target will be present in a given range cell is determined by the target velocity and the range resolution. This limits the coherent integration time of present day radars to R R TCV v v Here TCV is the maximum coherent integration time for a constant velocity target with radial velocity v and R is the change in range during that time. If the target is accelerating in the radial direction, the maximum integration time is now a quadratic function of both velocity and acceleration T ACC v v 2 2a ( R ) a 12 0.5 v v 2 2a ( R ) a 0.5
- 7. Constraints on Time-Bandwidth Product or Pulse Compression Ratio Because range resolution is determined by bandwidth and integration time is determined by velocity, there is a natural limit on the product of the instantaneous bandwidth and the duration of the coherent processing interval or pulse width. This is called the "timebandwidth product." The radar's pulse compression ratio is limited to no more than its time bandwidth product. By combining Equations for range resolution and integration time it is easy to see that the time bandwidth product is limited to: Bv a BT ac 1 Bv 2 1 a 0 c 2v 13 BT Limit Maximum time-bandwidth product BT 1 10 6 a=0 g BT i 1 BT i 2 a=1 g BT i 5 g a=2 BT i 10 a=5 g BT1 i 10 a= g Acceleration 0, 1,2, 5, 10 g's Velocity=300m/s 1 10 5 4 1 10 5 1 10 bi Signal Bandwidth B (Hz) Bandwidth Figure 2-414 Limit on Time x Bandwidth 6 1 10
- 8. Constraints on Doppler Resolution If the radar coherently integrates the echoes in one range cell for the entire integration time, the minimum doppler filter bandwidth, Bf, is approximately the reciprocal of the integration time,.T, which is either TCV for constant velocity targets or TACC for accelerating targets:. 1 T Bf However if the target is accelerating, the doppler shift changes. Clearly there is a relationship between acceleration and the time the doppler shift of the moving target remains within the doppler filter bandwidth. f acc 2aTf o c 2aT Bf 15 Because the coherent integration time is approximately equal to 1/Bf, substituting Bf=1/T into 2-12 gives the maximum allowable coherent integration time and the minimum doppler filter bandwidth as T 2a , Bf 16 2a
- 9. 1 10 6.502 10 3 1 10 Doppler Spread( kHz) 4 a=10g 3 fi 1 100 fi 2 a=1g fi 5 10 f i 10 1 0.65 0.1 3 1 10 1 10 0.01 0.1 3 1 Ti 1 Coherent Integration time T (s) Figure 2.5 Doppler Spread and Maximum Signal Bandwidth 17 1 10 3 1000 1 10 Doppler Spread( kHz) 1 10 3 ple Dop fi 1 fi 2 100 r ad Sp r e fi 5 f i 10 - ri gh le t sca Ma xi m um 10 a=10g a=5g a=2g g a=1 Bi Sig n 1 al B 10 and w 0.65 0.1 3 1 10 0.01 100 idt h -le f t sc ale 1 0.1 .001 Ti Coherent Integration time T (s) Figure 2.5 Doppler Spread and Maximum Signal Bandwidth 18 1 1 1 Bandwidth (MHz) 6.502 10 4 3
- 10. The doppler filter bandwidth must be no wider than the spread of doppler frequencies expected. Figure 2-5 also shows the maximum radar signal bandwidth. For the case where acceleration has a minimal effect on the integration time, the maximum acceleration of the target can be expressed in terms of the radar signal's bandwidth as a max v2 2B 2 c( RF ) 19 Long integration times require small target acceleration. The radar designer must choose a bandwidth that suits the range resolution required and integration to suit the target motion expected. Long integration time implies either slow targets with little acceleration or else poor range resolution. High acceleration targets require wider signal bandwidths. An aircraft target approaching at 300m/s and maneuvering at 3 g’s needs a radar signal bandwidth of at least 2.5 MHz at 10 GHz. Radar signals exhibit relatively constant characteristics during coherent integration--important to know for ELINT analysis. Tracking radars extend the coherent integration time when target velocity and acceleration are known. Examining all possible target velocities and accelerations requires huge processor throughput and is generally not practical today. 20
