FMCW Radar Concepts Challenges Implementation Results A joint project Thanks to BSU Department of...

FMCW Radar

ConceptsChallenges

ImplementationResults

A joint projectThanks to BSU Department of

GeosciencesHans-Peter Marshall

FMCW Outline

• Some radar history and evolution

• FMCW concepts and benefits• Design Considerations• Testing and Results• Refinements – Current and

Future

Early History

Thanks, Wikipedia et al

Scotland

James Clerk Maxwell -- Theory of the Electromagnetic Field

Germany

Heinrich Hertz demonstrated RF reflections

Italy Guglielmo Marconi demonstrated long distance transmission of electromagnet waves using a tent pole – l’antenna

Germany

Christian Hülsmeyer – telemobiloscope for traffic monitoring on water in poor visibility. First radar test

U.S. Nikola Tesla outlined radar concept

U.S. Albert Wallace Hull invented the Magnetron – efficient transmitting tube

U.S. Hetcalf & Hahn, GE, develop the Klystron

UK Randall & Boot build small powerful radar with multicavity magnetron, installed on B-17, and could see German submarines at night and in fog

19401945

Many countries

Radar technology development mushrooms during the war years in USA, Russia, Germany, France, Japan

Some Historical Perspective

• Early radars were pulse radar systems• Time domain transmit and detection• Fundamental radar distance resolution: • Problem:

– Narrow pulse needed to get wide bandwidth.– Wide pulse needed to receive sufficient energy

for SNR

• Solution: Chirp radar systems – use wider pulse but modulate its frequency to increase BW.

More about Pulse Chirp Radar

• Increase BW with wider pulse by sweeping the frequency during the pulse

• Reconstruct narrow pulse with dispersive delay line in the receiver (Pulse compression).

• Practical approach using ASP methods when DSP capabilities were slow and expensive.

Using a SAW Filter as a Chirp ASP

http://www.radartutorial.eu/17.bauteile/bt28.en.html

Evolution from Chirp Radar to FMCW

• FMCW is the logical extension to Chirp Radar when:– DSP capabilities become practical.– PLL technology evolved to support

highly linear frequency sweeping

What were the most important commercial outcomes from WWII

Radar Research?

The Microwave Ovenwhich caused the FCC to abandon the

2.45 GHz band as licensable frequencieswhich enabled WiFi and Bluetooth bands

FMCW Outline

Future

General FMCW BenefitsRelative to Pulse Radar

+Constant power improves transmitter efficiency

+Ability to choose frequency ranges of operation+Lower cost to achieve wider bandwidth+More constant power over bandwidth of

operation+More difficult to detect and jam

- Requires lots of DSP data analysis- Requires very linear FM swept signal

FMCW Sawtooth Wave Concept

𝜏=2𝑑𝑣

𝛼≡𝛿 𝑓𝛿𝑡 𝑓 𝐼𝐹=𝛼𝜏

T 𝐵𝑊 =𝛼𝑇

∆ 𝑓 𝐼𝐹=1𝑇

𝐵𝑊∆ 𝑑=

𝑣 ∆ 𝑓 𝐼𝐹

2𝛼= 𝑣2∙𝐵𝑊FFT

Resolution:

SplitterSplitt

𝑣=𝑐

√𝜀𝑟

𝑑=𝑣𝜏2

=𝑣2𝛼

𝑓 𝐼𝐹

FMCW Triangle Wave Concept

𝜏=2𝑑𝑣

𝛼≡𝛿 𝑓𝛿𝑡

𝑓 𝐼𝐹=𝛼𝜏

𝑑=𝑣𝜏2

=𝑣 𝑓 𝐼𝐹

T 𝐵𝑊 =𝛼𝑇

∆ 𝑓 𝐼𝐹=1𝑇

𝐵𝑊 ∆ 𝑑=𝑣 ∆ 𝑓 𝐼𝐹

2𝛼= 𝑣2∙𝐵𝑊

FFT Resolution:

FMCW Triangle with Doppler Shift

fIFu fIFd

𝑣𝑑=𝑣 𝑓 𝑑

2 𝑓 𝑐

𝑓 𝑑=2 𝑓 𝑐

𝑣 𝑑

𝑣 𝑣𝑑=𝑣 ( 𝑓 𝐼𝐹 𝑑− 𝑓 𝐼𝐹 𝑢 )

