Signal processing with heterogeneous digital filterbanks: lessons from the MWA and EDA

Transcription

1 Signal processing with heterogeneous digital filterbanks: lessons from the MWA and EDA Randall Wayth ICRAR/Curtin University with Marcin Sokolowski, Cathryn Trott

2 Outline "Holy grail of CASPER system is multi-user system Jack H on Monday Goal: Ingest digital data from EDA into MWA correlator to measure the SEFD of EDA 22

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4 MRO (operated by CSIRO) On site: data rate into central building ~60 Gbps 41,000 sq. km = The Netherlands Geraldt on Off site: data rate into science archive ~3 Gbps Perth Pawsey Centre 20 PB storage ~200 km 4

5 Antenna tiles: 4x4 array of dual pol dipoles Beamformer

6 Receivers: Each receiver services 8 tiles Sky signal is digitised and sent to central processing facility

7 Central Signal Processing: 128 dual pol tiles MHz bandwidth, 10 khz spectral resolution 8128 baselines Visibilities integrated to ~1s time resolution

8 MWA digital signal path 10 khz fine channels 12(?) tap PFB 24 x 1.28 MHz coarse channels. 8-tap PFB Tremblay et al, 2015 Software correlator 10G ethernet 88

9 Engineering Development Array (EDA) Signatec PX-1500 GTX 750 9

10 MWA correlator inputs MWA: Sample rate Msamp/sec 8-tap critically sampled PFB for coarse channels (1.28 MHz) 12-tap critically sampled PFB for fine channels (10 khz) EDA: Sample rate Msamp/sec Uses MWA clock Do sample FFT to directly transform to 10 khz channels (easy on GPU) Result: Brute-force fringe search using Sun as source Clear lag, but at equal magnitude for 5 and 6 samples SNR of cross-correlation at either lag is lower than expected, but roughly equal WTF? 10 10

11 Analysis Consider weighted-overlap-add model of a PFB Each chunk of signal appears in the window n_taps times For even-sized PFB, signal appears twice with equal power (but mirror reflected weights) with largest weights For FFT-based spectrometer, signal from any block of input samples only appears in output once. From Crochiere & Rabiner, 1983 Multirate digital signal processing 11

12 Analysis Coarse chan data FFT only The correlator works on the fine channels out of the DFT Fine channels will correlate iff the same (broadband) signal went into the filterbank at time t. Obvious from inspection that signal contributing to time t in PFB also contributes to time t+1. If we lag correlate fine channel time series from FFT and PFB we would expect equal amplitude for times t and t+1. BUT, for a given lag, more than 50% of DFT output will not correlate. -> Low SNR Fine chan data 12 12

13 Analysis + DFT DFT 13 13

14 Analysis + DFT DFT 14 14

15 Analysis + DFT DFT 15 15

16 Analysis + DFT DFT 16 16

17 Analysis + DFT DFT 17 17

18 Analysis + DFT DFT 18 18

19 Simulation summary Noise data streams d1 Fine chan data streams FFT direct to fine chans 0% common signal power d2 PFB to coarse chans. Select 1 EDA Even PFB to fine chans MWA Odd PFB to fine chans FFT to fine chans 19 19

20 Simulation even sized PFB Generate noise time series Channelise to coarse channels using PFB Fine channelise using Even-sized PFB and FFT Find lag in fine channel time series Equal lag magnitude and t=0 and t=1 20

21 Simulation odd sized PFB Generate noise time series Channelise to coarse channels using PFB Fine channelise using Odd-sized PFB and FFT Find lag in fine channel time series Significant lag only at t=0 Inspecting time series of fine channels, the effect is obvious. 21

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23 By eye comparison of odd vs even vs fft 23

24 Simulation - SNR Simulate MWA/EDA system: PFB for coarse chans, then fine channelisation FFT x FFT (ideal case) FFT x ( options) Stddev in phase = proxy for SNR Results: method of coarse channelisation not important Odd-sized PFB better SNR than even sized PFB when correlated with FFT fine channels 24

25 Proof of the pudding EDA into MWA EDA sensitivity (via SEFD) as measured by noise in calibrated visibilities All data correlated in MWA correlator Calibration via normal MWA calibration on strong compact source Using 4-tap PFB in EDA improves SNR by 2x vs straight FFT 25 25

26 Summary heterogeneous filterbanks Odd and even-sized filterbanks do not play nice when correlated There is no fundamental reason why an even or power-of-two number of taps is required in a PFB Odd-sized number of taps gives closer representation to intuitive FFT result SNR of correlated data is affected by match (or mismatch) in PFB window used 26

27 International Centre for Radio Astronomy Research Perth, Western Australia Partners in MWA ICRAR CAASTRO ASTRO-3D SKA-Low