introduction to stepped-frequency radar -...

8/1/2013

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1

Approved for Public Release


Introduction to

Stepped-Frequency Radar

Gregory Mazzaro Brian Phelan

Kelly Sherbondy Francois Koenig

ALC 204/3D013

June 7, 2013

Overview

2

• High Range Resolution Radar

• Impulse, Chirp, Stepped-Frequency

• Properties of the Stepped-Frequency Waveform

• Step-Frequency Radar Architecture

• Theory-of-Operation & Basic Design

• Penn State University Design (B. Phelan)

• Transmission, Data Capture, Processing

• Tx/Rx Sequence of Events

• Inverse Discrete Fourier Transform

• Radar Design Parameters

• Resolution, Unambiguous Range

• Design Strategy & Example

• RailSAR



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Overview

3













• RailSAR



High Range Resolution Radar

from [1,2]

• Range Resolution

DR = c/2B, B = bandwidth, c = speed of light

• Waveforms

• Impulse (e.g. Synchronous Impulse Reconstruction radar)

• extremely narrow pulses of high power

• Pulse compression (e.g. linear frequency-modulated chirp)

• modulated transmit pulses instead of reduced time duration

• received pulses are processed by correlating with transmitted pulses

• Stepped-frequency

• successive pulses increase frequency linearly in discrete steps

• modulation occurs across pulses instead of within pulses

t 1Bt

4



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Impulse Waveform

5

SIRE transmitter

waveform (#10456)

recorded using

Lecroy Wavemaster

8300A oscilloscope

(measured)



Linear FM Chirp Waveform

fstart = 200 MHz, fend = 1800 MHz,

Tenv = 1 ms, Dc = 20%

(simulated)

env startcos 2 2A f k t t s t

end start env

env

c

c

s t u t u t D T s t T

k f f T

D T T

6



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7

• Coherent pulses -- frequency increases in linear steps

• fn = f0 + nDf f0 = starting carrier frequency, Df = step size

t = pulse length (active, per frequency), T = repetition interval

• n = 1…N, each burst consists of N pulses (frequencies)

coherent processing interval (CPI) = N · T = 1 full burst

• range resolution = DR = c / 2B

DR = c / 2N·Df because effective bandwidth B = N·Df

• does not depend on instantaneous bandwidth

• can be increased arbitrarily by increasing N·Df

from [1]

Stepped-Frequency Waveform



Stepped-Frequency Waveform

8

from [4]

Tx/Rx

Rx

Tx/Rx

Rx

Tx/Rx

Rx

Tx/Rx

Rx

Tx/Rx

Rx



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Stepped-Frequency vs. Others

9 from [1]

• Advantages

• achieves high effective bandwidth with narrow instantaneous bandwidth

• Rx bandwidth is smaller lower noise bandwidth, higher SNR

• A-to-D sampling rates are lower (vs. pulse-compression)

• peak power is smaller (vs. impulse)

• provides flexible Tx frequency control

• can “hop” over restricted

or undesired Tx frequencies

• enables adaptive/cognitive frequency use

• rejects later Rx clutter from earlier Tx pulses

• returns from clutter in ambiguous ranges

have frequencies that are different

from returns from targets

• ambiguous clutter returns will be

rejected by the receiver IF filter

from [3]



S-F Spectrum: Time vs. Freq

10

fstart = 500 MHz, fend = 1250 MHz, Df = 250 MHz (N = 4)

t = 1 ms, T = 10 ms (Dc = 10%)

n =

1

n =

2

n =

3

n =

4

n =

1

n =

2

n =

3

n =

4

spacing

= Df

(simulated)



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S-F Spectrum: Wide vs. Narrow

11

n =

1

n =

2

n =

3

n =

4

n = 3

spacing

= 1/T spacing

= Df


t = 1 ms, T = 10 ms (Dc = 10%)

(simulated)

Note: Compared to

impulse & chirp

waveforms, the Tx/Rx

spectrum is not smooth.



S-F Spectrum Notching

12


t = 1 ms, T = 10 ms (Dc = 10%);

signal blanked between 850 and 900 MHz

(simulated)

Note: Compared to

impulse & chirp

waveforms, the Tx/Rx

spectrum is not smooth.