- 11. Frequency Agility From one coherent processing interval to the next, the radar can change its carrier frequency without changing its range resolution properties. The agility band is limited by the radar designer’s ability to obtain sufficient power and to maintain beam width and pointing angle--typically about 10% of the center frequency. (For example, a 1 GHz agility band centered at 10 GHz.) What this means for ELINT is that narrowband receivers have a low probability of intercepting the complete radar transmission. If it is sufficient to intercept only portions of the radar transmission, narrowband receivers can be slowly tuned across the radar band and the entire agility band can still be determined if the signals is present for enough time. The coherent processing interval determines the Doppler resolution. When FA is used with doppler processing, the frequency is changed on a pulse-burst to pulseburst basis, not a pulse-to-pulse basis. 21 PRI Agility Modern multifunction radar systems make use of multiple pulse repetition intervals (PRI) values during one look at the target. It is a requirement of today’s pulse doppler radars that the PRI remain constant during each coherent processing interval. For moving target indicating (MTI) radar designs, there is usually a sequence of PRI values that must be completed during one processing interval. This repeated sequence is known as "stagger" and ELINT analysts call the period of the stagger the stable sum. This is because when consecutive PRIs are added, the sum is constant when one adds together the PRIs which make up the stagger period--regardless of which PRI is selected as the starting point for the sum. 22
- 12. MTI radars operate by subtracting (in amplitude and phase) the echoes from one PRI from those in the next PRI. Stationary targets have the same phase and amplitude and thus “cancel.” Echoes from moving targets generally do not have then same amplitude and phase and so do not cancel. However if the target moves an integer multiple of half wavelengths in one PRI, the phase of the second echo is shifted by a multiple of 360 degrees from the first and the echoes cancel. Such speeds are “blind speeds.” Changing the PRI changes the blind speed. A PRI sequence is selected to detect targets regardless speed Moving target detection (MTD) radar systems use a doppler filter bank to divide the frequency region between the PRF lines into several filter bands (for example: 8 bands). This requires repeated constant PRIs (say 10 pulses at one PRI and then 10 pulses at another, etc.) Multiple PRIs are required due to range and velocity ambiguities and make visible target ranges and velocities “eclipsed” by transmitted pulses (in 23 time) or spectral lines (in frequency). For constant PRI and RF, the maximum unambiguous range (Ru) and the maximum unambiguous velocity (Vu) are given by: Ru c(PRI ) 2 c 2( RF )( PRI ) Vu Examples at 10 GHz: PRI 1000 us, Vu=15 m/s and Ru=150 km PRI 100 us, Vu=150 m/s and Ru=15 km PRI 10 us, Vu=1500 m/s and Ru=1.5 km As can be seen, the product of unambiguous range and velocity is a constant. This means that the total ambiguity is fixed but changes in PRI can increase the unambiguous range but decrease the unambiguous velocity and vice versa. c2 RuVu 24 4( RF )
- 13. 6 1 10 6 10 Inverse relationship of unambiguous range and unambiguous velocity at common radar frequencies Rui 1 Rui 31 105 22 5M Rui 4 1 .3 Rui 5 Rui 6 10 4 1 10 Rui 7 35 Rui 8 1000 15 GH z GH z GH z 5 .5 3G Hz GH z 42 5M GH z Hz Hz 3 1 10 10 10 3 100 4 1 10 1 10 Vui 1 Vui 2 Vui 3 Vui 4 Vui 5 Vui 6 Vui 7 Vui 8 10 25 Unambiguous Velocity (m/s) Fi 2 7R /V l it R l t d Frequency Agility Band Frequency Unambiguous Range (m) Rui 2 (Depends on Component Design, ECM Factors, Designer Ingenuity) * Coherent Processing Interval (depends on radar mission) Time Determines Range Resolution *BandwidthDepends on Radar Mission Which Figure 2-8. Modern frequency Agile Radar with 100% Duty Factor 26 4
- 14. USES OF PRI 27 UNAMBIGUOUS RANGE AND VELOCITY DEPENDENCE c c Analysis p. 147 28
- 15. RANGE-VELOCITY AMBIGUITY Analysis p. 148 29 OPTIMUM PRI FOR MEDIUM PRF RADAR 30 Text p. 149
- 16. OPTIMUM PRI FOR MEDIUM PRF RADAR Band “Be” Obscured at each PRF line 31 NOMINALLY CONSTANT PRI 32
- 17. PRI DRIFT 33 Analysis p. 153 CRYSTAL OSCILLATORS AND COUNTDOWN CIRCUITS 34 Analysis pp. 191, 192
- 18. SCR-584 35 SEARCH RADAR PRI SELECTION 36
