Pulsar acceleration searches are methods for recovering signals from radio telescopes, that may otherwise be lost due to the effect of orbital acceleration in binary systems. The vast amount of data that will be produced by next generation instruments such as the Square Kilometre Array (SKA) necessitates real-time acceleration searches, which in turn requires the use of HPC platforms. We present our implementation of the Fourier Domain Acceleration Search (FDAS) algorithm on Graphics Processor Units (GPUs) in the context of the SKA, as part of the Astro-Accelerate real-time data processing library, currently under development at the Oxford e-Research Centre (OeRC), University of Oxford

Armour, WG

Dimoudi, S

arXiv

Dimoudi, Sofia

Armour, Wesley

ORA - Oxford University Research Archive

Pulsar acceleration searches on the GPU for the Square Kilometre Array

Oxford University Research Archive

arXiv:1511.07343v2  [astro-ph.IM]  24 Nov 2015 Pulsar Acceleration Searches on the GPU for theSquare Kilometre ArraySofia Dimoudi1 and Wesley Armour11University of Oxford, Oxford, United Kingdom ,sofia.dimoudi@oerc.ox.ac.ukAbstractPulsar acceleration searches are methods for recovering signals fromradio telescopes, that may otherwise be lost due to the effect of orbitalacceleration in binary systems. The vast amount of data that will beproduced by next generation instruments such as the Square Kilome-tre Array (SKA) necessitates real-time acceleration searches, which inturn requires the use of HPC platforms. We present our implementa-tion of the Fourier Domain Acceleration Search (FDAS) algorithm onGraphics Processor Units (GPUs) in the context of the SKA, as part ofthe Astro-Accelerate real-time data processing library, currently underdevelopment at the Oxford e-Research Centre (OeRC), University ofOxford.1 IntroductionPulsars are highly magnetized rotating neutron stars which emit a beamof electromagnetic radiation from their magnetic poles. When the beampasses our line of sight it is observed as a pulse of radiation. The periodof the pulses is very precise and extremely regular, a property that makesthese objects interesting for a variety of astronomical studies. Pulsars inbinary systems which are found typically with millisecond pulse periods,are particularly interesting as they enable very high precision measurementswhich can be used to test theories of gravity [1].The standard way to identify pulsar signals in a radio telescope signalis to run a periodicity search by applying the Discrete Fourier Transform(DFT) on the incoming time series data. The power spectrum produced bythe DFT can reveal periodic signal power concentrated in the frequencies1of the received pulse harmonics. In the case of binary pulsars however,due to the Doppler effect, orbital motion creates a drift in the apparentfrequency as the object is moving towards and away from us. As a result,the recovered power spreads over neighbouring frequencies, which can havea significant effect on the amount of power that can be recovered with thismethod, and can potentially prevent detection. In order to correct for thiseffect, a simple model is used which assumes a constant acceleration fora small fraction of the orbital period. A search over a number of trialsfor different constant acceleration values can then show increased detectionat trials corresponding to an accelerated pulsar. This type of search iscalled an acceleration search. Acceleration search techniques have by nowbeen well studied (e.g. in [2, 3, 4, 5]), and currently there are two mainmethods that are commonly used. The first one works in the time domain byresampling the time series according to a time offset caused by the constantacceleration, followed by a standard periodicity search for each accelerationvalue. This technique can be computationally very expensive, as it requiresthe calculation of many long DFTs. A different approach is to create a setof Finite Impulse Response (FIR) filters in the Fourier domain that describethe effect of constant acceleration, and then correlate each one with thesignal. This is the correlation technique [5] and can be much more efficientbecause the filter size can be small and the computations can be performedin parallel, as many short independent Fourier transforms and convolutions.Acceleration searches are critical in fulfilling some of the key scientificobjectives for the next generation radio telescope, the Square KilometreArray (SKA). The SKA will use pulsars to search for gravitational waves,and test general relativity under very strong-field gravity conditions. Priorto conducting any periodicity search, the signals need to be analysed fordetermining their Dispersion Measure (DM). This process, known as de-dispersion will result in a large number of data series that will need to besearched individually for the existence of periodic signals. The total process-ing must be done in real-time, which is limited to the observation period. Wework with the assumption that a time series produced from an SKA beamwill contain approximately 8 million samples, the de-dispersion will produce∼ 6000 DMs and the observation period will be approximately 530 seconds.These restrictions, along with the vast data volume produced by the SKA,increase the demand for fast algorithms and for the use of energy efficientHPC. A real-time time-domain data processing library, Astro-Accelerate[6], is currently being developed at the Oxford e-Research centre as part ofthe time domain science efforts for the SKA. Astro-Accelerate will be usingspecialised algorithms, targeted in many-core accelerators, with the aim of2fulfilling these limitations, and has been successfully used in [7].This document presents an overview of the implementation of the FDASon GPUs that will form part of this work.2 Fourier Domain Acceleration Search MethodThe FDAS method was proposed by Ransom et al. [5] who devised a corre-lation technique and derived the mathematical form of a finite impulse re-sponse filter template in the Fourier space that models the effect of constantacceleration. By applying the inverse filter, that is, the complex conjugateof the filter to