Developing a Dual-Frequency Developing a Dual-Frequency FM-CW Radar to Study PrecipitationFM-CW Radar to Study Precipitation

Christopher R. WilliamsChristopher R. Williams Cooperative Institute for Research in Environmental Sciences (CIRES)Cooperative Institute for Research in Environmental Sciences (CIRES)

University of Colorado at Boulder, University of Colorado at Boulder,

and and

Physical Sciences Division (PSD)Physical Sciences Division (PSD)

NOAA Earth System Research Laboratory (NOAA ESRL), NOAA Earth System Research Laboratory (NOAA ESRL),

This work is supported: University of Colorado at Boulder

CIRES Innovative Research Program

With collaborations from Paul Johnston and David Carter

MotivationMotivation

Technically, pulse radars can not observe rain at close Technically, pulse radars can not observe rain at close ranges as they switch from transmit to receive modes.ranges as they switch from transmit to receive modes. Monostatic pulse radars have a “cone of silence”Monostatic pulse radars have a “cone of silence”

Proof of concept study to develop an inexpensive radar Proof of concept study to develop an inexpensive radar to observe precipitation between the surface and the first to observe precipitation between the surface and the first range gate of a pulse radar (~150mrange gate of a pulse radar (~150m).). Bistatic FM-CW radar technology is well suited Bistatic FM-CW radar technology is well suited

Scientifically, raindrops are not uniformly distributed. Scientifically, raindrops are not uniformly distributed. Raindrops cluster at small spatial and temporal scales Raindrops cluster at small spatial and temporal scales due to dynamics and turbulence.due to dynamics and turbulence. ““Cat paws” of raindrops falling on lakesCat paws” of raindrops falling on lakes

Mathematically, at what scales should we treat rain as a Mathematically, at what scales should we treat rain as a continuum of raindrops or as discrete objects?continuum of raindrops or as discrete objects? Need to sample to small scales to observe the discrete nature of Need to sample to small scales to observe the discrete nature of

individual objectsindividual objects

Technology & MethodologyTechnology & Methodology

Utilize technologies developed for the mobile Utilize technologies developed for the mobile phone, the police radar, and the video gaming phone, the police radar, and the video gaming industries. industries. One radar operated in the frequency band used for One radar operated in the frequency band used for

point-to-point Internet service (5.8 GHz). point-to-point Internet service (5.8 GHz). The other radar operated in the police radar The other radar operated in the police radar

frequency band (10.5 GHz). frequency band (10.5 GHz). A Sony Playstation 3 was used as the numerical A Sony Playstation 3 was used as the numerical

workhorse. Installed Linux as Other OS.workhorse. Installed Linux as Other OS.

The radar hardware for both radar systems cost The radar hardware for both radar systems cost less than $12k. (no labor costs were included)less than $12k. (no labor costs were included)

Presentation OutlinePresentation Outline

Hardware LayoutHardware Layout Radar Block DiagramRadar Block Diagram FMCW Signal ProcessingFMCW Signal Processing

Range EquationRange Equation Doppler ProcessingDoppler Processing

ObservationsObservations

Hardware LayoutHardware Layout

Antennas in my backyardAntennas in my backyard(an understanding wife)(an understanding wife)

C-band Antennas – 5.8 GHz

X-band Antennas – 10.4 GHz

Antennas are designed forpoint-to-point Internet service

Hardware LayoutHardware Layout

Costs forC-bandRadar~$US 6k

Simplified Tx and Rx SchematicSimplified Tx and Rx Schematic

Timing Diagram: Frequency Chirp and Data Collection TriggerTiming Diagram: Frequency Chirp and Data Collection Trigger

f0

f1

B = f1 - f0

Frequency Chirp

Data Collection Trigger

Tdelay

Tdwell Tend

Twait

TIPP

Tsweep

Sweep Trigger

Data is being collected

Timing EquationsTiming Equations TTsweepsweep -Duration the DDS is linearly sweeping from f -Duration the DDS is linearly sweeping from f00 to f to f11

TTwaitwait -Duration after sweep before next sweep -Duration after sweep before next sweep Allows system to stabilizeAllows system to stabilize

TTIPPIPP - “Inter-Pulse Period”, time between sweeps - “Inter-Pulse Period”, time between sweeps TTIPPIPP = T = Tsweepsweep + T + Twaitwait