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S-F Spectrum Notching

13


t = 1 ms, T = 10 ms (Dc = 10%);

signal blanked between 850 and 900 MHz

850 to 9

00 M

Hz

850

to

900

MHz

(simulated)

Note: Energy from

neighboring

frequencies “bleeds”

into the notched

frequencies because

all frequencies are

pulsed.



Stepped-Frequency vs. Others

14 from [1]

• Disadvantages

• range resolution cannot be achieved with a single pulse

• requires Tx, Rx, and processing of a group of pulses for any one bin

• range-Doppler coupling is more pronounced

• e.g. different Doppler shifts for each frequency

• additional signal processing is required for tracking moving targets

• not an issue for the RF Branch’s new forward-looking GPR [3]

• range spread & range shift << 1 range bin



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Overview

15













• RailSAR



Theory-of-Operation

A1

f1

A2

f2

A3

f3

A4

f4

A5

f5

f0 f0 + Df f0 + 2Df f0 + 3Df f0 + 4Df

amplitude

phase

frequency

…

…

…

…

Tra

ns

mit

ted

R

ec

eiv

ed

P

roc

es

se

d

IDFT

2

cR t NOT a direct sampling

scheme (e.g. impulse).


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Pulse Width

Coarse Range Gate = Pulse width (in meters) divided by 2

Tx

Rx

Sample Now!

animation courtesy

of B. Phelan

Basic S-F Architecture

Antenna

duplexer = passes Tx signal to antenna

stalo = stable local oscillator

coho = coherent oscillator

IF = intermediate frequency

TRANSMIT

coho stalof f n f f D

18

modified

from [1]



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Antenna

duplexer = passes Rx signal to amplifier




RECEIVE


19

modified

from [1]




Antenna

duplexer = passes Tx signal to antenna

passes Rx signal to amplifier





20 from [1]


(omitted from PSU design)



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Brian Phelan’s SFR Design

21

Tx Rx

fcoho

f0 + nDf

fcoho (10 MHz)

fcoho+ f0 + nDf

fcoho +

f0 + nDf

f0 + nDf

fcoho

fcoho

I, Q

splitt

er

splitt

er

splitt

er

splitt

er

DAQ

modified from [3]

f0 + nDf (300 to 2000 MHz)

16 copies of the reference frequency

2 transmit channels

16 r

eceiv

e c

hannels

16 copies of the transmit frequency



Overview

22













• RailSAR



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Tx/Rx Sequence of Events

Tx Pulse Rx Sample Rx Sample Rx Sample Rx Sample Rx Sample …



Range

bin 1

Range

bin 2

Range

bin 3

Range

bin 4

Range

bin 5

… … … … … …



Tx/Rx Sequence of Events




Range

bin 1

Range

bin 2

Range

bin 3

Range

bin 4

Range

bin 5

I11 = 0

Q11 = 0

I12 = A12 cos(f12)

Q12 = A12 sin(f12)

I13 = 0

Q13 = 0

I14 = A14 cos(f14)

Q14 = A14 sin(f14)

I15 = A15 cos(f15)

Q15 = A15 sin(f15) f0

f0 + Df

f0 + 2Df

I21 = 0

Q21 = 0

I22 = A22 cos(f22)

Q22 = A22 sin(f22)

I23 = 0

Q23 = 0

I24 = A24 cos(f24)

Q24 = A24 sin(f24)

I25 = A25 cos(f25)

Q25 = A25 sin(f25)

I31 = 0

Q31 = 0

I32 = A32 cos(f32)

Q32 = A32 sin(f32)

I33 = 0

Q33 = 0

I34 = A34 cos(f34)

Q34 = A34 sin(f34)

I35 = A35 cos(f35)

Q35 = A35 sin(f35)

… … … … … …



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Data Sampling & Processing

modified

from [1]

A12

f12

A22

f22

A32

f32

A42

f42

A52

f52

A62

f62

A72

f72

A82

f82

A92

f92

f 0

f 0 +

Df

f 0 +

2D

f

f 0 +

3 D

f

f 0 +

4 D

f

f 0 +

5 D

f

f 0 +

6 D

f

f 0 +

7 D

f

f 0 +

8 D

f

amplitude

phase

frequency

1 complex sample

per range bin

per frequency

1 Range Bin:



Inverse Discrete

Fourier Transform

modified

from [1]