- 19. PRI STAGGER Definition: Two or more discrete PRI intervals (elements) are alternating in a periodic fashion. T • Desired Parameters - Number of intervals - Number of positions - Interval values - Sequence - Stable sum T T T Unmodulated Pulse Train T+ T- T+ • Stagger Ratio T- Typical Staggered Pulse Train Two Interpulse Intervals Shown • Stagger Versus Jitter 37 RADARS WITH STAGGER Radar Pulse Width (μs) Average PRI (μs) Actual PRI’s Stagger Mode (μs) Stagger Ratio Stagger Purpose Radar Function 1. 6,18 100 2500 3500 5:7 To eliminate blind speeds Surveillance 2. 4 3049 3032 3066 89:90 To eliminate blind speeds Height Finder 3. 6 3000 2954.55 3045.45 0:97 (almost 100:103) To eliminate blind speeds Surveillance 4. 6 3000 2897 3103 613 1167 14:15 To eliminate blind speeds Experimental surveillance 1000 5:7 5. 24 3000 2750 3250 11:13 To eliminate blind speeds Surveillance 6. 3 1375 1250 1500 5:6 To eliminate blind speeds Acquisition 7. 20 5247 5000 5494 0:91 (almost 10:11) To eliminate blind speeds Surveillance 8. 2 2777.9 2572.0 2777.8 2983.5 25:27:29 To eliminate blind speeds Air route surveillance 9. 1.4, 4.2 1250 1240 1260 0.984 (almost 125:127) To identify second-time-around pulses Gap filter, surveillance and interrogator 10. 2 2632-3226 Unknown 8-pulse stagger with three programs Unknown To eliminate blind speeds Air route surveillance 11. 42 1551.6 1408 (3) 1667 (3) 1460 (3) Almost 1033:1225:1073 3 pulses at each interval for double cancellation MTI to eliminate blind speeds Detection; threat evaluation and target designation (long range mode given here) 12. 6.7 4000 3571.4 (3) 4405.1 (3) 3745.3 (3) 4255.3 (3) 4081.6 (3) Exact order of 1 pulse intervals is not known 3 pulse canceller for MTI. Stagger to eliminate blind speeds Surveillance 13. 1-100 400 62.1 2500 For first sequence only: 623.3 818.0 740.1 662.0 701.1 Various Sequences 16:21:19:17:20:18 16:17:16:17 16:19:16:19 38 16:21:16:21 16:17 To eliminate blind speeds. Has various digital MTI processing including double double-cancellation Surveillance, tracking, kill assessment, missile guidance
- 20. DESCRIPTION OF PRI VARIATIONS Nature of Pulse-to-Pulse PRI Variations Periodic Discrete Large Type 1 Small Random (non-periodic) Continuous Large Small 3 Discrete 4 2 Large 5 Continuous Small 6 Large 7 Small 8 (Large implies intentional, small implies incidental) 39 JITTERED PRI Definition: Pulse repetition intervals are intentionally varied on interval-to-interval basis in a random or pseudorandom fashion. The variations are usually more than one percent. • Intentional Jitter - Discrete or continuous • Desired Measurements - Mean PRI - Peak PRI deviation limits - PRI distribution (histogram) - Number of discrete PRIs 40
- 21. RADARS WITH JITTER PRI (μs) Pulse Width (μs) Peak-to-Peak Jitter (μs) 6, 18 3000 1000 505 26 4629 92.6 200 4000 50 20 5 400 10204 10204 6666 999.9 918.4 653.3 0.9 416-1515 (Variable) 4-50 4-2.67 500-2777.7 3.3-4.0 Peak-to-Peak Jitter (%) 1.7 5 Radar Function Anti-ECM and interference Target tracking Anti-ECM and interference Long-range surveillance Random Or Programmed Anti-ECM. Results from PRF being submultiple of RF which is jumping Decoy discriminator target tracking acquisition Unknown Unknown High resolution synthetic aperture mapping Random 2.2-12 None Sruveillance Random 9.8 9.0 9.8 Anti-ECM and interference Random 20 20 60 Jitter Purpose Random 3.75 83-303 Jitter Type To reduced inward range gate stealers, antiinterference, reduce second-time around echoes Multifunction 41 PRI DWELL/SWITCH – PULSE DOPPLER Definition: Rapid (automatic) switching between discrete PRIs with a dwell at each PRI PRI = T1 PRI = T2 Dwell Time 1 • Dwell Time 2 Desired measurements - Number of PRIs - Value of PRIs - Dwell times - Total dwell time for sequence - Dwell sequence - Time to switch 42
- 22. SLIDING PRI Definition: The pulse train has a PRI (PGRI) that is continuously changing in either a monotonically increasing or decreasing manner between maximum and minimum PRI limits. • Desired Parameters - PRI limits (min and max) - Sweep waveform - Sweep time (limits) 43 OTHER PRI TYPES 1 • Periodic Modulation Definition: Pulse train consists of discrete or continuous intervals that periodically increase and decrease, e.g., with sinusoidal, sawtooth or triangular waveform - Modulating waveform and rate - Mean PRI and peak deviation limits • Pulse Interval Displacement Definition: Insertion of a different pulse interval into an otherwise periodic pulse train - Displacement value 44
