A Digital Instantaneous Frequency Measurement Technique

A Digital Instantaneous Frequency Measurement Technique Utilising High-Speed ADC’s and FPGA’s

2006 CSIR Research and Innovation Conference

CSIR Defence, Peace, Safety and Security

Dr PL Herselman

Visiting Researcher at the University College Londo n

27 February 2006

© CSIR 2006 www.csir.co.za

Electronic Warfare

Image courtesy of Altera, www.altera.com


Signal Intelligence (SIGINT)

• Complex battlefield � multiple RF emitters• Receiver analyses intercepted waveforms

• Situational awareness• Queuing of defensive/evasive action(s)

• Compact packaging for operational systems• Employed on a range of systems

• Airborne Warning and Control System (AWACS)

Image courtesy of Rockwell Collins

Movie courtesy of Macom

Image courtesy of NATO, www.nato.intImage courtesy of Northrop Grumman


Agenda

• BackgroundDIFM research as part of CSIR Defence, Peace, Safety and Security R&D strategy

• IFM TheoryOverview of basic theory

• Optimal Time DelayLed to DIFM invention

• DIFM BasicsDigital implementation of IFM using innovative parallel DSP techniques

• Example ImplementationShared aperture DIFM on SWIFT500 DRFM system

• Simulation ResultsBit-true functional simulations for a range of input signals

• Experimental VerificationResults of a prototype system

• Conclusions

Background


Digital Radio Frequency Memory (DRFM) Research and Development at the CSIR

• Active R&D field since 1999

• Advanced and highly configurable repeater• Analog to digital converter � memory � digital to analog converter• Information bandwidth limited to half the sampling rate

• Utilised in a range of applications• Field (electronic countermeasures)

• Obscure the platform (e.g aircraft)• Deceive the hostile radar

• Laboratory (test equipment)• Coherently simulate the signals emitted by electronic

countermeasures and the signals reflected from targets


Digital Radio Frequency Memory (DRFM) Research and Development at the CSIR

• Levels of developmentDigital DRFM ModuleDRFM KernelDRFM-based simulator system


Need for Frequency Measurement in DRFM-Based Systems

• Pulse qualificationDeceive and obscure only hostile systems

• Frequency dependant techniquesAccurate Doppler responseRF bandwidth is a scarce resourceMaximise ECM effectiveness

• Compensate DRFM-induced phase perturbationsPoster presentation

Estimate required in less than a

microsecond


Frequency Measurement Solutions

• Instantaneous Frequency Measurement (IFM)• Analog technique• Combined with analog-to-digital

converter � DFD• Multiple parallel IFM’s• Single output• Dual aperture

• Discrete Fourier Transform (DFT)• Measures spectral response• Aliased to [0,fs/2) frequency

range• Multiple input signals• Multiple outputs

Preferred frequency estimation technique

Graph courtesy of AlteraTable taken from Schleher (1986)

Instantaneous Frequency Measurement Theory


Instantaneous Frequency MeasurementDigital Frequency Discriminator

AnalogInput

RL

I

Low-passFilter ADC

c0*arccos[c1*yfilt(tn)]

yfilt(tn) f0(tn)

DigitalOutput

Mixer

3 dBCoupler Analog

Delay lineLookup Table

• Multiply signal with delayed replica

• Low-pass filter

• Inverse cosine operation• Typically preceded with ADC• Lookup table• Digital Frequency Discriminator (DFD)

( ) ( ) ( )[ ]τππτπ 000

20 24cos2cos

8ftff

Atymix −+=

( ) ( ) ( ) ( ) ( )02 , 2cos08 00

20 HfHfH

Aty filt <<≈ τπ

( )( )

≈

0

8arccos

2

120

0 HA

tyf filt

πτ

Optimal Time Delay


Delay Line Calculation

• One-to-one mapping: Input frequency � output value• Maximum one-to-one input frequency calculated as

