1. Nithyanandan Thyagarajan (or just “Nithya”) Arizona State University
Design Guidelines for EoR science with SKA-low and Efficient Scalability of Next-generation Low-frequency Radio Telescopes
Nithyanandan Thyagarajan (or just “Nithya”)
Arizona State University
MWA+, HERA+

2. MWA Collaboration

3. HERA Collaboration

4. Why study the Epoch of Reionization?
Formation of large scale structures and evolution of astrophysical objects need to be probed
Neutral Hydrogen is a direct probe of the Reionization epoch
Current instruments have enough sensitivity for statistical detection of HI from the EoR

5. Motivation for High Precision Modeling
Thyagarajan et al. (2013)
Beardsley et al. (2013)
>10-sigma statistical detection expected with ~1000 hours data
Currently heavily limited by foregrounds and instrument systematics (e.g. PAPER64 - Ali et al. 2015, Pober et al. 2015; MWA – Dillon et al. 2013)

6. The Foreground Problem
Bright Foregrounds
(but smooth)
HI signal extremely faint
(but not smooth)
Parsons et al. (2012)

7. Fourier Space and Delay Spectrum
Parsons et al. (2012)

8. Foreground “Wedge” and EoR window

9. Precision Radio Interferometry Simulations (PRISim)
Objectives with PRISim:
Comprehensive all-sky simulations (with good match to data)
Role of Wide-field measurements
Role of compact, diffuse foregrounds
Role of instrument such as antenna aperture and its chromaticity
Solutions to mitigate systematics

10. Model-Data Agree well

11. Impact of diffuse, compact emission – “Pitchfork” effect
Diffuse Emission
Point sources

12. Mitigation of systematics via Antenna Geometry
(e.g. PAPER)
(e.g. MWA)
(e.g. HERA)
Foreground spillover from
Pitchfork drops significantly
Thyagarajan et al. (2015a)

13. HERA Example HERA (Hydrogen Epoch of Reionization Array) B = 100MHz
1024 channels
~100 kHz channels
14m dishes
FoV ~ 10 deg. at 150 MHz
Compact hexagonal array

14. HERA HI/FG Sensitivity vs. Beam Chromaticity
Thyagarajan et al. (2016),
Accepted in ApJ
Uniform Disk Airy Pattern
Simulated Chromatic HERA beam
Differences seen only due to spectral differences in Antenna beam
Beam chromaticity worsens foreground contamination
HERA is sensitive to EoR nevertheless

15. Design Specs on Reflections in Instrument
Reflections are inevitable in electrical systems
Reflections extend foregrounds and contamination in delay spectrum
Require reflected foregrounds to be below HI signal levels
HERA will aim for these specs
Similar study is essential for SKA for guaranteeing success
Thyagarajan et al. (2016),
Accepted in ApJ

16. EoR Observing Window Efficiency
150 MHz subband (z=8.47)
170 MHz subband (z=7.36)
All HERA baselines sensitive to EoR for most of observing window
Robust to different models and redshifts
HERA has extreme control over instrumental systematics and foreground contamination
Working on SKA point of view

17. Summary
Solutions to tackle systematics and the way forward for HERA and SKA-low:
Critical to explore antenna apertures and spectral features in future designs
HERA design robust to systematics - offers great promise for EoR detection
SKA design under study
PRISim – high precision simulations for wide-field radio interferometry – publicly available (
Discovery of new instrument + foreground physics:
Foregrounds through the instrument are not smooth
Wide-field effects lead to pitchfork effect - diffuse emission near horizon even on long baselines
Contamination significant from far away from primary field of view due to small but non-zero beam response
Antenna beam chromaticity and reflections worsen contamination

18. E-field Parallel Imaging Correlator: An Ultra-efficient Architecture for Future Radio Interferometers
Nithyanandan Thyagarajan (ASU, Tempe)
Adam P. Beardsley (ASU, Tempe)
Judd Bowman (ASU, Tempe)
Miguel Morales (UW, Seattle)

19. Outline Motivations for Direct Imaging
Modular Optimal Frequency Fourier Imaging (MOFF) – A generic direct imaging algorithm
EPIC implementation of MOFF in software
EPIC imaging in action
Imaging performance of EPIC vs. FX
EPIC calibration in action (Adam Beardsley)
EPIC on future large-N dense array layouts
Time-domain capability of EPIC
Testing GPU-based EPIC on HERA

20. Motivations for Direct Imaging
Technological
Scientific
EoR studies
Transient studies, Inter-Planetary Scintillations, Ionospheric monitoring
Large collecting areas require large-N arrays
Cost of the correlator scales as N2
Require fast writeouts
Fast writeouts under technical
Thornton et al. (2013)

21. Concept of Direct Imaging
Antennas placed on a grid and perform spatial FFT of antenna voltages on grid to get complex voltage images
Square the transformed complex voltage image to obtain real-valued intensity images
Current implementation:
8x8 array in Japan (Daishido et al. 2000)
4x8 BEST-2 array at Radiotelescopi de Medicina, Italy (Foster et al. 2014)

