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.com1

Pulse Repetition Intervals (PRIs) are often the key to identifying the signals of many radar systems. The first step isto deinterleave signals from multiple radar systems. This briefing is a a brief introduction to PRI analysis anddeinterleaving from the ELINT/EW point of view

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 two-way 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 aspectsof ELINT is what separates one who only observes signals from one who both observes and analyzes signals.

Reference: ELINT, Chapter 2

4

RTR

RTTR LLR

GGPS 43

2

)4(

ETE

ETETE LLR

GGPS 22

2

)4(

Radar and ELINT Range Equations

5

)( RE SS2/1

14

R

E

R

E

T

TER

R

E

LL

GG

GGR

RR

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:

Ratio of ELINT Range to Radar Range

6

1 10 100 1 1031

10

100

1 103

Figure 2-1 ELINT to Radar Range Ratio Range (km)

ELIN

T R

ange

/Rad

ar R

ange

RangeRatioSLi

RangeRatioMBi

Ri

1 sq. m

GR 30GR dB

100

GE 1

ARE/

RR

Mainbeam

: G TE=30 dB

Sidelobe: G

TE=0 dB

2/14

R

R

R

E

GR

RR

2/14

RR

R

E

GR

RR

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

BcR

2

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:

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

1 106 1 107 1 1081

10

100

1 103

Bandwidth (MHz)

Ran

ge R

esol

utio

n (m

eter

s)

RngRes bi

bi

Figure 2.2. Range resolution Related to Radar Coherent Bandwidth

Bandwidth B (MHz)

Ran

ge R

e so l

uti o

n (m

eter

s )

10

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.

1.Count A/C in attack formation

3060

52.5

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

Range Resolution Required Resolution (m) Bandwidth (MHz)

11

Moving Targets and Integration Time ConstraintsIf 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

vR

vRTCV

Here TCV is the maximum coherent integration time for a constantvelocity 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 bothvelocity and acceleration

aRavv

aRavvTACC

5.025.02 )(2)(2

12

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 "time-bandwidth product." The radar's pulse compression ratio is limited to no more than its time bandwidth product. By combining Equationsfor range resolution and integration time it is easy to see that the time bandwidth product is limited to:

021 12a

Bv ac cBTa Bv v

13

1 104 1 105 1 1061 105

1 106

Figure 2-4 Limit on Time x Bandwidth

Bandwidth

BT

Lim

it

BTi 1

BTi 2

BTi 5

BTi 10

BT1i

bi

Acceleration 0, 1,2, 5, 10 g's

Signal Bandwidth B (Hz)

Max

imum

tim

e -ba

ndw

idth

pro

d uc t

BT

a=0 g

a=1 g

a=2 g

a=5 g

a=10 g

Velocity=300m/s

14

Constraints on Doppler ResolutionIf 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:.

TB f

1

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.

fo

acc BaTc

aTff 22

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 dopplerfilter bandwidth as

2, 2 f

aT Ba

16

1 10 3 0.01 0.1 10.1

1

10

100

1 103

1 104

Coherent Integration time T (s)

Dop

pler

Spr

ead(

kH

z)

6.502 103

0.65

fi 1

f i 2

f i 5

f i 10

11 10 3 Ti

a=10g

a=1g

Figure 2.5 Doppler Spread and Maximum Signal Bandwidth

17

1 10 3 0.01 0.1 10.1

1

10

100

1 103

1 104

1

10

100

1 103

Coherent Integration time T (s)

Dop

pler

Spr

ead(

kH

z)

Ban

dwid

th (M

Hz)

6.502 103

0.65

fi 1

f i 2

f i 5

f i 10

1000

1

Bi

1.001 Ti

Maximum Signal Bandwidth-left scale

a=10g

a=1gDoppler Spread-right scale

a=5g

a=2g

Figure 2.5 Doppler Spread and Maximum Signal Bandwidth

18

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 accelerationhas 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

)(2

22

max RFcvBa

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 duringcoherent integration--important to know for ELINT analysis. Tracking radars extend the coherent integration time when targetvelocity and acceleration are known. Examining all possible target velocities and accelerations requires huge processor throughput and is generally not practical today.

20

Frequency AgilityFrom one coherent processing interval to the next, the radar canchange 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 dopplerprocessing, the frequency is changed on a pulse-burst to pulse-burst basis, not a pulse-to-pulse basis.