• Inverse of twice the maximum input frequency

• IFM with frequency range equal to ADC IBW• Unambiguous input frequency range [0,fs/2) chosen

• Optimal time delay = one ADC sampling period

( )( )

( )( )

( )0 ,

2

121

2

11arccos

2

1

max0max0max0

==+=−= nf

nff

πππ

τ

( )s

ss

tfff

==

== 1

22

1

2

1

max0

τ

Digital Instantaneous Frequency Measurement Basics


Steps 1&2: Sampling, Quantisation and Multiplication

• Sampling and quantisation

• Multiplication with time-delayed replica

( ) ( )[ ] ( )[ ]

( ) ( ) ( )nnFD

AnF

D

Around

f

fFnFAQn

f

fAQntyQny

qNN

sssq

εππ

ππ

+=

=

==

==

−0

00

10

0000

00

2cos22cos22

, 2cos2cos

( ) ( ) ( )

( ) ( )[ ]

( ) ( ) ( )[ ] ( ){ } ( ) ( )112cos12cos2

24cos2cos2

1

000

00012

2

20

−+−+−+

−+=

−=

−

nnnnFnnFD

A

FnFFD

A

nynyny

qqqqN

N

qqmix

εεεπεπ

πππ


Step 3: Low-Pass Filtering

• Finite Impulse Response (FIR) digital filter

where

( ) ( )

( ) ( ) ( ) ( )( )[ ] ( ) 22cos2cos02 0000012

2

20

0

nFHFnFFHFHD

A

knycny

qLPFLPFLPFN

N

kmixkfilt

επππ ′+′∠+−′′+=

−=

−

=∑

4 , 21

4 , 2

000

000

s

s

ffFF

ffFF

>−=′

≤=′


Step 3: Low-Pass Filtering

• Interactive filter design tools (e.g. MATLAB FDATool)


Step 4: Inverse Cosine Operation

• Digital inverse cosine estimation• Cordic algorithm• Lookup table

• Output of low-pass filter is used as the input to a lookup table• Lookup table output estimates frequency of the input signal

( ) ( )( )

−= − 02arccos

2

12122

0

2

LPFN

filtN

out HA

Dnyny

out

π


Digital Instantaneous Frequency Measurement

• Advantages

Mixing product relatively linear yielding lower spurious response

Filter response can be optimised for the specific requirements, i.e. fast response versus measurement accuracy

• Issues

FPGA clock speeds > 100 MHz

DIFM up to 50 MHz bandwidth with serial processing

Exhibit the same amplitude sensitivity as an analog IFM


Parallel Processing DIFM

• High-speed flash converter ADC’s • > 10 bits • > 2 GSPS

• Techniques often employed include time-domain demultiplexing, i.e. wider bus, lower data rate• ASIC or commercial demultiplexers• For 1.2 GSPS 10-bit ADC

• 16x demulitplex• 75 MSPS 160-bit

• Calculate in a single FPGA clock cycle• 15 multiplications• 14th order FIR filter

• Possible to artificially extend the bus width


Amplitude Insensitive DIFM

• Suppose an estimate of the input amplitude was available

• Technique analogous to DIFM with time delay equal to 0

• Multiply

• Low-pass

( ) ( )( )

( )( )[ ]

( ) ( )

( ) ( ) ( ) ( )( )[ ] ( )20

0000012

2

020

20

2

22cos2cos024

,

A

nFHFnFFHFH

D

nAA

ny

nA

ny

nA

nyny

qLPFLPFLPF

N

afilt

a

filtfiltdiv

επππ

εε

′+′∠+−′′+≈

>>≈+

==

−

( ) ( ) ( ) ( ) ( ) ( )ny0 2q==−=′ nynynynyny qqqqmix

( ) ( ) ( ) ( )( )[ ] ( )nFHnFFHHD

Any qLPFLPFLPF

Nfilt επ ′′+′∠+′′+=′ −

00012

2

20 2cos02


Amplitude Insensitive DIFM

• Divide basic DIFM filter output with amplitude estimation

• Inverse cosine lookup table yield frequency estimation

• Advantages• Amplitude estimation exactly aligned with frequency estimation• No external calibration or alignment required• Time-domain multiplex hardware