4 𝑓 𝑐

𝛼≡𝛿 𝑓𝛿𝑡

𝜏=𝑓 𝐼𝐹𝑢+ 𝑓 𝐼𝐹 𝑑

𝑑=𝑣𝜏2

=𝑣 ( 𝑓 𝐼𝐹𝑢+ 𝑓 𝐼𝐹𝑑 )

The Radar Power Equation (1)

Consider the power density arriving at the target from the transmitter:

𝑄𝑖=𝑃 𝑡 𝐺𝑡

4 𝜋 𝑅2

is the transmitted power

is the transmitter antenna gain

is the distance from transmitter to target

𝑃 𝑡

𝐺𝑡

The power reflected from the target toward the radar is:

𝑃𝑟𝑒𝑓𝑙=𝑄𝑖𝜎

where σ is the Radar Cross Section (RCS).

The power density received at the radar antenna is: 𝑄𝑟 =

𝑃𝑟𝑒𝑓𝑙

4𝜋 𝑅2

The received power from the receive antenna is:

𝑃𝑟=𝑄𝑟 𝐴𝑟

where Ar is the effective area of the receive antenna.

Combining the power equations results in the received power being:

𝑃𝑟=𝑃 𝑡 𝐺𝑡 𝐴𝑟 𝜎

(4𝜋 )2 𝑅4

Summary – All you need to know about FMCW Radar

𝑃𝑟=𝑃 𝑡 𝐺𝑡 𝐴𝑟 𝜎

(4𝜋 )2 𝑅4For a given radar system and object, received power reflected from the object is proportional to

∆ 𝑑=𝑣

2 ∙𝐵𝑊In order to resolve and distinguish two objects, they must be separated by a distance from the radar of

𝑑=𝑣2𝛼

𝑓 𝐼𝐹

The distance of an object (assuming no Doppler shift) from the radar can be determined by the IF frequency

FMCW Outline

Future

The Objective

• Develop a radar system that can, from a distance:

• Profile the bottom surface of a saline ice sheet and

• Determine if there is oil under the sheet

System Constraints

• Minimum frequency for antennas is 500 MHz

• Maximum frequency for saline ice penetration is 2 GHz

• Therefore, maximum BW is 1.5GHz

System Implications

• Signal source– Heterodyne vs. YIG– Spurious signals– Nonlinearity– Phase noise

• IF frequency response• Digitization resolution• I/Q Demodulator

Signal Source• The frequency range is 0.5 – 2.0 GHz• Multi-octave sources in this range are either:

– YIG Oscillator• Terrific multi-octave bandwidth capabilities• Have low Q and performance problems below 1-2 GHz• Specified “nonlinearity” is typically 1% -- differential or integral?• Expensive, requires a lot of power

– Heterodyne VCO oscillators• VCO oscillators are generally limited to a single octave of

frequency range.• Multi-octave source can be created by heterodyning two VCOs.• Heterodyne oscillators create spurious signals.• Slope of frequency vs. voltage is typically 2:1 or more

• Spurious signals create images at multiples of the distance of a dominant reflection.

Heterodyne Signal Source

2nd |f2 - f1|2nd f2 + f1

6.3 – 7.1 GHz

5.9 – 5.1 GHz

0.4 – 2.0 GHz12.2 – 12.2 GHz

2.2 GHz

Frequencies are selected to keep the third order product |2f1 - f2 | out of the range of interest.

System Implications

• IF response• Digitization resolution• I/Q Demodulator

Heterodyne Signal Sourceand associated spurious signals

2nd |f2 - f1|2nd f2 + f1

6.3 – 7.1 GHz

5.9 – 5.1 GHz

0.4 – 2.0 GHz12.2 – 12.2 GHz

2.2 GHz

RF 4th |2f2 - 2f1|

6th |3f2 - 3f1|

5th |2f2 - 3f1|

Frequencies are selected to keep the third order product |2f1 - f2 | out of the range of interest.