- 23. OTHER PRI TYPES 2 • Interrupted Pulse Train Definition: Intentional interruption of the pulse train with no apparent periodicity - Range of on-period - range of off-period • Burst Pulse Train Definition: Pulse train that is transmitted for some purpose for a relatively short time and then is off for a relatively long time - Burst definition - Number of bursts per second - Relationships of burst to scan 45 SCHEDULED PRIs • Scheduled PRIs Definition: PRIs are computer controlled, vary with the target environment and function being performed by radar, and cannot be described by other definitions - Number of intervals - Interval values - Typical sequences - Reason for sequence 46
- 24. MUTLIPLE PULSE GROUPS • Constant and Cyclic Patterns Definition: Pulse group characteristics remain constant or vary cylically in predictable manner - Number of pulses in group - Pulse intervals - Group position data • Frames/formatted pulse trains (data encoded format) Definition: Pulse train includes marker and data pulses 47 SUMMARY OF PRI TYPES Analysis p. 151 48
- 25. DOPPLER EFFECT v = radial velocity c = 3(108) m/sec fo = transmitted RF v km/hr FIGURE 3-1. DOPPLER EFFECT f 1 fo c v c-v Doppler Shift fo f d 1 f 1 100 2v c fo Doppler Shift (Hz) @ 3 GHz @ 10 GHz 555.5 1851.8 1000 fo 49 50 18518.5 2000 2v c 5,555 11,111 37,037.0
- 26. FOURIER TRANSFORMS 51 IDEAL VS. ACTUAL SPECTRA FOR CW SIGNAL 52
- 27. FM THEORY V(t) A sin(2 f c t (t)) Phase Disturbance Total Phase (t) 1 d (total phase) 2 dt Instantaneous Freq. ASSUME 2 f ct (t) 1 d 2 dt fc 1d 2 dt sin2 f m t fm cos2 f m t Let F/f m , then 1 d 2 dt Fcos2 f m t THEN : V(t) f sin2 f m t) fm Asin(2 f c t INDEX OF 53 MODULATION" M" BESSEL EXPANSION V(t) A Jo (m) sin c t J (m) sin( c 1 J (m) sin( c 2 2 m )t m )t sin( c J (m) . . . . . 3 J0(m) J1(m) J1(m) J2(m) J2(m) fc-2fm fc fc+2fm fc-fm fc+fm 54 sin( c 2 m t) m )t
- 28. BESSEL FUNCTIONS 55 MOD. INDEX LESS THAN 1 FOR COHERENT SIGNALS: m f fm 1 J o (m) 1 J (m) 2 0 i.e. f is small m 2 J (m) 1 J (m) 3 0 ....... etc. THEREFORE V(t) A[sin c t m sin( c 2 A m )t m sin( c 2 m )t] V SB Vc m 2 f 2f m mA/2 mA/2 in dB fc-fm fc V 20 log SB Vc fc+fm 56 20 log f 2f m
- 29. EXAMPLES 20 log f 2f m f 2f m 40 dB 1 kHz e.g. f m 1 kHz f 20 Hz IF f c 10 GHz, STABILITY IS 20 Hz 10 x 109 Hz 2 parts in 109 (AT 1 kHz RATE) 57 RANGE AMBIGUITY RESOLUTION VIA MULTIPLE PRIs 12 μs = X T1 = 40 μs 2 μs = Y T2 = 30 μs Actual Round Trip Echo Time is T = 92 μs N1 T1 + X = T Trial and Error Solution and N2 T2 + Y = T N1 N2 N1 T1 + X N2 T2 + Y 1 1 2 2 1 2 2 3 52 52 92 92 32 62 62 92 Unambiguous Range c x Least Common Multiple of T , T 1 2 2 c x 120 s 2 58 Analysis p. 196
- 30. ERICSSON PS-05/A MULTIMISSION RADAR 59 ERICSSON PS-05/A MULTI-MODE OPERATION (1) 60
- 31. ERICSSON PS-05/A MULTI-MODE OPERATION (2) 61 MTI VIDEO 62
- 32. MTI PHASE SHIFTS 63 MTI BLOCK DIAGRAM 64
- 33. BIPOLAR VIDEO 65 DOPPLER RETURNS TRAIN CAR Typical images displayed on TPS-25 ground Surveillance radar. Shown are target images of: 1) a train, 2) an automobile, 3) a walking man, and 4) a walking girl. (US Army photograph.) MAN WALKING WOMAN WALKING 66
- 34. PULSED-OSCILLATOR MTI = 2E sin( fdT) cos [2 fd(t + T/2) + Zeros at 0, , n f d when n T so blind speeds are V b c n 2RF T n 2 Barton, p. 192 67 Page M50.ppt 68 PRF o]
- 35. BLIND SPEED ELIMINATION No Stagger 6 T vb = n c/2(PRI)(RF) T T 1 T Vbn = Vb (7 + 5)/2 5 7 Deep lobe at 32/T T T 63 65 Null at 64/T Ref: Barton, page 222 69 IMPROVEMENT FACTOR OF CANCELLER I (S/C)out (S/C) in signal to clutter ratio at output of canceller signal to clutter ratio at input of canceller Overall improvement factor I is found from: 1 I 1 I 1 1 I 2 1 I 3 .... I1, I2, I3 are the individual improvement factors calculated on basis of PRI, pulse amplitude, pulsewidth, transmitter frequency, ……….. stabilities 70
- 36. INSTABILITY LIMITATIONS 71 CLUTTER STRENGTH 72
- 37. MTI + PULSE DOPPLER = MTD Weighting And Magnitude 8-Pulse Doppler Filter Bank 3-Pulse Canceller I,Q Data From A/D Converters Threshold Zero Doppler Filter Clutter Map (Recursive Filter) Magnitude (I2 + Q2)1/2 Typical Applications New FAA ASR radars (10 pulse dwell) AN/SPS-49 USN-adjunct to AEGIS (6-pulse dwell) RAMP (Canada) Clutter Memory 15 – 20 radar scans are needed to establish the clutter map 73 MTD PERFORMANCE • Theoretical RMS Clutter Width Processor 0.01 PRF 0.1 PRF MTI Improvement Factor 1 canceller 2 cancellers 3 cancellers 25 dB 50 dB 72 dB 8 dB 12 dB 16 dB FFT Improvement Factor 8 pulses 35 dB 22 dB MTI + FFT Improvement Factor 1 canceller + 8 pulse FFT 2 cancellers + 8 pulse FFT 3 cancellers + 60 dB 28 dB 80 dB 34 dB 100 dB 36 dB (Reference: NRL Report 7533, G.A. Andrews, Jr.) • Practical Performance of FAA ASR radar: 3 pulse MTI alone 25 dB 3 pulse MTI + 8 pulse FFT 45 dB (Reference: Skolnik, Introduction to Radar Systems, 1980, p. 127-128) 74 Target Detection
