FPGA-based Dedispersionfor Fast Transient Search

John Dickey

23 Nov 2005

Orange, NSW

ALTIUM, Ltd. corporate donation: FPGA applicationdevelopment software, nanoboard platform, design tools, and training, retail purchase price of everything ~$150,000.Partial funding by an ARC Discovery grant.

UTas Staff: JD,Simon Ellingsen (senior lecturer)Eric Baynes (sr. electronics tech)Aidan Hotan (postdoc)Jamie Stevens (postdoc)three grad students (associated)

David Warren (Altium and UTas)Brett Muir (design engineer)John Russell (digital engineer)

FPGA applications in Radio Astronomy

• Pulsar and transient searches (dedispersion)• Autocorrelators (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

UTas - Altium Board

• design nearly finished (Brett Muir, John Russell)

chips purchased, board fabrication in ~1.5 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 boardto replace all observatory backends!

Xilinx Virtex-4 SX55

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

512 times:

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

55,296 times:

Correlator Implementation

Using Altium Virtex 4 SX35 daughterboard with nanoboard

Device performs autocorrelation and cross correlationof 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.

August 2005 -- Aidan Hotan:

digitised signal in

shift withadjustabletime step

present data

x

x

x

x

x

x

x

x

x

x

x

x

multiply andaccumulate

Correlator Architecture

FourierTransformusingsynthesizedTSK3000processoron-boardFPGA

autocorrelationfunction

Example of SX55 application:

Fourier Transform Dedispersion

February? 2006:

digitised signal in

shift atadjustabletime step

latch

FFT, bit-reverse, magnitude Dynamic Spectra

Floating-pointProcessors

frequency

time

Dedispersion from Dynamic Spectra

timeseries

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

The Observing Frequency and the DM Determine the Storage and Computation

Load

t

N

t

Nyquist Cells: t = 1/2

The Observing Frequency and the DM Determine the Storage and Computation

Load

t

for DM=100, = 100 MHzt = 30ms = 6000 t where

N

t

t

for N=1000 frequency channels, t = 5 s

example: observing at 1.4 GHz

Xilinx Virtex 4 SX55

This FPGA chip is effectively a

512 processor supercomputer,with

a substrate of 55,296 logic cells

Speed is No Problem…For a 64 channel spectrum,the SX55 could use a DSPfor every block. Thus it cancompute 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 DSPfor every row. Thus it cancompute a new spectrum every 36 clock cycles = 90 ns,for a sample rate of 0.18 ns,bandwidth of 2.8 GHz.

… so the DSP’s can do several jobs.

timeseries

thresholding, RFI suppression…

For a 100 MHz bandwidth, the FPGA could take the Fouriertransform 30 times in the N t time it takes to collect the data.

Want Correlators?

The EVLA correlator will handle 40 antennas (780 baselines)with 8 bands of 2 GHz each. This would require about 400FPGA’s 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 4’s.Today’s cost, a few 107 $. In 2015, by Moore’s Law, ~105 $.(This is without any grouping of the antennas into “stations”,and assuming direct FT rather than cross correlation.)

Conclusions

• FPGA technology offers the advantages of the “software correlator”, i.e. to 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!!