( ) ( ) ( )( ) ( )( ) ( )

( )0

0000

0

2cos

22cos0

2cos

F

nFHFnFH

FHFny qLPF

LPF

LPFdiv

π

επππ

≈

′′′+′∠+−′′

+≈

( )s

lt f

fFny 0

0 22 ππ =≈

Example Implementation


SWIFT500 Digital DRFM Module with Built-In Amplitude Insensitive DIFM

• 1.2 GSPS , 500 MHz IBW• 16x demultiplexing• Stratix 1S30 with 96 9x9 multipliers



yq(n)yq(n-1)

yq(n-15)

yq(n-2)

InputCast0InputCast1InputCast2

InputCast15UnitDelay0UnitDelay1UnitDelay2

UnitDelay15UnitDelay16UnitDelay17UnitDelay18

UnitDelay24

y'q(n-32)y'q(n-33)

y'q(n-40)

y'q(n-31)

y'q(n-18)y'q(n-17)y'q(n-16)

y'q(n-2)y'q(n-1)y'q(n)

y'q(n-15)

Uni

tD

elay

8

MuxMult24

14c0

22c1

38c2

57c3

81c4

109c5

138c6

168c7

196c8

221c9

240c10

252c11

255c12

252c13

240c14

221c15

196c16

168c17

138c18

109c19

81c20

57c21

38c22

22c23

14c24

y'q(

n-24

)y'

q(n-

25)

Flip-Flop

MuxMult1

MuxMult0

Adder

DeMux1Select

0 1

DeMux2Select

0 1

UnitDelay25

UnitDelay26

InverseLookupTable

Multiply

ArccosLookupTable

yout

y1mm

y2mm

y24mmya

UnitDelay25

ydm1 ydm2

ym

Mux#A

Mux#BSelect

0

1

Select

0

1y'q(n-#)

y'q(n-#-1)

y'q(n-#-16)

Select In

Multiply#A Multiply

#B

Coeff In #

Y#mm(m+d1)



• Key specifications• 9-bit multiplication • 24th order low-pass FIR filter with Chebyshev windowing• Cut-off frequency of 100 MHz and 48 dB side-lobe suppression• Frequency response 50 MHz to 550 MHz• Time-multiplexed resources to estimate amplitude and frequency• Division implemented in a two-step process

• Inversion of denominator using lookup table (12-bit x 12-bit)• Multiplication of numerator with inversed denominator

• 12-bit by 10-bit inverse cosine lookup table

Simulation Results


Monochromatic Input Signal With Additive Coloured Noise


Analysis of DIFM Accuracy


Key Performance Specifications• High signal-to-noise ratios

• Mean deviation less than ± 2 MHz• Absolute error less than 6 MHz across bandwidth• Absolute error less than 2 MHz in > 300 MHz bandwidth• RMS error less than 3 MHz across bandwidth• RMS error less than 1 MHz in > 300 MHz bandwidth

• Low signal-to-noise ratios• Bias in frequency estimation• Due to bias in amplitude estimation• Reduced by implementing higher order FIR filter (longer latency)

• Latency (processing time)• 13 FGPA clock cycles (173.33 ns)

• Throughput rate• 2 FGPA clock cycles (37.5 MHz)

Experimental Verification


Quantitative Laboratory Experiments

Conclusions


Conclusions

• Viable, shared aperture, frequency estimation technique• Implemented efficiently in current commercial hardware• Results comparable to existing analog techniques• Flexibility and ability to be optimised for the specific

requirements• Real-time changing the filter coefficients• Insensitive to temperature• Does not require periodic calibration to maintain accuracy• Operationally superior to its analog counterparts

• South African provisional patent application 2006/00946, 2006-02-01

A Digital Instantaneous Frequency Measurement Technique

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