TTippipp = 310 us + 10 us = 320 us = 310 us + 10 us = 320 us

TTdwelldwell -Duration the DAS is collecting data -Duration the DAS is collecting data TTdwelldwell = 256 us = 256 us

TTdelaydelay -Delay until first collected data point data -Delay until first collected data point data Want to wait for sweep signal to reach maximum rangeWant to wait for sweep signal to reach maximum range TTdelaydelay > 2R > 2Rmaxmax / c / c

Set RSet Rmaxmax = 1.5 km, T = 1.5 km, Tdelaydelay = 10 us = 10 us

Range EquationsRange EquationsFor a linear FM signal, a hard target located at range For a linear FM signal, a hard target located at range RR will generate a will generate a

delayed version of the transmitted signal delayed version of the transmitted signal tt = 2 = 2RR//cc seconds later. seconds later.

Target

Tx

Rx

R

Range EquationsRange EquationsFor a linear FM signal, a hard target located at range For a linear FM signal, a hard target located at range RR will generate a will generate a

delayed version of the transmitted signal delayed version of the transmitted signal tt = 2 = 2RR//cc seconds later. seconds later.

Target

Tx

Rx

R

f0

f1

B = f1 - f0

Tsweep

Tx

Range EquationsRange Equations

Target

Tx

Rx

R

f0

f1

B = f1 - f0

Tsweep

Tx Rx

c

Rt2=

For a linear FM signal, a hard target located at range For a linear FM signal, a hard target located at range RR will generate a will generate a delayed version of the transmitted signal delayed version of the transmitted signal tt = 2 = 2RR//cc seconds later. seconds later.

Range EquationsRange EquationsFor a linear FM signal, a hard target located at range For a linear FM signal, a hard target located at range RR will generate a will generate a

delayed version of the transmitted signal delayed version of the transmitted signal tt = 2 = 2RR//cc seconds later. seconds later.

Target

Tx

Rx

R

f0

f1

B = f1 - f0

Tsweep

Tx Rx

=

c

R

T

Bf

sweepIF

2

c

Rt2=

Range EquationsRange EquationsThe range equation is give by:The range equation is give by:

B = Sweep frequency bandwidthB = Sweep frequency bandwidth TTsweepsweep = Duration of sweep = Duration of sweep R = Distance to TargetR = Distance to Target C = speed of light in free airC = speed of light in free air

Frequency resolution determined by Digital Acquisition System (DAS)Frequency resolution determined by Digital Acquisition System (DAS) TTdwelldwell = time data is collected = time data is collected n = number of samplesn = number of samples ∆∆t = time between samplest = time between samples

Rearranging the range equation, the range resolution is given byRearranging the range equation, the range resolution is given by

=

c

R

T

Bf

sweepIF

2

tnTf

dwellIF ∆

==∆ 11

( )

∆

=∆

=∆

tnB

cTf

B

cTR sweep

IFsweep 1

22

Range EquationsRange EquationsThe range resolution:The range resolution:

B = 36.328 MHzB = 36.328 MHz TTsweepsweep = 310 us = 310 us n = 128n = 128 ∆∆t = 2 ust = 2 us

Frequency resolution determined by Digital Acquisition System (DAS)Frequency resolution determined by Digital Acquisition System (DAS)

nn R=(n-1)∆RR=(n-1)∆R ff IFIF=(n-1)∆f=(n-1)∆f IFIF 11 0 0 DC DC

22 5 m 5 m 3.9 kHz 3.9 kHz

33 10 m 10 m 7.8 kHz 7.8 kHz

1111 50 m 50 m 39 kHz 39 kHz

6464 315 m315 m 245.7 kHz245.7 kHz

( )

∆

=∆

=∆

tnB

cTf

B

cTR sweep

IFsweep 1

22

tnTf

dwellIF ∆

==∆ 11

∆R = 5 m

∆fIF = 3.9 kHz

Doppler ProcessingDoppler ProcessingTwo FFTs generate Doppler velocity spectra at each range Two FFTs generate Doppler velocity spectra at each range First FFT is the range-FFT and is applied to the 128 First FFT is the range-FFT and is applied to the 128

voltages collected during Tvoltages collected during Tdwelldwell

This range-FFT converts the This range-FFT converts the nn real valued voltages into complex real valued voltages into complex intermediate frequenciesintermediate frequencies

