Applications of FPGAs in Radio Astronomy

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Applications of FPGAsin Radio Astronomy

• John Dickey
• University of Tasmania
• 8 Dec 2005

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ALTIUM, Ltd. corporate donation FPGA
application development software, nanoboard
platform, design tools, and training, retail
purchase price of everything 150,000. Partial
funding by an ARC Discovery grant, gifts from
Xilinx.
UTas Staff JD, Aidan Hotan (postdoc) Simon
Ellingsen (senior lecturer) Peter McCulloch
(prof. emeritus) Eric Baynes (sr. electronics
tech) Jamie Stevens (postdoc) three grad students
(associated) David Warren (Altium and
UTas) Brett Muir (design engineer) John Russell
(digital engineer)
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FPGA applications in Radio Astronomy

• Pulsar and transient searches (dedispersion)
• Autocorrelators (and FT spectrometers)
• Cross-correlators (interferometry, VLBI)
• Data editing, calibration, mapping
• Real-time adjustment of receivers, delays
• Multi-beaming, focal plane array processing
• Studying the E-field at the Nyquist rate

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UTas - Altium Board

• design finished (Brett Muir, John Russell)
• chips purchased, board fabrication in 1 month
• Xilinx virtex 4 - SX55 workhorse FPGA
• Xilinx spartan 3 (for jtag chain) and
• virtex 2-pro (for control)
• memory, ethernet, config devices
• high speed scsi-2 input plus up/down links

The goal a general purpose board to replace all
observatory backends!
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• Xilinx Virtex-4 SX55

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Correlator Implementation
August 2005 -- Aidan Hotan

• Using Altium Virtex 4 SX35 daughterboard with
  nanoboard

Device performs autocorrelation and cross
correlation of RF input signals plus noise at
speeds up to 80 M s/s. FPGA substrate provides
latch in, shift register, multiply and
accumulate, readout, and VGA graphics
display. Embedded (simulated) processors provide
program control.
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• Correlator Architecture

digitised signal in
multiply and accumulate
autocorrelation function
present data
Fourier Transform using synthesized TSK3000 proces
sor on-board FPGA
shift with adjustable time step
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February? 2006
Example of SX55 application Fourier Transform
Dedispersion
digitised signal in
FFT, bit-reverse, magnitude
Dynamic Spectra
Floating- point Processors
latch
shift at adjustable time step
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time
Dedispersion from Dynamic Spectra

• Sum along dispersion lines
• fast algorithm
• addition (can use gates only)

frequency
timeseries
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The Observing Frequency and the DM Determine the
Storage and Computation Load
t
n
Dn N dn
dt
dn
Nyquist Cells dn dt 1/2
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The Observing Frequency and the DM Determine the
Storage and Computation Load
t
example observing at 1.4 GHz
Dt
n
Dn N dn
for DM100, Dn 100 MHz Dt 30ms 6000 dt where
dt
dn
for N1000 frequency channels, dt 5 ms
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Xilinx Virtex 4 SX55

• This FPGA chip is effectively a
• 512 processor supercomputer,with
• a substrate of 55,296 logic cells

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Speed is No Problem
For a 64 channel spectrum, the SX55 could use a
DSP for every block. Thus it can compute a new
spectrum every 4 clock cycles 10 ns, for a
sample rate of 0.16 ns, bandwidth of 3.2 GHz.
For a 512 channel spectrum, the SX55 could use a
DSP for every row. Thus it can compute a new
spectrum every 36 clock cycles 90 ns, for a
sample rate of 0.18 ns, bandwidth of 2.8 GHz.
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so the DSPs can do several jobs.
time series
thresholding, RFI suppression
For a 100 MHz bandwidth, the FPGA could take the
Fourier transform 30 times in the N dt time it
takes to collect the data.
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Want Correlators?
The EVLA correlator will handle 40 antennas (780
baselines) with 8 bands of 2 GHz each. This
would require about 400 FPGAs similar to the
SX55, cost 500K (vs. 12M budget). The LN-SD
SKA (4000 antennas ?), say 107 baselines, BW
1GHz(?) could be done with a few 104 Virtex
4s. Todays cost, a few 107 . In 2015, by
Moores Law, 105 . (This is without any
grouping of the antennas into stations, and
assuming direct FT rather than cross
correlation.)
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Conclusions

• FPGA technology offers the advantages of the
  software correlator, i.e. upgrade to new
  platforms without reworking the design.
• Altium design tools make programming the FPGA as
  easy as (as programming a computer?).
• We can finally do our signal processing at the
  Nyquist rate, in real time!!
• FPGA design supplants the von Neumann paradigm-
• the sequential processor, stored program model is
  obsolete