fmcw radar concepts challenges implementation results a joint project thanks to bsu department of...
TRANSCRIPT
1
FMCW Radar
ConceptsChallenges
ImplementationResults
A joint projectThanks to BSU Department of
GeosciencesHans-Peter Marshall
2
FMCW Outline
• Some radar history and evolution
• FMCW concepts and benefits• Design Considerations• Testing and Results• Refinements – Current and
Future
3
Early History
Thanks, Wikipedia et al
1865
Scotland
James Clerk Maxwell -- Theory of the Electromagnetic Field
1886
Germany
Heinrich Hertz demonstrated RF reflections
1897
Italy Guglielmo Marconi demonstrated long distance transmission of electromagnet waves using a tent pole – l’antenna
1904
Germany
Christian Hülsmeyer – telemobiloscope for traffic monitoring on water in poor visibility. First radar test
1917
U.S. Nikola Tesla outlined radar concept
1921
U.S. Albert Wallace Hull invented the Magnetron – efficient transmitting tube
1936
U.S. Hetcalf & Hahn, GE, develop the Klystron
1939
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
4
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.
5
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.
6
Using a SAW Filter as a Chirp ASP
http://www.radartutorial.eu/17.bauteile/bt28.en.html
7
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
8
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
9
FMCW Outline
• Some radar history and evolution
• FMCW concepts and benefits• Design Considerations• Testing and Results• Refinements – Current and
Future
10
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
11
FMCW Sawtooth Wave Concept
Carr
ier
Fre
qu
en
cy
f C
Time
fIF
st sr
𝜏=2𝑑𝑣
δf
δt
𝛼≡𝛿 𝑓𝛿𝑡 𝑓 𝐼𝐹=𝛼𝜏
T 𝐵𝑊 =𝛼𝑇
∆ 𝑓 𝐼𝐹=1𝑇
=𝛼
𝐵𝑊∆ 𝑑=
𝑣 ∆ 𝑓 𝐼𝐹
2𝛼= 𝑣2∙𝐵𝑊FFT
Resolution:
SplitterSplitt
er
sI
F
stsr
dLPF
𝑣=𝑐
√𝜀𝑟
𝑑=𝑣𝜏2
=𝑣2𝛼
𝑓 𝐼𝐹
BW
12
FMCW Triangle Wave Concept
Time
fIF
st
sr
𝜏=2𝑑𝑣
fIF
δf
δt
𝛼≡𝛿 𝑓𝛿𝑡
𝑓 𝐼𝐹=𝛼𝜏
𝑑=𝑣𝜏2
=𝑣 𝑓 𝐼𝐹
2𝛼
T 𝐵𝑊 =𝛼𝑇
∆ 𝑓 𝐼𝐹=1𝑇
=𝛼
𝐵𝑊 ∆ 𝑑=𝑣 ∆ 𝑓 𝐼𝐹
2𝛼= 𝑣2∙𝐵𝑊
FFT Resolution:
Carr
ier
Fre
qu
en
cy
f C
13
FMCW Triangle with Doppler Shift
Time
τ
st
sr
fIFu fIFd
fd
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
Carr
ier
Fre
qu
en
cy
f C
δf
δt
𝛼≡𝛿 𝑓𝛿𝑡
𝜏=𝑓 𝐼𝐹𝑢+ 𝑓 𝐼𝐹 𝑑
2𝛼
𝑑=𝑣𝜏2
=𝑣 ( 𝑓 𝐼𝐹𝑢+ 𝑓 𝐼𝐹𝑑 )
4𝛼
14
The Radar Power Equation (1)
Consider the power density arriving at the target from the transmitter:
𝑄𝑖=𝑃 𝑡 𝐺𝑡
4 𝜋 𝑅2
where
is the transmitted power
is the transmitter antenna gain
is the distance from transmitter to target
𝑃 𝑡
𝐺𝑡
𝑅
15
The Radar Power Equation (2)
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
16
The Radar Power Equation (3)
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
17
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
18
FMCW Outline
• Some radar history and evolution
• FMCW concepts and benefits• Design Considerations• Testing and Results• Refinements – Current and
Future
19
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
20
System Constraints
• Minimum frequency for antennas is 500 MHz
• Maximum frequency for saline ice penetration is 2 GHz
• Therefore, maximum BW is 1.5GHz
21
System Implications
• Signal source– Heterodyne vs. YIG– Spurious signals– Nonlinearity– Phase noise
• IF frequency response• Digitization resolution• I/Q Demodulator
22
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.