21

PRI AgilityModern 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 isbecause 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

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 time) or spectral lines (in frequency).23

For constant PRI and RF, the maximum unambiguous range (Ru) and the maximum unambiguous velocity (Vu) are given by:

2)(PRIcRu

))((2 PRIRFcVu

Examples at 10 GHz: PRI 1000 us, Vu=15 m/s and Ru=150 kmPRI 100 us, Vu=150 m/s and Ru=15 kmPRI 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.

)(4

2

RFcVR uu

24

10 100 1 103 1 1041 103

1 104

1 105

1 106

Fi 2 7 R /V l it R l t dUnambiguous Velocity (m/s)

Una

mbi

guou

s Ran

ge (m

)

106

1000

Rui 1

Rui 2

Rui 3

Rui 4

Rui 5

Rui 6

Rui 7

Rui 8

10410 Vui 1 Vui 2 Vui 3 Vui 4 Vui 5 Vui 6 Vui 7 Vui 8

225 MHz425 MHz1.3 GHz3 GHz5.5 GHz

10 GHz15GHz35GHz

Inverse relationship of unambiguousrange and unambiguous velocity atcommon radar frequencies

25

FrequencyAgility Band

(Depends on Component Design, ECM Factors, Designer Ingenuity)

Freq

uenc

y

Coherent Processing Interval(depends on radar mission)

TimeBandwidth Determines Range Resolution Which

Depends on Radar Mission

*

*Figure 2-8. Modern frequency Agile Radar with 100% Duty Factor

26

USES OF PRI

27

UNAMBIGUOUS RANGE ANDVELOCITY DEPENDENCE

c

c

Analysis p. 14728

RANGE-VELOCITY AMBIGUITY

Analysis p. 14829

OPTIMUM PRI FOR MEDIUM PRF RADAR

Text p. 14930

OPTIMUM PRI FOR MEDIUM PRF RADARBand “Be” Obscured at each PRF line

31

NOMINALLY CONSTANT PRI

32

PRI DRIFT

Analysis p. 15333

CRYSTAL OSCILLATORS ANDCOUNTDOWN CIRCUITS

Analysis pp. 191, 19234

SCR-584

35

SEARCH RADAR PRI SELECTION

36

PRI STAGGER

Definition: Two or more discrete PRI intervals (elements) are alternatingin a periodic fashion.

• Desired Parameters- Number of intervals- Number of positions- Interval values- Sequence- Stable sum

• Stagger Ratio

• Stagger Versus Jitter

T T T TUnmodulated Pulse Train

T+ T- T+ T-

Typical Staggered Pulse TrainTwo Interpulse Intervals Shown

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 25003500

5:7 To eliminate blind speeds Surveillance

2. 4 3049 30323066

89:90 To eliminate blind speeds Height Finder

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 andtarget 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 pulseintervals is not known

3 pulse canceller for MTI. Stagger toeliminate blind speeds

Surveillance

3. 6 3000 2954.553045.45

0:97(almost 100:103)

To eliminate blind speeds Surveillance

4. 6 3000

1000

289731036131167

14:15

5:7

To eliminate blind speeds Experimental surveillance

5. 24 3000 27503250

11:13 To eliminate blind speeds Surveillance

6. 3 1375 12501500

5:6 To eliminate blind speeds Acquisition

7. 20 5247 50005494

0:91(almost 10:11)

To eliminate blind speeds Surveillance

8. 2 2777.9 2572.02777.82983.5

25:27:29 To eliminate blind speeds Air route surveillance

9. 1.4, 4.2 1250 12401260

0.984(almost 125:127)

To identify second-time-around pulses Gap filter, surveillance andinterrogator

10. 2 2632-3226 Unknown8-pulse stagger with three programs

Unknown To eliminate blind speeds Air route surveillance

13. 1-100 40062.12500

For first sequence only:623.3818.0740.1662.0701.1

Various Sequences16:21:19:17:20:1816:17:16:1716:19:16:1916:21:16:2116:17

To eliminate blind speeds. Has variousdigital MTI processing including doubledouble-cancellation

Surveillance, tracking, killassessment, missile guidance

38

DESCRIPTION OF PRI VARIATIONS

Nature of Pulse-to-Pulse PRI Variations

Periodic Random (non-periodic)