0.8 – 4.0 GHz1.1 – 5.1 GHz1.2 – 6.0 GHz

3rd |2f1 - f2| 3.1 – 5.5 GHz

Spur Tablem -1 2 2 -2 3 -3 3 2 1n 1 -1 -2 2 -3 3 -2 -3 -2

LO RF6.3 5.9 0.4 5.5 0.8 0.8 1.2 1.2 5.1 7.1 6.76.4 5.8 0.6 5.2 1.2 1.2 1.8 1.8 4.6 7.6 7.06.5 5.7 0.8 4.9 1.6 1.6 2.4 2.4 4.1 8.1 7.36.6 5.6 1.0 4.6 2.0 2.0 3.0 3.0 3.6 8.6 7.66.7 5.5 1.2 4.3 2.4 2.4 3.6 3.6 3.1 9.1 7.96.8 5.4 1.4 4.0 2.8 2.8 4.2 4.2 2.6 9.6 8.26.9 5.3 1.6 3.7 3.2 3.2 4.8 4.8 2.1 10.1 8.57.0 5.2 1.8 3.4 3.6 3.6 5.4 5.4 1.6 10.6 8.87.1 5.1 2.0 3.1 4.0 4.0 6.0 6.0 1.1 11.1 9.1

Classic Spur Chart

System Implications

NonlinearityThe differential nonlinearity is the variation in during the sweep.

d𝛼𝛼

=𝑑 𝑓 𝐼𝐹

𝑓 𝐼𝐹

Recall that the IF frequency ,

The bin width for is .Suppose we want variation due to variation to be less than where <.

𝛿𝛼𝛼≤

𝑘 ∙ Δ 𝑓 𝐼𝐹

𝑓 𝐼𝐹

= 𝑘𝑇 ∙ 𝑓 𝐼𝐹

= 𝑘𝑇 𝛼𝜏

= 𝑘𝐵𝑊 ∙𝜏

Nonlinearity Requirements

Distance, meters, r = 1, k = 0.1

Maximum Nonlinearity for several Bandwidths

1.5 GHz 3 GHz 6 GHz 12 GHz

System Implications

• Signal source– Heterodyne vs. YIG– Nonlinearity– Spurious signals– Phase noise

Phase Noise

• Phase noise will cause dominant signals to distribute energy over nearby frequency bins

• Effects of close-in phase noise are mitigated by the coherence between the transmitted and received signal.

• Cancellation is: [1] where is cancellation in dB, is offset frequency

[1] Beasley, The Influence of Transmitter Phase Noise on FMCW Radar Performance, Proceedings of the 3rd European Radar Conference, September 2006, Manchester, UK, pp 331-334

Phase Noise Cancellation

0 20 40 60 80 100-220

Distance, meters, r = 1

Phase Noise Cancellation for several foffsets

10 kHz 1 kHz0.1 kHz

Phase-Locked LoopSolution to nonlinearity and phase noise

2.2 GHz

Compensator

Shaping Ckt

Charge Pump

Divides loop gain by N.M

Pole @ f = 0

Zero below gain crossover

Compensate for N.M, Tuning nonlinearities

AD4158 PLL IC

AD4158 Registers

Assembly Challenge

Loop Design

• Sufficient loop gain to achieve good linearity.

• Gain crossover to optimize phase noise.

• Requires reasonably constant loop gain.

• Frequency dividers play significant role in the loop gain – must be compensated for in shaping circuit.

Typical VCO Phase Noise

Leeson's oscillator noise model

D. B. Leeson, “A Simple Model of Feedback Oscillator Noise Spectrum,” Proceedings of the IEEE, February 1966, pp. 329 – 330.

F = noise factor

80 MHz Crystal Oscillator Phase Noise

Source: Crystek

Phase Noise Contributions

1E+02 1E+03 1E+04 1E+05 1E+06 1E+07-160

Adjusted Crystal Reference

Frequency Offset, Hz

Simulator Results

10 100 1k 10k 100k 1MFrequency (Hz)

Phase Noise at 1.00GHz

TotalLoop FilterSDMChipRefVCO

Plot from Analog Devices ADIsimPLL

Loop Gain

10 100 1k 10k 100k 1MFrequency (Hz)

Open Loop Gain at 1.00GHzAmplitude Phase

Plot from Analog Devices ADIsimPLL

Tuning Sensistivity

0 2 4 6 8 10 120

f(x) = − 0.00277641075 x² + 0.18129640159 x + 0.40105311866

Measured Fout

Vshape

Shaping network

Shaping

Results

System Implications

IF Gain Shaping

• Radar Power Equation: Reflections from more distant objects are generally weaker than reflections from similar objects that are closer

• The IF frequency is proportional to distance, so a suitable frequency response can compensate for this

• Doing this compensation in the analog circuit provides considerable improvement in the A/D dynamic range.