23
Heterodyne Signal Source
st
VCO2
VCO1
f2
f1
vt2
vt1
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
LO
RF
Frequencies are selected to keep the third order product |2f1 - f2 | out of the range of interest.
24
System Implications
• Signal source– Heterodyne vs. YIG– Spurious signals– Nonlinearity– Phase noise
• IF response• Digitization resolution• I/Q Demodulator
25
Heterodyne Signal Sourceand associated spurious signals
st
VCO2
VCO1
f2
f1
vt2
vt1
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
LO
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
26
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
27
Classic Spur Chart
28
System Implications
• Signal source– Heterodyne vs. YIG– Spurious signals– Nonlinearity– Phase noise
• IF response• Digitization resolution• I/Q Demodulator
29
NonlinearityThe differential nonlinearity is the variation in during the sweep.
d𝛼𝛼
=𝑑 𝑓 𝐼𝐹
𝑓 𝐼𝐹
Recall that the IF frequency ,
then
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
then
30
Nonlinearity Requirements
100
101
102
10-3
10-2
10-1
100
101
Distance, meters, r = 1, k = 0.1
Max
/, p
erce
nt
Maximum Nonlinearity for several Bandwidths
1.5 GHz 3 GHz 6 GHz 12 GHz
31
System Implications
• Signal source– Heterodyne vs. YIG– Nonlinearity– Spurious signals– Phase noise
• IF response• Digitization resolution• I/Q Demodulator
32
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
33
Phase Noise Cancellation
0 20 40 60 80 100-220
-200
-180
-160
-140
-120
-100
-80
-60
-40
Distance, meters, r = 1
Can
cella
tion,
dB
Phase Noise Cancellation for several foffsets
10 kHz 1 kHz0.1 kHz
34
Phase-Locked LoopSolution to nonlinearity and phase noise
VCO2
fLO
fRF
vt2
vt1
st
2.2 GHz
Compensator
Shaping Ckt
PFD
fREF
N.M
Charge Pump
Divides loop gain by N.M
Pole @ f = 0
Pole @ f = 0
Zero below gain crossover
Compensate for N.M, Tuning nonlinearities
35
AD4158 PLL IC
36
AD4158 Registers
37
Assembly Challenge
38
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.
39
Typical VCO Phase Noise
40
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
41
80 MHz Crystal Oscillator Phase Noise
Source: Crystek
42
Phase Noise Contributions
1E+02 1E+03 1E+04 1E+05 1E+06 1E+07-160
-140
-120
-100
-80
-60
-40
-20
0
VCO
Adjusted Crystal Reference
Frequency Offset, Hz
Ph
ase
Nois
e d
Bc
43
Simulator Results
10 100 1k 10k 100k 1MFrequency (Hz)
-160
-150
-140
-130
-120
-110
-100
-90
-80
-70
-60
Ph
ase
No
ise
(dB
c/H
z)
Phase Noise at 1.00GHz
TotalLoop FilterSDMChipRefVCO
Plot from Analog Devices ADIsimPLL
44
Loop Gain
10 100 1k 10k 100k 1MFrequency (Hz)
-20
0
20
40
60
80
100
120
140
160
180G
ain
(d
B)
-180
-160
-140
-120
-100
-80
-60
-40
-20
0
Ph
as
e (
de
g)
Open Loop Gain at 1.00GHzAmplitude Phase
Plot from Analog Devices ADIsimPLL
45
Tuning Sensistivity
0 2 4 6 8 10 120
0.5
1
1.5
2
2.5
f(x) = − 0.00277641075 x² + 0.18129640159 x + 0.40105311866
Measured Fout
Vshape
Fre
qu
en
cy,
GH
z
46
Shaping network
47
Shaping
Results
48
System Implications
• Signal source– Heterodyne vs. YIG– Spurious signals– Nonlinearity– Phase noise
• IF response• Digitization resolution• I/Q Demodulator
49
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.