- 38. ELINT IMPLICATIONS OF MTD • Coherent carrier RF stability is necessary • Constant PRIs Constant RF (for a certain number of pulses) Several PRIs of the same interval must be transmitted at the same RF (typically 4, 8, or 16 pulses for the FFT plus pulses to fill the canceller. For example, a three-pulse canceller plus an eight-pulse FFT requires 10 pulses). • “Stagger” to eliminate blind speeds For these radars, the pulse interval stagger occurs not from pulse-to-pulse but from pulse group-to-pulse group • Long PRI MDT is generally used for long-range radars where the low PRF creates very ambiguous Doppler shifts. 75 PRI EXERCISES 1. The analyst found a signal at 6 GHz which had two-interval, two-position stagger. The intervals were 500 and 550 microseconds. What is the average PRI? What is the stagger ratio? What is ? What are the new blind speeds? 2. What is the improvement factor for MTI of a radar which has RMS jitter of 10 nanosec and a pulse duration of 1.41 microsec? 3. A discrete random jitter PRI train was analyzed and the PRIs were found to be one of the following 5 nominal values: Nom PRI (μsec) 2440.8 2428.7 2465.3 2453.1 2562.9 Is there a clock? If so, what countdowns are used and what is the clock frequency or period? What common range mark is that closest to? (This problem is discussed on p. 194-195 of analysis book.) 76
- 39. PRI EXERCISES #2 - ANSWERS 1. (500 + 550)/2 = 525 microsec = average PRI R = 550/500 = 1.1 (11:10) = 550 – 525 = 25 microsec Blind speed before stagger = nc/(2 • PRIave • RF) (3 x 108 ) m / sec VB 171.4 km / hr (106.5 mph ) 2(525)(10 6 ) sec x 6(109 ) x 1 / sec V/VB = (11 + 10/2 = 10.5) V = (10.5) (171.4) = 1800 km/hr (1118.4 mph) 2. Improvement factor due to PRI instability is: IdB = 20 log [ / 2 t B )], B = bandwidth = jitter, = pulse duration, 2 IdB = 20 log [1.41 (10-6) sec/ 2 • 10(10-9)sec)] = 20 log [102] = 40 dB 3. Period 2440.8 2428.7 2465.3 2453.1 2562.9 Periods In Order 2482.7 2440.8 2453.1 2465.3 2562.9 Difference 12.1 12.3 12.2 97.6 Nearest Countdown 199 200 201 202 210 Calculated Clock Period 12.20452 12.20400 12.20447 12.20445 12.20428 12.204392 average The differences 12.1, 12.3, 12.2 average 12.2 97.6 divided by 12.1 = 8 So use 12.2 to start for countdowns. The average clock period is 12.204392 μsec so reciprocal is 81.93777 kHz (2000 yards, see p. 192.) 77 NOISE EFFECT ON PRI Triggering Error T T RISE 0.8 A A A A T Noise A T TRISE/0.8 78 Slope A (TRISE / 0.8)
- 40. PRI VARIATION DUE TO NOISE 2 amplitude Noise Power 1 (Amplitude)2 Signal Power SNR T Rise 1 Time 0.8 SNR 2 2 2 2 2 PRI Time1 Time 2 Time T 2 Rise PRI 0.8 SNR 79 BANDWIDTH EFFECT ON SNR SNR 3.125 tr PRI 2 tr .35 Bandwidth SNR Required for Bandwidth (MHz) Rise Time Limit (ns) 1 ns Jitter 10 ns Jitter 100 ns Jitter 0.1 3.5 s 81 dB 61 dB 41 dB 1.0 0.35 s 61 dB 41 dB 21 dB 10.0 35 ns 41 dB 21 dB X 100.0 3.5 ns 21 dB X X 80
- 41. AMPLITUDE INDUCED ERROR 81 AMPLITUDE COMPENSATED TRIGGER 82
- 42. PERFORMANCE OF TRIGGER CIRCUIT 83 DOPPLER SHIFT OF PRI • In 1 PRI, the platform moves VR • PRI • Transmit time from transmitter to receiver changes by VR • PRI/c • Example: VR = 600 M/S PRI = 3000 μs 3 Observed PRI = 600 x 3 x 10 3 x 108 84 6 ns
- 43. DELAY AND PULSE JITTER Delay D2 Delay D1 Peak-to-Peak Jitter At Delay D1 Peak-to-Peak Jitter At Delay D2 85 DELAYED SWEEP JITTER PHOTOS ~ 1 μs Jitter Delay = 1 PRI ~ 2 μs Jitter Delay = 5 PRI 86
- 44. SYNTHESIS OF AVERAGE PRI 87 PRI DRIFT MEASUREMENT 88
- 45. REAL TIME RASTER DISPLAYS 89 DUAL AMPLITUDE AND TIME DELAYS 90 Analysis p.74
- 46. DTE MODE-CIRCULAR SCAN RADAR 91 RTR SIMULATION ON A PERSONAL COMPUTER 92
- 47. MEAN PRI ESTIMATES 93 MINIMIZING THE SQUARED ERROR 94
- 48. RMS ERRORS COMPARED 95 96
- 49. 97 NONCUMULATIVE AND CUMULATIVE JITTER 98
- 50. CRAMER-RAO BOUNDS COMPARED 99 PRI ESTIMATION PERFORMANCE 100