Discrete Continuous Discrete Continuous

Large Small Large Small Large Small Large Small

Type 1 2 3 4 5 6 7 8

(Large implies intentional, small implies incidental)

39

JITTERED PRI

Definition: Pulse repetition intervals are intentionally varied oninterval-to-interval basis in a random or pseudorandomfashion. 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

RADARS WITH JITTERPulseWidth(μs)

PRI(μs)

Peak-to-Peak Jitter(μs)

Peak-to-Peak Jitter(%)

Jitter Type Jitter Purpose Radar Function

6, 18 30001000

505 1.75

Random Anti-ECM and interference

Sruveillance

26 4629 92.6 20 Random Anti-ECM and interference

Target tracking

200 4000 50 3.75 Random Anti-ECM and interference

Long-range surveillance

0.9 416-1515(Variable)

83-303 20 Unknown Unknown High resolution synthetic aperture mapping

205400

10204102046666

999.9918.4653.3

9.89.09.8

RandomOrProgrammed

Anti-ECM. Results from PRF being submultipleof RF which is jumping

Decoy discriminator target tracking acquisition

4-504-2.67

500-2777.73.3-4.0

60 2.2-12None

Random To reduced inward range gate stealers, anti-interference, 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

SLIDING PRI

Definition: The pulse train has a PRI (PGRI) that is continuously changing in eithera monotonically increasing or decreasing manner between maximumand 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 thatperiodically 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 otherwiseperiodic pulse train

- Displacement value

44

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 shorttime 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 andfunction being performed by radar, and cannot be described by otherdefinitions

- Number of intervals- Interval values- Typical sequences- Reason for sequence

46

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. 15148

DOPPLER EFFECT

v = radial velocity

c = 3(108) m/sec

fo = transmitted RF

vkm/hr

Doppler Shift (Hz)@ 3 GHz @ 10 GHz

100 555.5 1851.8

1000 5,555 18518.5

2000 11,111 37,037.0

FIGURE 3-1. DOPPLER EFFECT

ofc

2vof1fdfShiftDoppler

c2v1of

v-cvc

of1f

49

50

FOURIER TRANSFORMS

51

IDEAL VS. ACTUAL SPECTRAFOR CW SIGNAL

52

FM THEORY

M""MODULATIONOFINDEX

t)mf sin2mfftcf Asin(2V(t)

:THEN

tmFcos2 fdtd

21

then,mF/fLet

tmcos2 fmfdtd

21

tmsin2 f(t)ASSUME

dtd

21

cfphase)(totaldtd

21Freq. ousInstantane

(t)tcf 2PhaseTotal

eDisturbancPhase

(t))tcfsin(2AV(t)

53

BESSEL EXPANSION

.....(m)3J

t)m2csin()tm2csin((m)2J

)tmcsin()tmcsin((m)1Jtcsin(m)oJAV(t)

J0(m)

J1(m) J1(m)

J2(m) J2(m)

fc-2fm fc fc+2fm

fc-fm fc+fm

54

BESSEL FUNCTIONS

55

MOD. INDEX LESS THAN 1

FOR COHERENT SIGNALS:

)t]mcsin(2m)tmcsin(

2mtcA[sinV(t)

THEREFORE

etc........0(m)3J0(m)2J

2m(m)1J1(m)oJ

smallisfi.e.1mffm

A

m2fflog20

cVSBV

log20

dBin

m2ff

2m

cVSBV

mA/2mA/2

fc-fm fc fc+fm

56

EXAMPLES

RATE)kHz1(AT

910inparts2Hz910x10

Hz20

ISSTABILITYGHz,10cfIF

Hz20f

kHz1mfe.g.

kHz1m2ff

dB40m2fflog20

57

RANGE AMBIGUITY RESOLUTION VIA MULTIPLE PRIs

12 μs = XT1 = 40 μs

2 μs = YT2 = 30 μs

Actual Round Trip Echo Time is T = 92 μs

N1 T1 + X = T and N2 T2 + Y = T

N1 N2 N1 T1 + X N2 T2 + Y

1122

1223

52529292

32626292

Trial and ErrorSolution

s120x2c

2T,1TofMultipleCommonLeastx2cRangesUnambiguou

Analysis p. 19658

ERICSSON PS-05/A MULTIMISSION RADAR

59

ERICSSON PS-05/A MULTI-MODE OPERATION (1)

60

ERICSSON PS-05/A MULTI-MODE OPERATION (2)

61

MTI VIDEO

62

MTI PHASE SHIFTS

63

MTI BLOCK DIAGRAM

64

BIPOLAR VIDEO

65

DOPPLER RETURNS

TRAIN

CAR

MAN WALKING

WOMANWALKING

Typical images displayed on TPS-25 groundSurveillance radar. Shown are target imagesof: 1) a train, 2) an automobile, 3) a walking man, and 4) a walking girl. (US Army photograph.)