50
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
51
RF System Block Diagram
52
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
τb
τt
53
Top and Bottom ReflectionsWith Non-contact Radar
𝑆𝑟𝑡
𝑆𝑟𝑏
>60dB
𝜏𝑏−𝜏𝑡=2𝑑𝑖√𝜀𝑟
𝑐
𝑓 𝑖𝑓𝑏− 𝑓 𝑖𝑓𝑡=𝛼 (𝜏𝑏−𝜏 𝑡 )=2𝛼𝑑𝑖√𝜀𝑟
𝑐
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!
54
Making Ice in Hanover, NHTesting the prototype
55
The Gantry
Test
56
The Gantry
57
The Radar on the Gantry
58
Example of Gantry Result
Data from 2500 segments in sequence
Dis
tanc
e, c
m
020812/OilCenterWE1 Up Magnitude
500 1000 1500 2000 2500
0
100
200
300
400
500
600
700
800-40
-30
-20
-10
0
10
20
59
Gantry Magnitude Example
0 100 200 300 400 500 600 700 800 900-50
-40
-30
-20
-10
0
10
20
30
Distance, cm
Mag
nitu
de,
dB020812/OilCenterWE1 Up Composite Magnitude
60
An Anti-aliasing Filter is Necessary!
61
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
)𝑛
62
Up/Down Testing
63
Up/Down Example
Data from 7250 segments in sequence
Dis
tanc
e, c
m020812/UDNoOilXb020812/UDOil Up Magnitude
1000 2000 3000 4000 5000 6000 7000
0
100
200
300
400
500
600
700
800
-50
-40
-30
-20
-10
0
10
20
64
Zoom into the first up/down data
Data from 1183 segments in sequence
Dis
tanc
e, c
m
UDNoOilXb Up Magnitude
600 800 1000 1200 1400 1600
0
100
200
300
400
15
20
25
30
65
Developing an algorithm to track the surface reflection
Data from 1183 segments in sequence
Dis
tanc
e, c
m
UDNoOilXb Up Magnitude
600 800 1000 1200 1400 1600
0
100
200
300
400
15
20
25
30
66
Doing a mean of convolution to find reflections below the surface
0 20 40 60 80 100 120 140 160 1800
5
10
15
20
25
30
35
Distance offset, cm
UDNoOilXb Up Autocorrelation of Magnitude
67
And taking the derivative of the convolution
0 50 100 150 200 250 300 350 400 450 500-14
-12
-10
-8
-6
-4
-2
0
2
Distance offset, cm
UDNoOilXb Up Derivative of Convolution of Magnitude
Bottom?
Second Harmonic of Bottom?
68
System Implications
• Signal source– Heterodyne vs. YIG– Spurious signals– Nonlinearity– Phase noise
• IF response• Digitization resolution• I/Q Demodulator
69
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
70
SNR
• 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.
71
Example of A/D-related SNR
From Analog Devices Tutorial MT-003
72
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
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
Time Domain SIF Signal
Vo
lts
Frequency of Sweep (GHz)
VRMS = 127 mV
= 8.2
73
More on SNR
• The number of usable bits is around 8.2 bits. This would lead to a SNR = 80 dB.
74
Fresh water ice results
75
Profile with shaping and LPF
0 10 20 30 40-180
-160
-140
-120
-100
-80
-60
-40
Mag
nit
ud
e, d
BFresh water ice profile Dec 19, 2012
Frequency, kHz
76
Some Results