FPGA-based Dedispersion for Fast Transient Search John Dickey 23 Nov 2005 Orange, NSW

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. 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 board to replace all observatory backends!

Xilinx Virtex-4 SX times: 55,296 times:

Correlator Implementation 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. August Aidan Hotan:

digitised signal in shift with adjustable time step present data x x x x x x x x x x x x             multiply and accumulate Correlator Architecture Fourier Transform using synthesized TSK3000 processor on-board FPGA autocorrelation function

Example of SX55 application: Fourier Transform Dedispersion February? 2006: digitised signal in shift at adjustable time step latch FFT, bit-reverse, magnitudeDynamic Spectra Floating- point Processors

frequency time Dedispersion from Dynamic Spectra time series 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t Nyquist Cells:   t = 1/2

The Observing Frequency and the DM Determine the Storage and Computation Load t for DM=100,  = 100 MHz  t = 30ms = 6000  t where  N   tt 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 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.

… so the DSP’s 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  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 400 FPGA’s similar to the SX55, cost ~$500K (vs. $12M budget). The LN-SD SKA (~4000 antennas ?), say 10 7 baselines, BW ~ 1GHz(?) could be done with a few 10 4 Virtex 4’s. Today’s cost, a few 10 7 $. In 2015, by Moore’s Law, ~10 5 $. (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!!