Data Sampling & Processing

1 complex sample

per range bin

per frequency

1 Range Bin:



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Example: 1 Rx Channel, 1 Target

amplitude

phase

target

1 Range Bin

27

2

cR t

(Matlab simulation)

tgt tgt

tgt

tgt tgt2 6

sinIDFT

10j f t

B t

t

e t

t

t

tgt

tgt

tgt

2

tgt

tgt

2Rx

0 2

j ff f

f f

e B

B

t

tgt tgt

tgt

800 MHz, 400 MHz

150 ns

f B

t



Overview

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• RailSAR



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GPR Design Parameters

Transmit power is chosen from the radar equation and models / empirical data [4]:

rec trans trans rec

1 1

4 4

l lP P G e e GR R

Tx power

(input to

antenna)

transmit

antenna

gain

propagation

loss

to target

ground

penetration

to target

RCS

of target

ground

penetration

from target

propagation

loss

from target

receive

antenna

gain

Rx power

(output from

antenna)

modeling of propagation loss, ground penetration, RCS does not change

processing of received data changes significantly


S-F Design Parameters

f 0

f 0 +

Df

f 0 +

2D

f

f 0 +

3 D

f

f 0 +

4 D

f

f 0 +

5 D

f

f 0 +

6 D

f

f 0 +

7 D

f

f 0 +

8 D

f

A11

f11

A21

f21

A31

f31

A41

f41

A51

f51

A61

f61

A71

f71

A81

f81

A91

f91

IDFT

1

2 2 2

c c cR t

N f N fD D

D D

bin2

cR t

30

Range bin size is calculated

from the length of 1 received pulse:

Resolution is calculated from the IDFT

using all N frequencies:

bin,IDFT2

cR R N

f D

D

The imaged distance per range bin is

calculated from the size of the IDFT:

To avoid aliasing,

bin,IDFT bin

12 2

R R

c cf

ft t

D D

t

AN1

fN1

…

…

f 0 +

(N-1

)Df



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A12 A22 A32

2 2u

c cR T Mt

31

Unambiguous range is calculated

using all M received pulses for 1 frequency:

For stationary targets, t = T (M = 1 range bin) is appropriate.

t < T (which requires faster sampling)

allows for “dead” time between pulses

and/or multiple range bins

(which is useful for tracking moving targets) [1]

A11 A21 A31

A13 A23 A33 t

T

(example, M = 3 bins)

bin2

u

cR R ft t D

Range bin size is calculated

from the length of 1 received pulse:




t sets the range bin size

T sets the unambiguous range

Without considering noise/clutter…

32

NDf sets the radar resolution

bin2

cR t bin,IDFT

2

cR

f

D

1f tD

2

cR

N fD

D

2u

cR T



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A11

f11

A21

f21

A31

f31

A12

f12

A22

f22

A32

f32

A13

f13

A23

f23

A33

f33

Range

bin 1

Range

bin 2

Range

bin 3

All frequencies must be

transmitted & received

before any one range

bin can be resolved.

33

… … … …

N ·T sets the data collection time



(1) Determine the unambiguous range (total area to be imaged)

and use this distance to calculate T.

bin2

cR t

(2) For moving targets, divide the image into multiple range bins [1].

For stationary targets, choose t = T (M = 1, Ru = Rbin).

2

cR

N fD

D

2u

cR T

(3) Decide the necessary fine resolution (DR) which will dictate

the total received bandwidth that must be captured (NDf).

(5) Choose N according to the maximum

data collection time allowed:

1f tD (4) Obey the (anti-aliasing) rule-of-thumb for maximum frequency steps:

trace

totalT N T

S-F Strategy

34



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Trade-Offs

35

• To improve resolution, increase N·Df… 2R c N fD D

Increasing N increases the data collection time. trace

totalT N T

Increasing Df decreases the range bin size

and, by extension, the overall radar range. bin2 1f c RD

binuR M R

• To increase range, increase T…

Increasing T increases the data collection time. trace

totalT N T

2R c N fD DDecreasing N worsens the radar resolution.

• To shorten data collection time, decrease N ·T…

2uR T c

trace

totalT N T

2R c N fD DDecreasing N worsens the radar resolution.