the Fourier transformed series, it is shown that the signalpower that has leaked to surrounding Fourier bins is recovered in a singlefrequency bin. The corrected signal response resulting from the correlationtechnique is expressed by the relationshipFr0 =k=r0+m/2∑k=r0−m/2FkF∗r0−k , (1)where F∗r0−k is the inverse filter template and Fk the signal Fourier responseat bin k, with a frequency offset |r0 − k| from a reference frequency r0.Each template is related to orbital acceleration via a frequency derivativeḟ which expresses the frequency drift due to the Doppler effect correspondingto the constant acceleration, and is directly proportional to the number offrequency bins the signal would spread into, i.e. ṙ = ḟT 2, where T 2 is theobservation period. To examine the signal for a range of orbital accelerationvalues, multiple templates must be used. The result from this processing canbe visualised on a two-dimensional f − ḟ plane which reveals the position ofthe signal Fourier power in frequency and orbital acceleration. An exampleof this plane is shown in figure 1.Technically, the correlation of the signal with multiple templates is amatched filtering process, and can be done efficiently in the Fourier domainusing the convolution theorem with an overlap-save method [8].3 High Performance ComputingIn the last decade there has been an increasing interest in using co-processorswith parallel architectures as hardware accelerators, such as Graphical Pro-cessing Units (GPU), Field Programmable Gate Arrays (FPGA), and morerecently the Intel Xeon Phi. NVIDIA GPUs are now well established as high3Figure 1: Example of a theoretical one harmonic with orbital acceleration on an f − ḟplane.performance devices. They have a rich software ecosystem, a proven trackrecord, and are one of the highest performing co-processors.The FDAS method as described earlier has a significant part devoted toapplying DFTs, and as such, we use the proven CUFFT library [9] for thistask. The problem structure is also suitable as the data are arranged in smallmostly independent blocks which fits the GPU programming model. Trendstowards increasing the GPU performance per Watt ratio make NVIDIAGPUs a viable solution for the FDAS component of the SKA signal process-ing pipeline.4 Implementation and Preliminary ResultsAfter an initialization stage that includes computation of the templates to beused, the algorithm performs the following conceptual steps for each receivedtime series: 1. The time series is transferred to the GPU via PCI-express,this can be done asynchronously; 2. Real to complex DFT of the time series;3. Complex DFT output is divided in segments. Each segment contains aregion from the previous segment to correct for edge effects; 4. Complexto complex DFT of each segment; 5. Fourier Domain convolution of eachsegment with all templates (complex multiply - scale), 2-dimensional f − ḟplane produced; 6. Inverse complex to complex DFT of each f − ḟ segment;and 7. Power spectrum operations. Steps 2, 4 and 6 were done using theCUFFT library. Step 3 is a simple copy of overlapped data segments to anextended array so that they are independent and contiguous, and has a neg-4ligible cost. The actual filtering operations are performed as Fourier domainconvolutions via complex element-wise multiplications in step 5. This stepuses a custom GPU kernel which has been optimized for memory transfersand data reuse. The power spectrum operations in step 7 currently consistsof the main calculation of Fourier powers and edge removal of the convolvedsegments. We performed tests on time series containing 223 samples withover 100 templates, which we believe is consistent with the current SKAspecification. The tests were run on two NVIDIA cards: a GeForce Titan Xof the newest Maxwell architecture, and a dual-GPU Tesla K80, using onlyone of its 2 GPUs. Figure 2 illustrates the real-time performance of the al-gorithm relative to the number of acceleration templates applied. As can beseen, at this stage, we are able to achieve better than real-time performancefor the SKA requirement.Figure 2: Real-time performance of Fourier domain acceleration search on a GeForce TitanX and a Tesla K80 (using a single GPU on the card).AcknowledgementsThis work is supported by a Leverhulme Trust Project Grant (ARTEMIS:Real-time discovery in Radio Astronomy). It has also received supportfrom members of the Oxford pulsar group, namely Aris Karastergiou,Christopher Williams and Jayanth Chennamangalam, as well as supportfrom the Time Domain Team, a collaboration between Oxford, Manchesterand MPIfR Bonn, to design and build the SKA pulsar search capabilities.5References[1] D. R. Lorimer and M. Kramer, “Handbook of Pulsar Astronomy”,Cambridge University Press, Cambridge, UK, 2004.[2] J. Middleditch and W. C. Priedhorsky, “Discovery of rapidquasi-periodic oscillations in Scorpius X-1”, Astrophysical Journal 306(1986) 230–237.[3] S. B. Anderson, P. W. Gorham, S. R. Kulkarni, T. A. Prince, andA. Wolszczan, “Discovery of two radio pulsars in the globular clusterM15”, Nature 346 07 (1990) 42–44.[4] H. M. Johnston and S. R. Kulkarni, “On the detectability of pulsars inclose binary systems”, The Astrophysical Journal 368 (1991) 504–514.[5] S. M. Ransom, S. S. Eikenberry, and J. Middleditch, “Fouriertechniques for very long astrophysical time-series analysis”, TheAstronomical Journal 124 (2002), no. 3, 1788.[6] W. Armour, A. Karastergiou, M. Giles, C. Williams, A. Magro,K. Zagkouris, S. Roberts, S. Salvini, F. Dulwich, and B. Mort, “AGPU-based survey for millisecond radio transients using ARTEMIS”,ASP Conf. Ser. 461 (2012) 33–36, arXiv:1111.6399.[7] A. Karastergiou, J. Chennamangalam, W. Armour, C. Williams,B. Mort, F. Dulwich, S. Salvini, A. Magro, S. Roberts, M. Serylak,et al., “Limits on fast radio bursts at 145 MHz with artemis, areal-time software backend”, Monthly Notices of the RoyalAstronomical Society 452 (2015), no. 2, 1254–1262.[8] W. Press, “Numerical recipes in c: The art of scientific computing”,Cambridge University Press, 1992.[9] NVIDIA Corporation, cuFFT Library User’s Guide, v7.5, 2015.6

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