THE CITADEL, THE MILITARY COLLEGE OF SOUTH CAROLINA

171 Moultrie Street, Charleston, SC 29409

Stepped-Frequency Nonlinear Radar

Simulation

Anthony F. Martone

U.S. Army Research Laboratory

Adelphi, MD, 20783

Kyle A. Gallagher, Ram M. Narayanan

Pennsylvania State University

University Park, PA, 16802

Gregory J. Mazzaro

The Citadel, The Military College of South Carolina

Charleston, SC, 29409

2

Presentation Overview

• Nonlinear Radar

• Concept, Motivations

• Nonlinearity, Sources, Harmonics

• Harmonic Radar Measurements

• Nonlinear Stepped-Frequency Radar

• Stepped-Frequency

+ Harmonic Radar Concept

• Nonlinear SFR Measurements

• Summary & Future Work

U.S. Army Research Laboratory

Synchronous Impulse

Reconstruction (SIRE) Radar

3

Nonlinear Radar Concept

Applications:

Advantages:

• It is easier to separate targets from clutter because most clutter is linear.

Disadvantages:

• Targets require high incident power to drive them into non-linear behavior.

• Received responses are usually very weak compared to the transmitted “probe” signals.

Target presence/location

is indicated by receiving

frequencies that were

not transmitted.

Tx

Rx

• locate personal electronics during emergencies

• detect electronically-triggered devices

electronic

target

4

Linearity vs. Nonlinearity

For a linear system,

For a non-linear system,

1 1 2 2 1 1 2 2a x a x a y a y

1 1

2 2

x y

x y

?

input output

0 0 0 0 0 0cos cosA t A H t

0 0 0 0 0 0 0 0 0cos , cos , ,A t A H A A t A

1 1 2 2 1 1 2 2a x a x a y a y

transfer function depends on amplitude, and

output frequency does not necessarily equal input frequency

5

Sources of Nonlinearity

+

_ +

_

Active elements & components – by design; above system noise floor

Passive elements & components – unintended; below system noise floor

diodes transistors amplifiers mixers

f1

f2

f1 + f2

contacts [1,2]

metal 1

metal 2

oxide

metal

temperature

-dependent [5] connectors [3]

V R

ferro-electrics [4]

6

Temperature-Dependent Resistance

Vin R

Iout

voltage applied,

current flows

resistor

heats up

resistance

increases current

decreases

resistor cools

down resistance

decreases

current

increases

input: constant

output: sinusoidal

nonlinear system

Vin

time

Iout R

time time

0 01R T R T T

7

Nonlinear Radar Research

Tx

Rx

The target is viewed

as a collection of

nonlinearities. Ein

Erefl... LNA

BPF

one possible

signal path:

8

Harmonic Radar Theory

2 3

out 1 in 2 in 3 in ...E a E a E a E Let the nonlinearity

be approximated by

a power series [6]

Let the input waveform be a sinusoid: in 0 0cosE E t

Then the device response (output) is

2 3

out 1 0 0 2 0 0 3 0 0cos cos cos ...E a E t a E t a E t

2 3

2 0 3 0out 1 0 0 0 0 0cos 1 cos 2 3cos cos 3 ...

2 4

a E a EE a E t t t t

harmonics

input

output

from [7]

9

Recent 1-Tone Experiment

1-dB step

attenuator

Ptrans

targ

et

antenna

1.1

m

5 m

GTEM cell

Prec

Tektronix AWG7052

arbitrary waveform generator Amplifier Research

50-W 1-GHz RF amplifier

Rohde & Schwarz FSP

40-GHz spectrum analyzer GTEM = Gigahertz Transverse Electromagnetic

10

Transmitted Frequency (MHz)

Pow

er R

ecei

ved

at

2n

d H

arm

on

ic (d

Bm

)

10-12 W

10-15 W

PD = 16 mW/cm2

GTEM cell

Recent 1-Tone Measurements

Nonlinear (harmonic) device response is

experimentally verified,

but ranging/imaging is not possible when

receiving a single continuous frequency.