- 51. USING THE WRONG JITTER MODEL 101 PRI HISTOGRAMS 102
- 52. ACTIVITY IN 0.1S INTERVALS 103 INTERVALS FORMED BY PULSE PAIRS 104
- 53. DELTA-T HISTORGRAM (10% JITTER) 105 DELTA-T HISTOGRAM-STAGGER ••• 4 t0 = 0 5 t1 = 4 7 4 t2 = 9 t3 = 16 A. C. (tn – tn-3) = 16 D. t6 = 27 (tn – tn-5) = 25, 27, or 2 F. t5 = 25 4 (tn – tn-4) = 20, 21 or 23 E. 1 2 (tn – tn-2) = 9, 11 or 12 t4 = 20 7 (tn – tn-1) = 4, 5 or 7 B. 5 (tn – tn-6) = 32 3 4 5 (4 + 5, 4 + 7, 5 + 7) (4 + 5 + 7) 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 A B C D 106 E F 5 t7 = 31 ••• t7 = 37
- 54. THREE POSITION STAGGER 107 DELTA-T HISTOGRAM: TOA AUTOCORRELATION n f (t ) n 1 (t tn ) ..... t1 t2 . . . . . h( ) h( ) f (t ) f t tn ) n (t tn tk 0 tk tn k value only if t EXAMPLE t1 t4 . . . . . dt (t t3 0 and OR t n t = t2 tk t3 t=0 t = t1 + ) dt 108 t4
- 55. DELTA-T HISTOGRAM: TOA AUTOCORRELATION h( ) 2 n k h( ) 1 (t n t 2 ) k (t n n k 1 t k ) A count of the number of pulse pairs such that 1 tn t k 2 THEREFORE: A count of the number of pairs of pulses whose arrival times differ by a value between 1 and 2 is equal to the integral of the autocorrelation of the TOA’s 109 JITTER ANALYSIS MODEL Center Frequency (average PRF) Jitter Waveform Peak Amplitude FM Oscillator Trigger Generator Periodicities • Periods • Amplitudes Drifts/Trends • Slopes Random Components • Bandwidths • Variances • Probability Densities 110 Time of Arrival Sequence
- 56. INSTANTANEOUS FREQUENCY ESTIMATION 500 700 600 500 400 2500 Freq 2000 1428.5 1666.7 2000 PRIs (μs) 500 2000 Linear Interpolation Midpoints of Intervals 111 DEINTERLEAVING DEVICE 112
- 57. DEINTERLEAVING VIA DELTA- HISTOGRAM 113 “PURE” VS. “IMPURE” INTERVALS 114
- 58. NUMBER OF EMITTERS DEINTERLEAVED 115 COMPLEX DELTA- HISTORGAM - I 116
- 59. COMPLEX DELTA- HISTOGRAM - II 117 COMPARISON OF DELTA- 118 HISTOGRAMS
- 60. EFFECT OF A NEAR MULTIPLE PRI 119 EFFECTS OF JITTER ON DELTAHISTOGRAMS 120
- 61. Delta-T Histogram for Ten Interleaved Pulse Trains Delta-T Histogram Histogram Count 100 dhist b .75 max( dhist ) 50 0 5 8 10 1 10 4 1.2 10 4 1.4 10 int vb PRI k 10 4 1.6 10 4 6 PRI, Seconds N 820 10 Interleaved Pulse Trains 121 Comparison of the Delta-T and Complex Delta-T Histograms Comparing Delta-T Histograms 100 100 abchist b dhist b 0 1.05 max( abchist ) 1.05 max( dhist ) 50 100 0 1 10 4 2 10 4 3 10 int vb PRI k 10 N 820 6 4 4 10 int vb PRI k 10 PRI, Seconds 4 6 10 Interleaved Pulse Trains Top Trace is the regular Delta-T Histogram; Bottom Trace is the Complex Delta-T Histogram--Note how multiples of the PRIs are suppressed The dots above the peaks indicate the true PRI values 122 Delta-T Hisotgram bin Count Complex Histogram Absolute Value 150
- 62. Effect of Jitter on Delta-T Histograms (Jitter=1 microsecond) Comparing Delta-T Histograms abchist b 1.05 max( abchist) dhist b 0 50 1.05 max( dhist ) 50 0 5 5 10 1 10 4 4 1.5 10 2 10 4 intv b PRI k 10 2.5 10 6 4 4 3 10 intv b PRI k 10 3.5 10 100 4 6 PRI, Seconds Jitnc 0 0.5 Jitcum 0 0.5 N 820 width 5 10 7 10 Interleaved Pulse Trains 123 Effect of Jitter on Delta-T Histograms (Jitter=2 microseconds) Comparing Delta-T Histograms 100 100 50 dhist b abchist b 1.05 max( abchist) 0 50 1.05 max( dhist ) 50 0 5 5 10 1 10 4 1.5 10 4 2 10 4 intv b PRI k 10 2.5 10 6 4 3 10 intv b PRI k 10 4 3.5 10 4 100 6 PRI, Seconds Jitnc 0 1 Jitcum 0 1 N 820 width 124 5 10 7 10 Interleaved Pulse Trains Delta-T Hisotgram bin Count Complex Histogram Absolute Value Complex Histogram Absolute Value 50 Delta-T Hisotgram bin Count 100 100
- 63. Effect of Jitter on Delta-T Histograms (Jitter=5 microseconds) Comparing Delta-T Histograms 100 50 dhist b abchist b 1.05 max( abchist) 50 0 1.05 max( dhist ) 50 0 5 5 10 1 10 4 1.5 10 4 2 10 4 intv b PRI k 10 2.5 10 6 4 3 10 intv b PRI k 10 4 3.5 10 4 Delta-T Hisotgram bin Count Complex Histogram Absolute Value 100 100 6 PRI, Seconds Jitnc 0 2.5 Jitcum 0 2.5 N 820 width 5 10 7 10 Interleaved Pulse Trains 125 Complex Delta-T histogram: Original and Improved Original Complex Delta-T Histogram Improved Complex Delta-T Histogram Uniform Jitter=0.002 Uniform Jitter=0.02 Shift time origin To avoid excessive Phase variation Uniform Jitter=0.2 126 K Nishiguchi and M. Korbyashi, "Improved Algorithm for estimating Pulse Repetition Intervals,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 36, No. 2, April 2000.
