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

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

Motivation Ø Technically, pulse radars can not observe rain at close ranges as they switch from transmit to receive modes. l Ø Proof of concept study to develop an inexpensive radar to observe precipitation between the surface and the first range gate of a pulse radar (~150 m). l Ø 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. l Ø Monostatic pulse radars have a “cone of silence” “Cat paws” of raindrops falling on lakes Mathematically, at what scales should we treat rain as a continuum of raindrops or as discrete objects? l Need to sample to small scales to observe the discrete nature of individual objects

Technology & Methodology Ø Utilize technologies developed for the mobile phone, the police radar, and the video gaming industries. l l l Ø 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 $12 k. (no labor costs were included)

Presentation Outline Hardware Layout Ø Radar Block Diagram Ø FMCW Signal Processing Ø l l Ø Range Equation Doppler Processing Observations

Hardware Layout

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

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

Simplified Tx and Rx Schematic

Timing Diagram: Frequency Chirp and Data Collection Trigger Sweep Trigger TIPP Tsweep Twait Tdelay Tdwell Frequency Chirp f 1 B = f 1 - f 0 Data Collection Trigger Data is being collected Tend

Timing Equations Tsweep -Duration the DDS is linearly sweeping from f 0 to f 1 Ø Twait -Duration after sweep before next sweep Ø l Ø TIPP l l Ø - “Inter-Pulse Period”, time between sweeps TIPP = Tsweep + Twait Tipp = 310 us + 10 us = 320 us Tdwell -Duration the DAS is collecting data l Ø Allows system to stabilize Tdwell = 256 us Tdelay -Delay until first collected data point data l l l Want to wait for sweep signal to reach maximum range Tdelay > 2 Rmax / c Set Rmax = 1. 5 km, Tdelay = 10 us

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

Range Equations For a linear FM signal, a hard target located at range R will generate a delayed version of the transmitted signal t = 2 R/c seconds later. Tx Target Rx R Tsweep f 1 B = f 1 - f 0 Tx

Range Equations For a linear FM signal, a hard target located at range R will generate a delayed version of the transmitted signal t = 2 R/c seconds later. Tx Target Rx R Tsweep f 1 B = f 1 - f 0 Tx Rx

Range Equations For a linear FM signal, a hard target located at range R will generate a delayed version of the transmitted signal t = 2 R/c seconds later. Tx Target Rx R Tsweep f 1 B = f 1 - f 0 Tx Rx

Range Equations The range equation is give by: l l 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) l l l Tdwell = time data is collected n = number of samples ∆t = time between samples Rearranging the range equation, the range resolution is given by

Range Equations The range resolution: l l B = 36. 328 MHz Tsweep = 310 us n = 128 ∆t = 2 us ∆R = 5 m Frequency resolution determined by Digital Acquisition System (DAS) ∆f. IF = 3. 9 k. Hz n 1 2 3 11 64 R=(n-1)∆R 0 5 m 10 m 50 m 315 m f. IF=(n-1)∆f. IF DC 3. 9 k. Hz 7. 8 k. Hz 39 k. Hz 245. 7 k. Hz

Doppler Processing Two FFTs generate Doppler velocity spectra at each range Ø First FFT is the range-FFT and is applied to the 128 voltages collected during Tdwell l l l Ø This range-FFT converts the n real valued voltages into complex intermediate frequencies Range: –f. Nyquist < f. IF < +f. Nyquist (f. Nyquist = (2∆t)-1 = 250 k. Hz) Spacing: 3. 9 k. Hz 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 l l Similar to pulse radar processing Time between sweep is same as Inter-pulse Period (Tipp)

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

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

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

21 & 10. 5 Second Dwells Time: 0 -21 sec Time: 0 -10. 5 sec Time: 10. 5 -21 sec

5 second Dwells Time: 0 -5 sec Time: 5 -10 sec Time: 10 -15 sec Time: 15 -20 sec

21 Second Dwell, Mean Reflectivity & Doppler Velocity

21 Second Dwell processed into 1 second intervals 21 Seconds

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 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

Key Design Elements There are 3 key design elements 1. 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 2. The FM bandwidth and DAS sampling frequency control the range resolution allowing the DAS sampling frequency to be only 500 k. Hz 3. 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

Concluding Remarks Ø Key Result: Proof of Concept was a Success Separate the two radars so that they have their own data acquisition system Ø Remove the Sony Playstation 3 (SP 3) as the numerical workhorse Ø l l l Sony prohibits the installation of Linux on the SP 3 (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 Ø Acquired funds to develop a 915 MHz wind profiler to measure winds in the lowest 300 meters Ø