1. Developing a Dual-Frequency FM-CW Radar to Study Precipitation
Christopher R. Williams
Cooperative Institute for Research in Environmental Sciences (CIRES)
University of Colorado at Boulder,
and
Physical Sciences Division (PSD)
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

2. Motivation
Technically, pulse radars can not observe rain at close ranges as they switch from transmit to receive modes.
Monostatic pulse radars have a “cone of silence”
Proof of concept study to develop an inexpensive radar to observe precipitation between the surface and the first range gate of a pulse radar (~150m).
Bistatic FM-CW radar technology is well suited
Scientifically, raindrops are not uniformly distributed. Raindrops cluster at small spatial and temporal scales due to dynamics and turbulence.
“Cat paws” of raindrops falling on lakes
Mathematically, at what scales should we treat rain as a continuum of raindrops or as discrete objects?
Need to sample to small scales to observe the discrete nature of individual objects

3. Technology & Methodology
Utilize technologies developed for the mobile phone, the police radar, and the video gaming industries.
One radar operated in the frequency band used for point-to-point Internet service (5.8 GHz).
The other radar operated in the police radar frequency band (10.5 GHz).
A Sony Playstation 3 was used as the numerical workhorse. Installed Linux as Other OS.
The radar hardware for both radar systems cost less than $12k. (no labor costs were included)

4. Presentation Outline Hardware Layout Radar Block Diagram
FMCW Signal Processing
Range Equation
Doppler Processing
Observations

5. Hardware Layout

6. Antennas in my backyard (an understanding wife)
C-band Antennas – 5.8 GHz
X-band Antennas – 10.4 GHz
Antennas are designed for
point-to-point Internet service

7. Hardware Layout
Costs for
C-band
Radar
~$US 6k

8. Simplified Tx and Rx Schematic

9. Timing Diagram: Frequency Chirp and Data Collection Trigger
Sweep Trigger
TIPP
Tsweep
Twait
Tdelay
Tdwell
Tend
Frequency Chirp f1
B = f1 - f0 f0
Data Collection Trigger
Data is being collected

10. Timing Equations
Tsweep -Duration the DDS is linearly sweeping from f0 to f1
Twait -Duration after sweep before next sweep
Allows system to stabilize
TIPP “Inter-Pulse Period”, time between sweeps
TIPP = Tsweep + Twait
Tipp = 310 us + 10 us = 320 us
Tdwell -Duration the DAS is collecting data
Tdwell = 256 us
Tdelay -Delay until first collected data point data
Want to wait for sweep signal to reach maximum range
Tdelay > 2Rmax / c
Set Rmax = 1.5 km, Tdelay = 10 us

11. Range Equations
For a linear FM signal, a hard target located at range R will generate a delayed version of the transmitted signal t = 2R/c seconds later. Tx
Target Rx R

12. Range Equations
For a linear FM signal, a hard target located at range R will generate a delayed version of the transmitted signal t = 2R/c seconds later. Tx
Target Rx R
Tsweep f1
B = f1 - f0 Tx f0

13. Range Equations
For a linear FM signal, a hard target located at range R will generate a delayed version of the transmitted signal t = 2R/c seconds later. Tx
Target Rx R
Tsweep f1 Rx
B = f1 - f0 Tx f0

14. Range Equations
For a linear FM signal, a hard target located at range R will generate a delayed version of the transmitted signal t = 2R/c seconds later. Tx
Target Rx R
Tsweep f1 Rx
B = f1 - f0 Tx f0

15. Range Equations The range equation is give by:
B = Sweep frequency bandwidth
Tsweep = Duration of sweep
R = Distance to Target
C = speed of light in free air
Frequency resolution determined by Digital Acquisition System (DAS)
Tdwell = time data is collected
n = number of samples
∆t = time between samples
Rearranging the range equation, the range resolution is given by

16. Range Equations The range resolution:
B = MHz
Tsweep = 310 us
n = 128
∆t = 2 us
Frequency resolution determined by Digital Acquisition System (DAS)
n R=(n-1)∆R fIF=(n-1)∆fIF DC
m kHz
m kHz
m kHz
m kHz
∆R = 5 m
∆fIF = 3.9 kHz

17. Doppler Processing
Two FFTs generate Doppler velocity spectra at each range
First FFT is the range-FFT and is applied to the 128 voltages collected during Tdwell
This range-FFT converts the n real valued voltages into complex intermediate frequencies
Range: –fNyquist < fIF < +fNyquist (fNyquist = (2∆t)-1 = 250 kHz)
Spacing: 3.9 kHz
Spectrum is symmetric
Drop negative frequencies which are “Behind” the radar
Rename real and imaginary components “I” and “Q”
Second FFT is the Doppler-FFT and is applied to time series of I’s & Q’s at each range
Similar to pulse radar processing
Time between sweep is same as Inter-pulse Period (Tipp)

18. Sample Observations 20 to 300 m height coverage 5 m resolution
Need to put the antennas closer together
5 m resolution
Doppler velocity spectra at each range
System is not calibrated (need to deploy with a disdrometer for absolute calibration)
65,536 consecutive sweeps
21 second dwell period

19. 21 Second Dwell during Rain
300 m
5 m resolution
Downward Motion
Clutter
0 m

20. 21 Second Dwell during Rain
300 m
Downward Motion
Clutter
0 m

21. 21 & 10.5 Second Dwells Time: 0-21 sec Time: 0-10.5 sec

22. 5 second Dwells Time: 0-5 sec Time: 5-10 sec Time: 10-15 sec

23. 21 Second Dwell, Mean Reflectivity & Doppler Velocity

24. 21 Second Dwell processed into 1 second intervals
21 Seconds

25. C- and X-band Observations During Snow
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.
C-Band Radar
X-Band Radar

26. Key Design Elements There are 3 key design elements
The Data Acquisition System (DAS) commands all time signals and collects all data so that the sample voltage phases are coherent from sweep-to-sweep
The FM bandwidth and DAS sampling frequency control the range resolution allowing the DAS sampling frequency to be only 500 kHz
Doppler velocity power spectra are generated at each range using 2 FFTS: one range-FFT applied to each FM sweep followed by a Doppler-FFT that detects the phase changes over several FM sweeps

27. Concluding Remarks Proof of Concept was a Success Key Result:
Separate the two radars so that they have their own data acquisition system
Remove the Sony Playstation 3 (SP3) as the numerical workhorse
Sony prohibits the installation of Linux on the SP3 (since 2010)
GPU’s can be used if intense signal processing is needed
Plan to use FPGA for range-FFT
Need to calibrate system with a disdrometer
Acquired funds to develop a 915 MHz wind profiler to measure winds in the lowest 300 meters