2uR T c Decreasing T decreases the radar range.



bin , 200 ns2

u

cR R Tt t

8

9

1500 MHz 500 MHz

3 1015 cm

2 2 10

N f

cR

N f

D

D

D

30 m , 200 ns2

u

cR T T

6 9

1 5 MHz

5 10 10 , 200

f

N N

tD

S-F Example

(1) Choose the range to be imaged:

(2) For stationary targets,

use only 1 range bin:

(3) Use the middle of the SIRE band

to image the target:

(4,5) Use the maximum Df and calculate N:

36

30 ft = 9.1 m

MiniCircuits

CBL-15FT-SMSM+ x2

Tektronix

AWG7052

Lecroy

WM 8300A

HP 778D



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S-F Strategy + Example

(6) Generate a series of frequency steps and transmit them to the target,

one frequency at a time.

40μsN T 1GHzN fD

Note: Since the Rx data

must contain phase vs.

frequency, each frequency

must be transmitted with a

known reference phase.

Tra

nsm

itte

d

37

Note: Since the Rx data is

processed as a scaled

version of the frequency

response of the radar

environment, the Tx power

should be constant vs.

frequency.




(7) Record amplitude & phase for each frequency as it is received.

Receiv

ed

38

Note: I-Q sampling

should be performed at

the end of each Rx pulse

to ensure that the steady-

state response of the

environment is captured.



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(8) Zero-pad the data (at frequencies above/below those transmitted).

(9) Perform the inverse discrete Fourier transform (IDFT) on this data set.

(10) Transform time to range using R = t·c/2 .

IDF

T

(measured, 30-ft line

depicted on Slide 34)

39



Overview

40













• RailSAR



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RailSAR

41

f1 f2 f3 f4

Vtrans

…

f1 f2 f3

Vrec, H-H polarization

…

T

IDFT

Range profile, 1 range bin

Agilent

N9923AN

Port 1

Agilent

N9923AN

Port 2

Vrec

Vtrans

RF

relays

ETS Lindgren

3164-06

horn antennas

digital

I/O

H

V

H

V

Tx

Rx

S211 S212 S213 S214 S215

f 0

f 0 +

Df

f 0 +

2D

f

f 0 +

3 D

f

f 0 +

4 D

f

amplitude

& phase

frequency

…

…

N9

92

3A

N


Take-Away

42

(1) Stepped-frequency radar is another form of UWB radar that achieves

• high range resolution,

• narrow instantaneous bandwidth, and

• a greater degree of spectrum control than impulse and chirp systems.

(2) The RF SP&M Branch is moving away from impulse radar

and (with the help of PSU) is constructing 2 SFR systems:

• forward-looking vehicle-mounted GPR (SIRE vehicle + antenna mount)

• RailSAR (in Building 207, overlooking the “sandbox”)

(3) The theory-of-operation of an SFR system is

• transmit a wide band of frequencies, one at a time

• capture the frequency response of the radar environment, and

• convert the response to a range profile using the Inverse DFT.

(4) A disadvantage of the SFR technique is that all frequencies

must be received before any one range bin can be imaged.

(5) The most important design equations are 2R c N fD D 2uR T c trace

totalT N T



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References

43

[1] J. D. Taylor, Ultra-Wideband Radar Technology, Boca Raton: CRC Press,

2001. pp. 303-25 (Chapter 11, “High-Resolution Step-Frequency Radar”, by G. S. Gill).

[2] E. F. Knott, J. F. Shaeffer, and M. T. Tully, Radar Cross Section,

Raleigh: Scitech Publishing, Inc., 2004.

[3] B. Phelan, “Design of Spectrally-Versatile Forward-Looking Ground Penetrating

Radar for Detection of Concealed Threats,” ARL Summer Student Report, Aug. 2012.

[4] B. R. Phelan, M. A. Ressler, G. J. Mazzaro, K. D. Sherbondy, and R. M. Narayanan,

“Design of Spectrally Versatile Forward-Looking Ground-Penetrating Radar

for Detection of Concealed Targets,” SPIE Defense, Security, and Sensing 2013,

paper #8714-10, Baltimore, MD, Apr. 2013.



introduction to stepped-frequency radar -...

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