IF Gain ResponseFrom the power equations showing that , and given that

a system designed to have the IF response to be relatively independent of distance R would have the frequency response:

𝐻 𝑖𝑓 (𝜔 )=𝑘𝜔2

RF System Block Diagram

The ApplicationWith ground penetrating radar (GPR), the dominant signal is the reflection from the bottom surface. But it requires near-contact with the top surface

Non-contact radar

Dominant signal is from top surface.

diτ εr εr

Top and Bottom ReflectionsWith Non-contact Radar

𝑆𝑟𝑡

𝑆𝑟𝑏

𝜏𝑏−𝜏𝑡=2𝑑𝑖√𝜀𝑟

𝑓 𝑖𝑓𝑏− 𝑓 𝑖𝑓𝑡=𝛼 (𝜏𝑏−𝜏 𝑡 )=2𝛼𝑑𝑖√𝜀𝑟

High attenuation in saline ice creates a huge difference in top surface and bottom surface reflected signal. Early data suggests that:

The difference in the travel time of the two reflections:

The difference in the fIF from the two reflections:

For a 40 cm saline ice sheet with εR = 4.5 and with α = 1.5 GHz/20 ms, the difference in fIF from the two reflections will be:

≈ 424 Hz

The simple problem: Isolate and detect a signal that is 424 Hz away from another signal in the 500 MHz – 2 GHz range with more than a million times as much power!

Making Ice in Hanover, NHTesting the prototype

The Gantry

The Radar on the Gantry

Example of Gantry Result

Data from 2500 segments in sequence

020812/OilCenterWE1 Up Magnitude

500 1000 1500 2000 2500

800-40

Gantry Magnitude Example

0 100 200 300 400 500 600 700 800 900-50

Distance, cm

dB020812/OilCenterWE1 Up Composite Magnitude

An Anti-aliasing Filter is Necessary!

IF Gain ResponseFrom the power equations showing that , and given that

a system designed to have the IF response to be relatively independent of distance R and to provide an n-pole anti-aliasing low-pass filter would have the frequency response:𝐻 𝑖𝑓 (𝜔 )=𝑘 𝜔2

(1+ 𝜔𝜔𝑝

Up/Down Testing

Up/Down Example

m020812/UDNoOilXb020812/UDOil Up Magnitude

1000 2000 3000 4000 5000 6000 7000

Zoom into the first up/down data

UDNoOilXb Up Magnitude

600 800 1000 1200 1400 1600

Developing an algorithm to track the surface reflection

UDNoOilXb Up Magnitude

600 800 1000 1200 1400 1600

Doing a mean of convolution to find reflections below the surface

0 20 40 60 80 100 120 140 160 1800

Distance offset, cm

UDNoOilXb Up Autocorrelation of Magnitude

And taking the derivative of the convolution

0 50 100 150 200 250 300 350 400 450 500-14

Distance offset, cm

UDNoOilXb Up Derivative of Convolution of Magnitude

Bottom?

Second Harmonic of Bottom?

System Implications

The A/D Converter used

•Consider the NI USB-6251 for 1.25 MS/s, 16-bit analog input; built-in connectivity; and more•Two 12-bit analog outputs, 8 digital I/O lines, two 24-bit counters•Use with the LabVIEW PDA Module for handheld data acquisition applications•NIST-traceable calibration and more than 70 signal conditioning options•Superior LabVIEW, LabWindows™/CVI, and Measurement Studio integration for VB and VS .NET•Included NI-DAQmx driver software and additional measurement services

• A/D SNR (Ideal) = (6.02N + 1.76) dB.

• This noise power is distributed equally to all M/2 FFT bins, referred to as the FFT process gain.

• For a system with T = 20ms, fs = 100 kHz, M/2 = 1000, or 30 dB.

• With a 12-bit A/D, ideal SNR will be 104 dB.

• This assumes full-scale signal over entire sweep.

Example of A/D-related SNR

From Analog Devices Tutorial MT-003

Typical Time Domain Signal

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5-2.5

Time Domain SIF Signal

Frequency of Sweep (GHz)

VRMS = 127 mV

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