This document provides an introduction to pulse repetition interval (PRI) analysis and deinterleaving from an electronic intelligence (ELINT) perspective. It discusses key concepts such as PRI, unambiguous range and velocity, range-velocity ambiguity, optimum PRI for medium PRF radars, and PRI stagger. The document explains how understanding radar constraints such as range resolution, integration time limits, Doppler resolution, and frequency agility can help an ELINT analyst correctly interpret radar signals and anticipate signal characteristics.

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
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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
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72. EXAMPLE OF PRE-DETECTION RADAR
PULSE RECORDING
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CALCULATION OF AMPLITUDE, TOA,
PW
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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
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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.
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74. EXAMPLE OF PULSE WIDTH
ACCURACY
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PULSE FREQUENCY COMPUTATION
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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.
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EXAMPLE OF PULSE FREQUENCY
COMPUTATION
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76. Pulse Bandwidth
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EXAMPLE OF PULSE FREQUENCY
COMPUTATION
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