66

PULSED-OSCILLATOR MTI

= 2E sin( fdT) cos [2 fd(t + T/2) + o]

PRF2

n

T2RFnc

bVarespeedsblindso

Tn

df

whenn,0,atZeros

Barton, p. 19267

Page M50.ppt

68

BLIND SPEED ELIMINATION

vb = n c/2(PRI)(RF)No Stagger

T1

75

TT Vbn = Vb (7 + 5)/2

T6

Deep lobeat 32/T

6563

TT

Null at64/T

Ref: Barton, page 22269

IMPROVEMENT FACTOR OF CANCELLER

cancellerofinputatratiocluttertosignalcancellerofoutputatratiocluttertosignal

in(S/C)out(S/C)

I

Overall improvement factor I is found from:

I1, I2, I3 are the individual improvement factors calculated on basis of PRI, pulseamplitude, pulsewidth, transmitter frequency, ……….. stabilities

....3I1

2I1

1I1

I1

70

INSTABILITY LIMITATIONS

71

CLUTTER STRENGTH

72

MTI + PULSE DOPPLER = MTD

ZeroDoppler

Filter

Magnitude(I2 + Q2)1/2

ClutterMemory

Clutter Map(Recursive

Filter)

Threshold

3-PulseCanceller

8-PulseDoppler

Filter Bank

WeightingAnd

Magnitude

TargetDetection

I,Q DataFrom A/DConverters

15 – 20 radar scans areneeded to establishthe clutter mapTypical Applications

New FAA ASR radars (10 pulse dwell)AN/SPS-49 USN-adjunct to AEGIS (6-pulse dwell)RAMP (Canada)

73

MTD PERFORMANCE

• Theoretical

(Reference: NRL Report 7533, G.A. Andrews, Jr.)

• PracticalPerformance 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)

RMS Clutter Width

Processor 0.01 PRF 0.1 PRF

MTI Improvement Factor

1 canceller2 cancellers3 cancellers

25 dB50 dB72 dB

8 dB12 dB16 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

80 dB

100 dB

28 dB

34 dB

36 dB

74

ELINT IMPLICATIONS OF MTD

• Coherent carrier RF stability is necessary

• Constant PRIs Several PRIs of the same interval must beConstant RF transmitted at the same RF (typically 4,(for a certain 8, or 16 pulses for the FFT plus pulsesnumber of pulses) to fill the canceller. For example, a

three-pulse canceller plus an eight-pulseFFT requires 10 pulses).

• “Stagger” to eliminate For these radars, the pulse intervalblind speeds stagger occurs not from pulse-to-pulse but

from pulse group-to-pulse group

• Long PRI MDT is generally used for long-range radarswhere the low PRF creates very ambiguousDoppler shifts.

75

PRI EXERCISES

1. The analyst found a signal at 6 GHz which had two-interval, two-position stagger. Theintervals were 500 and 550 microseconds. What is the average PRI? What is thestagger 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 nanosecand a pulse duration of 1.41 microsec?

3. A discrete random jitter PRI train was analyzed and the PRIs were found to be one ofthe following 5 nominal values:

NomPRI (μsec)

2440.82428.72465.32453.12562.9

Is there a clock? If so, what countdowns are used and what is the clock frequency orperiod? What common range mark is that closest to?

(This problem is discussed on p. 194-195 of analysis book.)

76

PRI EXERCISES #2 - ANSWERS1. (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)

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 = jitter, = pulse duration,B = bandwidth

IdB = 20 log [1.41 (10-6) sec/ • 10(10-9)sec)]= 20 log [102] = 40 dB

3. Periods Nearest CalculatedPeriod In Order Difference Countdown Clock Period2440.8 2482.7 199 12.204522428.7 2440.8 12.1 200 12.204002465.3 2453.1 12.3 201 12.204472453.1 2465.3 12.2 202 12.204452562.9 2562.9 97.6 210 12.20428

12.204392 averageThe differences 12.1, 12.3, 12.2 average 12.2

97.6 divided by 12.1 = 8So 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.)