22. Need for generic direct imaging
Hurdles with current implementations
MOFF algorithm
Morales (2011)
Uniformly arranged arrays have poor point spread functions – thus not ideal for imaging
Aliasing of objects from outside field of view
Assumptions of identical antennas => poor calibration
Calibration still requires antenna correlations
Antennas need not be on a grid but still exploit FFT efficiency
Can customize to science needs
Accounts for non-identical antennas
Calibration does not require forming visibilities
Can handle complex imaging issues - w-projection, time-dependent wide-field refractions and scintillations
Optimal images

23. Mathematical basis for MOFF
Measured visibility is the spatial correlation of measured antenna E-fields
Antenna power pattern is the correlation of individual voltage patterns
Visibility measurement equation is separable into antenna measurement equations
Allows application of “multiplication route” in multiplication-convolution theorem of Fourier Transform (while visibility imaging uses “convolution route”)
FFT efficiency leveraged by gridding E-fields using antenna voltage illumination pattern

24. MOFF vs. FX FX MOFF Na2 (vs.) Ng log Ng
Parallelization for efficiency – not production-level
Na2 (vs.) Ng log Ng

25. Imaging with EPIC vs. FX Simulated Example: Nchan = 16 df = 100 kHz
f0 = 150 MHz
MWA core layout inside 150 m (51 antennas)
Square antenna kernels

26. EPIC on actual LWA Data LWA1 TBN data with a total of 2s and 100 kHz
Image obtained with 20 ms, 80 kHz
Cyg A and Cas A prominently visible

27. Calibration
*Need to apply calibration before gridding.

28. Calibration Problem E-field incident on ground related to sky by FT:
Antenna integrates with voltage pattern:
Further corruption modeled as complex gain and noise
Goal is to solve for the gain factor

29. Calibration Requirements
No visibilities
MOFF algorithm mixes antenna signals
⇒ Must apply calibration at front end
Scale <

30. Calibration Loop
An iterative approach
Scales O(N)

31. Math behind EPICal … Inspect this product
Prime means current estimate and tracks the actual gain

32. Convergence of Antenna Gains
Gain Amplitudes
Gain Phase Errors
Each iteration = 400 timestamps totaling 10 ms,
No receiver noise, only sky noise
Remind about phase wrap
Initial dip in amplitude is overcompensating for initial high gains
Nyquist timeseries length = 25 micro-seconds
Gain update after 10 ms of integration

33. EPICal in action

34. Calibrating LWA data Same LWA data 150 channels ~ 29 kHz bandwidth
Cal loop on 51.2 ms cadence
total 1.5 s (30 cal. iterations)
Model Cyg A and Cas A as point sources
If you use the new plots from Evernote, 10 timestamps per cal update, 30 cal updates, total of 1.5s
Get auto-subtraction term from Adam’s paper on github

35. Calibrating LWA data Gain Amplitudes Gain Phases
Real data implies phases and gains converge to different values but are locked in
Nyquist timeseries length = 5 micro-seconds
Gain update after 51 ms of integration

36. Calibrating LWA data 55% increase in dynamic range
Comment on image quality
55% increase in dynamic range

37. Implications from Scaling Relations
EPIC FX
Most expensive step – 2D spatial FFT at every ADC output cycle – O(Ng log Ng)
For a given Ng, it does not depend on Na. e.g., dense layouts like HERA, LWA, CHIME
Thus the array layout can get dense with no additional cost
Most expensive step – FX operations on N2 pairs at every ADC output cycle – O(Na2)
Accumulation in visibilities before imaging offers some advantage
Advantage lost for large arrays requiring fast writeouts (due to fast transients, rapid fringe rate, ionospheric changes, etc.)
Na2 (vs.) Ng log Ng

38. Current and future telescopes in MOFF-FX parameter space
Top left is where MOFF is more efficient than FX
Dashed line shows where expanded HERA will be
Shaded area is where LWA will evolve to be
Large-N dense layouts favor EPIC
EPIC will benefit most of future instruments, definitely SKA
MOFF (EPIC) FX

39. Current and future telescopes in MOFF-FX parameter space

40. Writeout rates for Transients
Data rate
(EPIC)
GB/s
Data rate
(FX/XF)
GB/s
Data rate ~Ng for MOFF with EPIC
Data rate ~Na2 for visibilities to be written out
MOFF using EPIC lowers data rates significantly in modern/future telescopes
MOFF with EPIC also yields calibrated images on short timescales
Ideal for bright, fast (FRBs) and slow transients with large-N dense arrays
Telescope
Assumes writeout timescale of 10 ms

41. Planned EPIC demonstration
Design a GPU-based EPIC and EPICal
Design a GPU-based, image-based transient search backend
Test machine set up at ASU to experiment the porting
Cost-effective way to test it since we have already the hardware.
Test machine set up at ASU to experiment the porting.

42. EPIC Summary
EPIC is promising for most modern/future telescopes (SKA1, HERA, LWA, CHIME, MWA II core, etc.)
EoR studies
Large-N dense arrays for sensitivity to large scales
Radio Transients & Inter-planetary Scintillation
Fast writeouts
Economic data rates
Calibrated images at no additional cost
EPIC paper - Thyagarajan et al. (2016) in review
(arXiv: )
Highly parallelized EPIC implementation in Python publicly available -
Results of calibration (EPICal) studies by Beardsley et al.(2016) in review (arXiv: )