- 64. Example of Automated Peak Processing Results Delta-T Hist. Complex Delta-T Input PRI Values 0 0 0 1 2 0 1 2 1. 15·10-4 1. 162· 10-4 1. 176· 10-4 1. 19·10-4 3 4 5 6 1. 15·10-4 1. 164· 10-4 1. 178· 10-4 1. 192· 10-4 7 8 9 10 11 1. 21·10-4 1. 23·10-4 1. 26·10-4 0 0 7 8 9 10 11 1. 21·10-4 1. 23·10-4 1. 26·10-4 0 0 12 13 14 15 0 0 0 0 12 13 14 15 0 1· 10-4 1. 05·10-4 1. 11·10-4 3 4 5 6 pk 1· 10-4 1. 048· 10-4 1. 11·10-4 0 0 0 0 pkc 0 1 6 2 3 4 5 6 1. 11·10-4 1. 15·10-4 1. 163· 10-4 1. 177· 10-4 1. 191· 10-4 7 8 9 PRI 10 1· 10-4 1. 05·10-4 1. 21·10-4 1. 23·10-4 1. 26·10-4 This example based on the method of B. Frankpitt, J. Baras, A. Tse, "A New Approach to Deinterleaving for Radar Intercept Receivers," Proceedings of the SPIE, Vol 5077, 2003, pages 175-186 Jitter =10 ns cumulative and 10 ns non-cumulative Histogram Bin size 200 ns.127 Pulse Train Spectrum of Ten Interleaved Pulse Trains k Amplitude PRF Spectrum 0.01 Xj 0.00011 max( X) 0.005 0 6000 8000 4 1 10 1.2 10 4 1.4 10 f j PRF k N 8.705 3 10 PRF (Hz) 10 Interleaved pulse Trains PRF Resolution 10 Hz 128 4 1.6 10 4 1.8 10 4 2 10 4 This plot is the FFT of TOA phase 2 ( ) T R. Orsi, J. Moore and R. Mahony, "Interleaved Pulse Train Spectrum Estimation," International Symposium on Signal Processing and its applications, ISSPA, Gold Coast, Australia, August 25-30, 1996
- 65. k PRF Spectrum Amplitude 0.03 Xj .025 0.02 .015 0.01 0 4000 6000 8000 4 4 1 10 1.2 10 1.4 10 4 1.6 10 4 1.8 10 4 4 2 10 f j 1 PRF k 2 PRF k PRF (Hz) 10 Interleaved pulse Trains N 1.741 3 10 Fewer Pulses--Degraded PRF Resolution (50 Hz) 129 Figure 13.10 Pulse Train Spectrum for a Shorter Record k PRF Spectrum Amplitude 0.03 Xj .03 0.02 .02 0.01 0 4000 6000 8000 4 4 1 10 1.2 10 4 1.4 10 4 1.6 10 f j 1 PRF k 2 PRF k PRF (Hz) 10 Interleaved pulse Trains N 871 Fewer Pulses--Degraded PRF Resolution (100 Hz) 130 4 1.8 10 4 2 10
- 66. PULSE SORTING ALGORITHM C C C B B C B B B B B B B A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A 3 Adjacent Matching Intervals Step 1. Find 3 adjacent matching intervals Step 2. Extend in both directions to discover other numbers of the pulse train Step 3. Remove this pulse train and go back to Step 1. If no more pulses can be removed, go to Step 4. Step 4. Consider all pairs of pulses to search for intervals which match; go to Step 2. 131 SORTER SOFTWARE PERFORMANCE Score Amp On (Pulses Pr ocessed) 10 (Pulses Wrong) Total Pulses Noise Pulses Amp On: 0.2 amp Tolerance from pulse-to-pulse 0% Jitter 100 90 Amp Off 80 n 1% Jitter f Of mp A 70 Score pO Am 60 50 pO Am Simulated Data Average Density 200 pps 40 n Amp Off 30 20 8% Jitter 10 0 1 10μs 100μs 132 Tolerance Time 1000μs
- 67. SIMULATION SCENARIOS File Name I.P. #† PRI Variation C2-3009-V05 2 1 30.0 70.0 0.5 0.5 C2-3009-V20 2 1 30.0 70.0 2.0 2.0 C3-3009-V05 1 3 3.0 120.0 0.5 0.5 C3-3009-V20 1 3 3.0 120.0 2.0 2.0 C4-3009-V05 1 50.0 0.5 C5-3009-V05 1 2 3 100.0 100.0 100.0 0.5 0.5 0.5 C5-3009-V20 1 2 3 100.0 100.0 100.0 2.0 2.0 2.0 † Denotes initial pulse number. Table 1. Simulation scenarios. Ref: Kofler and Leondes 133 FIXED GATE DEINTERLEAVING RESULTS File Name I.P.D. PRI % Misses C2-3009-V05 20 28 30 35 63 69 90.0 105.0 60.0 69.9 180.1 90.0 90.9 37.5 50.0 81.8 0.0 0.0 C2-3009-V20 20 28 30 35 90.3 104.9 59.8 69.7 81.8 37.5 42.9 63.6 16 . . . 473 9.1 . . . 36.0 62.9 . . . 100.0 7 117 395 3.7 50.0 32.8 3.2 77.3 60.0 C3-3009-V05 C3-3009-V20 C4-3009-V05 No emitters detected C5-3009-V05 19 30 47 48 56 100.0 100.2 199.9 99.9 200.0 16.7 92.9 25.0 75.0 0.0 C5-3009-V20 19 30 47 48 56 99.9 100.7 199.7 99.7 200.0 16.7 92.9 25.0 75.0 0.0 134 Ref: Kofler and Leondes
- 68. ADAPTIVE GATE DEINTERLEAVING RESULTS File Name I.P.D. PRI % Misses C2-3009-V05 7 18 30.0 70.0 0.0 0.0 C2-3009-V20 7 18 30.0 70.0 0.0 0.0 C3-3009-V05 5 168 3.0 120.0 0.0 0.0 C3-3009-V20 5 168 3.0 119.9 0.0 12.5 C4-3009-V05 5 50.0 0.0 C5-3009-V05 15 20 25 100.0 100.0 100.0 0.0 0.0 0.0 C5-3009-V20 15 20 25 100.0 100.0 100.0 0.0 0.0 0.0 Kofler and Leondes 135 ^ĐĞŶĂƌŝŽ ŽŵƉůĞǆ ĞůƚĂͲd ,ŝƐƚŽŐƌĂŵ WĞĂŬƐ /ŶƉƵƚ WZ/Ɛ 136