)mph5.106(hr/km4.171sec/1x)910(6xsec)610)(525(2

sec/m)810x3(BV

)],Bt2/[2

2

77

NOISE EFFECT ON PRI

AA

8.0RISET

TErrorTriggering

TRISE/0.8

A

T

A

)8.0/RISET(ASlopeT

ANoise

78

PRI VARIATION DUE TO NOISE

SNRRiseT

8.02

PRI

2Time22

2Time2

1Time2PRI

SNR1

8.0RiseT

Time

SNR1

PowerSignalPowerNoise

2)Amplitude(

2amplitude

79

BANDWIDTH EFFECT ON SNR

Bandwidth35.

rt2

PRIrt125.3SNR

SNR Required forBandwidth (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

AMPLITUDE INDUCED ERROR

81

AMPLITUDE COMPENSATED TRIGGER

82

PERFORMANCE OF TRIGGER CIRCUIT

83

DOPPLER SHIFT OF PRI

• In 1 PRI, the platform movesVR • PRI

• Transmit time from transmitter to receiver changes by VR • PRI/c

• Example: VR = 600 M/S PRI = 3000 μs

Observed PRI = ns6810x3310x3x600

84

DELAY AND PULSE JITTER

Delay D2

Delay D1

Peak-to-Peak JitterAt Delay D1

Peak-to-Peak JitterAt Delay D2

85

DELAYED SWEEP JITTER PHOTOS

~ 1 μs JitterDelay = 1 PRI

~ 2 μs JitterDelay = 5 PRI

86

SYNTHESIS OF AVERAGE PRI

87

PRI DRIFT MEASUREMENT

88

REAL TIME RASTER DISPLAYS

Analysis p.7489

DUAL AMPLITUDE AND TIME DELAYS

90

DTE MODE-CIRCULAR SCAN RADAR

91

RTR SIMULATION ON APERSONAL COMPUTER

92

MEAN PRI ESTIMATES

93

MINIMIZING THE SQUARED ERROR

94

RMS ERRORS COMPARED

95

96

97

NONCUMULATIVE ANDCUMULATIVE JITTER

98

CRAMER-RAO BOUNDS COMPARED

99

PRI ESTIMATION PERFORMANCE

100

USING THE WRONG JITTER MODEL

101

PRI HISTOGRAMS

102

ACTIVITY IN 0.1S INTERVALS

103

INTERVALS FORMED BY PULSE PAIRS

104

DELTA-T HISTORGRAM(10% JITTER)

105

DELTA-T HISTOGRAM--STAGGER

• • • 4 5 7 4 5 7 4 5 • • •

t0 = 0 t1 = 4 t2 = 9 t3 = 16 t4 = 20 t5 = 25 t6 = 27 t7 = 31 t7 = 37

A. (tn – tn-1) = 4, 5 or 7

B. (tn – tn-2) = 9, 11 or 12 (4 + 5, 4 + 7, 5 + 7)

C. (tn – tn-3) = 16 (4 + 5 + 7)

D. (tn – tn-4) = 20, 21 or 23

E. (tn – tn-5) = 25, 27, or 2

F. (tn – tn-6) = 32

1 2 3 4 5 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 E F

106

THREE POSITION STAGGER

107

DELTA-T HISTOGRAM:TOA AUTOCORRELATION

. . . . .n

1n)ntt()t(f

t1 t2 . . . . . t3 t4 . . . . .

ktntOR0ktnt

and0nttifonlyvalue

dtn k

)ktt()ntt()(h

dttf)t(f)(h

EXAMPLEt1 t = t2 t3 t4

t = t1 +

t = 0

108

DELTA-T HISTOGRAM:TOA AUTOCORRELATION

2ktnt1 thatsuch pairs pulse

of number theofcount A

2

1

2

1 n k)ktnt()(h

n k)ktnt()(h

THEREFORE:A count of the number of pairs of pulses whose arrivaltimes differ by a value between 1 and 2 is equal tothe integral of the autocorrelation of the TOA’s