11

Stepped-Frequency Radar

A1

f1

A2

f2

A3

f3

A4

f4

A5

f5

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

amplitude

phase

frequency

…

…

…

…

Tra

nsm

itte

d

Rec

eived

P

roce

ssed

IDFT

2

cR t

12

Nonlinear Stepped-Frequency Radar

A1

f1

A2

f2

A3

f3

A4

f4

A5

f5

2f0 2f0 + 2Df 2f0 + 4Df 2f0 + 6Df 2f0 + 8Df

amplitude

phase

frequency

…

…

…

…

Tra

nsm

itte

d

Rec

eived

P

roce

ssed

IDFT

2

cR t

13

Transmitter

Receiver

Vrec

Tektronix

AWG7052

Simulated Radar

Environment

MiniCircuits

NLP-1000+

MiniCircuits

NLP-1000+

Amplifier Research

AR4W1000

Lecroy 8300A

channel 2

Lecroy 8300A

channel 3

HP 778D

MiniCircuits

VHF-1320+

MiniCircuits

VHF-1320+MiniCircuits

VHF-1320+

MiniCircuits

VHF-1320+

MiniCircuits

PSA-5453+

MiniCircuits

PSA-5453+

MiniCircuits

PSA-545+

MiniCircuits

CBL-25FT x4

target

Vtrans

Tx coupled

Rx coupled

in out

Hardware Simulation Experiment

d = 100 ft

14

Hardware Simulation Measurements

blue = transmitted to target,

880 MHz to 920 MHz ,

Tenv = 1 ms , N = 40

red = received from target,

1760 to 1840 MHz

15

Hardware Simulation Results

d = 102 ft

1 ft0.34

2 nsr

cd t t

tgt

tgt

NL

2 21

0

sin 2

2

j f tM

M

B th t

t

E E e

As long as (a) the phase response of

the target is linear and (b) the amplitude

response is nearly flat over the band of

interest…

Range-to-target is found from

an inverse DFT of the nonlinear

SFR response, as with linear SFR.

nonlinear impulse response,

constructed from an IDFT

of the data in red

16

Transmitter

Receiver

Vrec

Tektronix

AWG7052

Simulated Radar

Environment

MiniCircuits

NLP-1000+

MiniCircuits

NLP-1000+

Amplifier Research

AR4W1000

Lecroy 8300A

channel 2

Lecroy 8300A

channel 3

HP 778D

MiniCircuits

VHF-1320+

MiniCircuits

VHF-1320+MiniCircuits

VHF-1320+

MiniCircuits

VHF-1320+

MiniCircuits

PSA-5453+

MiniCircuits

PSA-5453+

MiniCircuits

PSA-545+

MiniCircuits

CBL-25FT x4

target

Vtrans

Tx coupled

Rx coupled

in out

Nonlinear stepped-frequency radar was

demonstrated by hardware simulation of a

nonlinear target in a linear radar environment.

Summary & Near-Term Future

17

Summary & Near-Term Future

Nonlinear stepped-frequency radar was

demonstrated by hardware simulation of a

nonlinear target in a linear radar environment.

step

atten

uator

targ

et

3 m

Prec

Ptrans

Wireless experiments &

verification of the NL SFR concept

with multiple electronic targets.

Next step(s):

18

References

[1] C. Vicente and H. L. Hartnagel, “Passive-intermodulation analysis between rough rectangular waveguide flanges,”

IEEE Transactions on Microwave Theory and Techniques, Vol. 53, No. 8, Aug. 2005, pp. 2515–2525.

[2] H. Huan and F. Wen-Bin, “On passive intermodulation at microwave frequencies,” in Proceedings of the Asia-Pacific

Electromagnetic Conference, Nov. 2003, pp. 422–425.

[3] J. Henrie, A. Christianson, and W. J. Chappell, “Prediction of passive intermodulation from coaxial connectors in

microwave networks,” IEEE Transactions on Microwave Theory and Techniques, Vol. 56, No. 1, Jan. 2008.

[4] G. C. Bailey and A. C. Ehrlich, “A study of RF nonlinearities in nickel,” Journal of Applied Physics, Vol. 50, No. 1,

Jan. 1979, pp. 453-461.

[5] J. R. Wilkerson, K. G. Gard, A. G. Schuchinsky, and M. B. Steer, “Electro-thermal theory of intermodulation distortion

in lossy microwave components,” IEEE Transactions on Microwave Theory and Techniques, Vol. 56, No. 12, Dec.

2008.

[6] J. C. Pedro and N. B. Carvalho, Intermodulation Distortion in Microwave and Wireless Circuits. Boston, MA: Artech

House, 2003.

[7] G. J. Mazzaro and A. F. Martone, “Harmonic and multitone radar: Theory and experimental apparatus,”

U.S. Army Research Laboratory Technical Report, No. 6235, Oct. 2012.