- 69. WƵůƐĞ ƚĂŐƐ ĨŽƵŶĚ ŝŶ ƉĞĂŬ ηϮ 137 WƵůƐĞ dĂŐƐ ŝŶ WĞĂŬ ηϮ ǁŚŝĐŚ ŚĂǀĞ ƚŚĞ ŵŽƐƚ ƉƌĞǀĂůĞŶƚ WZ/ WŚĂƐĞ 138
- 70. PRI ANALYSIS EXERCISE Two signals are observed with the same angle of arrival but on different frequencies. The PRI of one is nearly stable at 3000 μs. The PRI of the second jitters randomly with a mean value of 1500 μs and a peak-to-peak jitter of about 20 μs. The analyst notices that the PRI’s of the second signal can be paired such that their sum is nearly stable at 3000 μs; i.e., PRI #1 + PRI #2 = PRI #3 + PRI #4 = PRI #5 + PRI #6, etc. However, PRI #2 + PRI #3 PRI #4 + PRI #5. He also notices that the mean value of the second signal’s PRI is exactly one-half that of the first signal’s PRI every time the two signals are reported. The first signal has a slow circular scan, the second a faster sector scan. What conclusions might be drawn about these two radars? What additional data would you request from the ELINT station? 139 PRI EXERCISE ANSWER There is a good possibility that the second radar operates in PRI synchronism with the first; but at one-half the PRI. Alternate pulses are triggered by the master clock, the intermediate pulses are generated by “one shot” type delay circuit which is not stable. The second radar may be a height finder using elevation sector scan and associated with a long range search radar. Confirmation of this would be aided by using two receivers and making a recording of both Signals simultaneously to investigate whether the second signal is synchronized to the first. 140
- 71. PRECISION PDWs • Pulse Descriptor Words are computed from pre-detection burst recordings • Digitizer has “detected” presence of high SNR pulses, and captured them • Different capture and processing techniques apply to low SNR pulses • Standard PDWs computed are: - Amplitude - Frequency - Time of Arrival - Bandwidth - Pulse Width • Algorithms and accuracies are described 141 Condor Systems, Inc. USEFULNESS OF PRECISION PDWs • Reveals fine details of pulse train jitter patterns • Permits very high accuracy computation of crystal controlled PRIs with few pulses • Can use very accurate pulse width to sort pulses • Fine variations of frequency pulse to pulse reveal unique emitter characteristics (e.g., frequency pulling effects due to VSWR changes in antenna rotary joint, etc.) • Amplitude droop in transponder pulse groups • Precise antenna pattern scan envelope measurement 142 Condor Systems, Inc.
- 72. EXAMPLE OF PRE-DETECTION RADAR PULSE RECORDING 143 Condor Systems, Inc. CALCULATION OF AMPLITUDE, TOA, PW 144 Condor Systems, Inc.
- 73. TOA MEASUREMENT ACCURACIES • Digitizer time base determines ultimate accuracy • Individual pulse time of arrival error determined by: t where tr 2SNR t RMS Error in TDOA t r Pulse Rise Time SNR Signal to Noise Ratio in Captured Pulse Bandwidth • Example: 30 ns rise time, 37 dB SNR yields RMS error of 300 picoseconds per pulse 145 Condor Systems, Inc. PULSE WIDTH MEASUREMENT ACCURACY pw where t2 r t2 f pw RMS error in pulse width t r RMS error of pulse risin g edge time t RMS error of pulse falling edge time f Example: RMS errors of captured pulse edge times of 300 picoseconds yield 1.414 x 300 = 423 picoseconds RMS pulse width error per pulse. Condor Systems, Inc. 146
- 74. EXAMPLE OF PULSE WIDTH ACCURACY 147 Condor Systems, Inc. PULSE FREQUENCY COMPUTATION 148 Condor Systems, Inc.
- 75. PULSE FREQUENCY ACCURACY 1 T SNR TW in f • Technique applies to high SNR cases (+15 dB), sine wave pulse where f T RMS frequency accuracy Integration time (~ pulse width) SNR Input Signal to Noise Ratio in BW , W in W Input Pr e det ection bandwidth Example: 1 microsec pulse, 30 dB SNR, 20 MHz Bandwidth yields RMS accuracy of 7 kHz. Condor Systems, Inc. 149 EXAMPLE OF PULSE FREQUENCY COMPUTATION 150 Condor Systems, Inc.
- 76. Pulse Bandwidth 151 Condor Systems, Inc. EXAMPLE OF PULSE FREQUENCY COMPUTATION 152 Condor Systems, Inc.

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