109

JITTER ANALYSIS MODEL

Center Frequency(average PRF)

FMOscillator

TriggerGenerator

JitterWaveform Time of

ArrivalSequencePeak

Amplitude

Periodicities• Periods• Amplitudes

Drifts/Trends• Slopes

Random Components• Bandwidths• Variances• Probability Densities110

INSTANTANEOUSFREQUENCY ESTIMATION

500 700 600 500 400 500 PRIs (μs)

1428.5 1666.72000

25002000

LinearInterpolation2000Freq

Midpointsof Intervals

111

DEINTERLEAVING DEVICE

112

DEINTERLEAVING VIA DELTA- HISTOGRAM

113

“PURE” VS. “IMPURE” INTERVALS

114

NUMBER OF EMITTERS DEINTERLEAVED

115

COMPLEX DELTA- HISTORGAM - I

116

COMPLEX DELTA- HISTOGRAM - II

117

COMPARISON OF DELTA- HISTOGRAMS

118

EFFECT OF A NEAR MULTIPLE PRI

119

EFFECTS OF JITTER ON DELTA-HISTOGRAMS

120

8 10 5 1 10 4 1.2 10 4 1.4 10 4 1.6 10 40

50

100Delta-T Histogram

PRI, Seconds

His

togr

am C

ount

dhist b

.75 max dhist( )

int vb PRIk 10 6

N 820 10 Interleaved Pulse Trains

Delta-T Histogram for Ten Interleaved Pulse Trains

121

1 10 4 2 10 4 3 10 4 4 10 40

50

100

150

100

0

100

Comparing Delta-T Histograms

PRI, Seconds

Com

plex

His

togr

am A

bsol

ute V

alue

Del

ta-T

Hiso

tgra

m b

in C

ount

abchist b

1.05 max abchist( )

dhist b

1.05 max dhist( )

int vb PRIk 10 6 int vb PRIk 10 6

N 820 10 Interleaved Pulse Trains

Comparison of the Delta-T and Complex Delta-T Histograms

Top Trace is the regular Delta-T Histogram; Bottom Trace is the Complex Delta-T Histogram--Note how multiples of the PRIs are suppressedThe dots above the peaks indicate the true PRI values

122

Effect of Jitter on Delta-T Histograms(Jitter=1 microsecond)

5 10 5 1 10 4 1.5 10 4 2 10 4 2.5 10 4 3 10 4 3.5 10 40

50

100

100

50

0

50

100Comparing Delta-T Histograms

PRI, Seconds

Com

plex

His

togr

am A

bsol

ute

Val

ue

Del

ta-T

His

otgr

am b

in C

ount

abchistb

1.05 max abchist( )

dhist b

1.05 max dhist( )

intvb PRIk 10 6 intvb PRIk 10 6

Jitnc0 0.5 Jitcum0 0.5 N 820 width 5 10 7 10 Interleaved Pulse Trains

123

5 10 5 1 10 4 1.5 10 4 2 10 4 2.5 10 4 3 10 4 3.5 10 40

50

100

100

50

0

50

100Comparing Delta-T Histograms

PRI, Seconds

Com

plex

His

togr

am A

bsol

ute

Val

ue

Del

ta-T

His

otgr

am b

in C

ount

abchistb

1.05 max abchist( )

dhist b

1.05 max dhist( )

intvb PRIk 10 6 intvb PRIk 10 6

Jitnc0 1 Jitcum0 1 N 820 width 5 10 7 10 Interleaved Pulse Trains

Effect of Jitter on Delta-T Histograms (Jitter=2 microseconds)

124

5 10 5 1 10 4 1.5 10 4 2 10 4 2.5 10 4 3 10 4 3.5 10 40

50

100

100

50

0

50

100Comparing Delta-T Histograms

PRI, Seconds

Com

plex

His

togr

am A

bsol

ute

Val

ue

Del

ta-T

His

otgr

am b

in C

ount

abchistb

1.05 max abchist( )

dhist b

1.05 max dhist( )

intvb PRIk 10 6 intvb PRIk 10 6

Jitnc0 2.5 Jitcum0 2.5 N 820 width 5 10 7 10 Interleaved Pulse Trains

Effect of Jitter on Delta-T Histograms (Jitter=5 microseconds)

125

Complex Delta-T histogram: Original and Improved

Uniform Jitter=0.002

Uniform Jitter=0.02

Uniform Jitter=0.2

Original Complex Delta-T Histogram Improved Complex Delta-T Histogram

Shift time originTo avoid excessive Phase variation

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.