Range: –fRange: –fNyquistNyquist < f < fIFIF < +f < +fNyquistNyquist (f (fNyquistNyquist = (2∆t) = (2∆t)-1-1 = 250 kHz) = 250 kHz) Spacing: 3.9 kHz Spacing: 3.9 kHz Spectrum is symmetricSpectrum is symmetric Drop negative frequencies which are “Behind” the radarDrop negative frequencies which are “Behind” the radar Rename real and imaginary components “I” and “Q”Rename real and imaginary components “I” and “Q”

Second FFT is the Doppler-FFT and is applied to time Second FFT is the Doppler-FFT and is applied to time series of I’s & Q’s at each rangeseries of I’s & Q’s at each range Similar to pulse radar processingSimilar to pulse radar processing Time between sweep is same as Inter-pulse Period (TTime between sweep is same as Inter-pulse Period (Tippipp))

Sample ObservationsSample Observations

20 to 300 m height coverage20 to 300 m height coverage Need to put the antennas closer together Need to put the antennas closer together

5 m resolution 5 m resolution Doppler velocity spectra at each rangeDoppler velocity spectra at each range System is not calibrated (need to deploy with a System is not calibrated (need to deploy with a

disdrometer for absolute calibration)disdrometer for absolute calibration) 65,536 consecutive sweeps65,536 consecutive sweeps 21 second dwell period21 second dwell period

21 Second Dwell during Rain21 Second Dwell during Rain

Clutter

Downward Motion

5 m resolution300 m

0 m

21 Second Dwell during Rain21 Second Dwell during Rain

Clutter

Downward Motion300 m

0 m

21 & 10.5 Second Dwells21 & 10.5 Second Dwells

Time: 0-10.5 sec Time: 10.5-21 sec

Time: 0-21 sec

5 second Dwells5 second Dwells

Time: 0-5 sec

Time: 10-15 sec

Time: 5-10 sec

Time: 15-20 sec

21 Second Dwell, Mean 21 Second Dwell, Mean Reflectivity & Doppler VelocityReflectivity & Doppler Velocity

21 Second Dwell processed into 21 Second Dwell processed into 1 second intervals1 second intervals

21 Seconds

C- and X-band Observations During SnowC- and X-band Observations During Snow

C-Band Radar X-Band Radar

A snow event passed over my house on 13 November 2009 and was observed by both the C-band and X-band radars. The X-band transmitted power was limited due to a bad amplifier which reduced its altitude coverage.

Key Design ElementsKey Design Elements

There are 3 key design elementsThere are 3 key design elements

2.2. The Data Acquisition System (DAS) commands all time The Data Acquisition System (DAS) commands all time signals and collects all data so that the sample voltage signals and collects all data so that the sample voltage phases are coherent from sweep-to-sweepphases are coherent from sweep-to-sweep

3.3. The FM bandwidth and DAS sampling frequency control The FM bandwidth and DAS sampling frequency control the range resolution allowing the DAS sampling the range resolution allowing the DAS sampling frequency to be only 500 kHzfrequency to be only 500 kHz

4.4. Doppler velocity power spectra are generated at each Doppler velocity power spectra are generated at each range using 2 FFTS: one range-FFT applied to each FM range using 2 FFTS: one range-FFT applied to each FM sweep followed by a Doppler-FFT that detects the phase sweep followed by a Doppler-FFT that detects the phase changes over several FM sweepschanges over several FM sweeps

Concluding RemarksConcluding Remarks

Key Result: Key Result:

Proof of Concept was a SuccessProof of Concept was a Success Separate the two radars so that they have their own data Separate the two radars so that they have their own data

acquisition systemacquisition system Remove the Sony Playstation 3 (SP3) as the numerical Remove the Sony Playstation 3 (SP3) as the numerical

workhorseworkhorse Sony prohibits the installation of Linux on the SP3 (since 2010)Sony prohibits the installation of Linux on the SP3 (since 2010) GPU’s can be used if intense signal processing is neededGPU’s can be used if intense signal processing is needed Plan to use FPGA for range-FFTPlan to use FPGA for range-FFT

Need to calibrate system with a disdrometerNeed to calibrate system with a disdrometer Acquired funds to develop a 915 MHz wind profiler to Acquired funds to develop a 915 MHz wind profiler to

measure winds in the lowest 300 meters measure winds in the lowest 300 meters