126

Example of Automated Peak Processing ResultsDelta-T Hist. Complex Delta-T Input PRI Values

PRI 10 6

00123456789

-41· 10-41. 05·10-41. 11·10-41. 15·10-41. 163· 10-41. 177· 10-41. 191· 10-41. 21·10-41. 23·10-41. 26·10

pk

00123456789

101112131415

-41· 10-41. 048· 10-41. 11·10-41. 15·10-41. 162· 10-41. 176· 10-41. 19·10-41. 21·10-41. 23·10-41. 26·10000000

pkc

00123456789

101112131415

-41· 10-41. 05·10-41. 11·10-41. 15·10-41. 164· 10-41. 178· 10-41. 192· 10-41. 21·10-41. 23·10-41. 26·10000000

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, Vol5077, 2003, pages 175-186

Jitter =10 ns cumulative and 10 ns non-cumulativeHistogram Bin size 200 ns.127

k

6000 8000 1 104 1.2 104 1.4 104 1.6 104 1.8 104 2 1040

0.005

0.01

PRF Spectrum

PRF (Hz)

Am

plitu

de

X j

0.00011 max X( )

fj PRFk

N 8.705 103 10 Interleaved pulse Trains

PRF Resolution 10 Hz

Pulse Train Spectrum of Ten Interleaved Pulse Trains

)(2T

TOAphase

This plot is the FFT of

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, 1996128

k

4000 6000 8000 1 104 1.2 104 1.4 104 1.6 104 1.8 104 2 1040

0.01

0.02

0.03

PRF Spectrum

PRF (Hz)

Am

plitu

de X j

.025

.015

fj 1 PRFk 2 PRFk

10 Interleaved pulse Trains N 1.741 103

Fewer Pulses--Degraded PRF Resolution (50 Hz)

129

k

4000 6000 8000 1 104 1.2 104 1.4 104 1.6 104 1.8 104 2 1040

0.01

0.02

0.03

PRF Spectrum

PRF (Hz)

Am

plitu

de X j

.03

.02

fj 1 PRFk 2 PRFk

10 Interleaved pulse Trains N 871

Fewer Pulses--Degraded PRF Resolution (100 Hz)

Figure 13.10 Pulse Train Spectrum for a Shorter Record

130

PULSE SORTING ALGORITHM

C

B B BB

B B B

B B

C

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

C C

3 Adjacent Matching Intervals

Step 1. Find 3 adjacent matching intervalsStep 2. Extend in both directions to discover other numbers of the pulse trainStep 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

PulsesNoisePulsesTotal)WrongPulses(10)ocessedPrPulses(Score

100

90

80

70

60

50

40

30

20

10

0

Amp On

Amp On

Amp On

Amp Off

Amp Off

Amp Off

Simulated DataAverage Density 200 pps

Amp On: 0.2 amp Tolerancefrom pulse-to-pulse

8% Jitter

1% Jitter

0% Jitter

Score

1 10μs 100μs 1000μsTime Tolerance 132

SIMULATION SCENARIOS

File Name I.P. #† PRI Variation

C2-3009-V05 2 30.0 0.51 70.0 0.5

C2-3009-V20 2 30.0 2.01 70.0 2.0

C3-3009-V05 1 3.0 0.53 120.0 0.5

C3-3009-V20 1 3.0 2.03 120.0 2.0

C4-3009-V05 1 50.0 0.5

C5-3009-V05 1 100.0 0.52 100.0 0.53 100.0 0.5

C5-3009-V20 1 100.0 2.02 100.0 2.03 100.0 2.0

† Denotes initial pulse number.Table 1. Simulation scenarios.

Ref: Kofler and Leondes133

FIXED GATE DEINTERLEAVING RESULTS

File Name I.P.D. PRI % Misses

20 90.0 90.928 105.0 37.5

C2-3009-V05 30 60.0 50.035 69.9 81.863 180.1 0.069 90.0 0.0

20 90.3 81.8C2-3009-V20 28 104.9 37.5

30 59.8 42.935 69.7 63.6

16 9.1 62.9C3-3009-V05 . . .. . .. . .

473 36.0 100.0

7 3.7 3.2C3-3009-V20 117 50.0 77.3

395 32.8 60.0

C4-3009-V05 No emitters detected

19 100.0 16.730 100.2 92.9

C5-3009-V05 47 199.9 25.048 99.9 75.056 200.0 0.0

19 99.9 16.730 100.7 92.9

C5-3009-V20 47 199.7 25.048 99.7 75.056 200.0 0.0

Ref: Kofler and Leondes134

ADAPTIVE GATE DEINTERLEAVINGRESULTS

File Name I.P.D. PRI % Misses

C2-3009-V05 7 30.0 0.018 70.0 0.0

C2-3009-V20 7 30.0 0.018 70.0 0.0

C3-3009-V05 5 3.0 0.0168 120.0 0.0

C3-3009-V20 5 3.0 0.0168 119.9 12.5

C4-3009-V05 5 50.0 0.0

15 100.0 0.0C5-3009-V05 20 100.0 0.0

25 100.0 0.0

15 100.0 0.0C5-3009-V20 20 100.0 0.0

25 100.0 0.0

Kofler and Leondes

135

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138

PRI ANALYSIS EXERCISE

Two signals are observed with the same angle of arrival but on different frequencies. The PRI of one is nearlystable 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, theintermediatepulses 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 bothSignals simultaneously to investigate whether the second signal is synchronized to the first.

140

PRECISION PDWs

• Pulse Descriptor Words are computed from pre-detectionburst recordings

• Digitizer has “detected” presence of high SNR pulses,and captured them

• Different capture and processing techniques apply to lowSNR pulses

• Standard PDWs computed are:- Amplitude - Frequency- Time of Arrival - Bandwidth- Pulse Width

• Algorithms and accuracies are described

Condor Systems, Inc.141

USEFULNESS OF PRECISION PDWs

• Reveals fine details of pulse train jitter patterns

• Permits very high accuracy computation of crystalcontrolled PRIs with few pulses

• Can use very accurate pulse width to sort pulses

• Fine variations of frequency pulse to pulse reveal uniqueemitter characteristics (e.g., frequency pulling effects dueto VSWR changes in antenna rotary joint, etc.)

• Amplitude droop in transponder pulse groups

• Precise antenna pattern scan envelope measurement

Condor Systems, Inc.142

EXAMPLE OF PRE-DETECTION RADARPULSE RECORDING

Condor Systems, Inc.143

CALCULATION OF AMPLITUDE, TOA, PW

Condor Systems, Inc.144

TOA MEASUREMENT ACCURACIES

• Digitizer time base determines ultimate accuracy

• Individual pulse time of arrival error determined by:

• Example: 30 ns rise time, 37 dB SNR yields RMS error of300 picoseconds per pulse

BandwidthPulseCapturedinRatioNoisetoSignalSNR

TimeRisePulsertTDOAinErrorRMStwhere

SNR2rtt

Condor Systems, Inc.145

PULSE WIDTH MEASUREMENT ACCURACY

timeedgefallingpulseoferrorRMSfttimeedgegsinripulseoferrorRMSrt

widthpulseinerrorRMSpwwhere

2ft

2rtpw

Example: RMS errors of captured pulse edge times of300 picoseconds yield 1.414 x 300 = 423picoseconds RMS pulse width error per pulse.

Condor Systems, Inc.

146

EXAMPLE OF PULSE WIDTH ACCURACY

Condor Systems, Inc.147

PULSE FREQUENCY COMPUTATION

Condor Systems, Inc.148

PULSE FREQUENCY ACCURACY

• Technique applies to high SNR cases (>+15 dB), sinewave pulse

Example: 1 microsec pulse, 30 dB SNR, 20 MHz Bandwidthyields RMS accuracy of 7 kHz.

bandwidthectioneInputW

WBWinRatioNoisetoSignalInputinSNR

widthpulsetimenIntegratioT

accuracyfrequencyRMSfwhere

TWinSNRTf

detPr

,

)(~

1

Condor Systems, Inc.149

EXAMPLE OF PULSE FREQUENCYCOMPUTATION

Condor Systems, Inc.150

Pulse Bandwidth

Condor Systems, Inc.151

EXAMPLE OF PULSE FREQUENCYCOMPUTATION

Condor Systems, Inc.152