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HIGH‐LEVEL SKA SIGNAL PROCESSING DESCRIPTION<br />
Document number .................................................................. WP2‐040.030.010‐TD‐001<br />
Revision ........................................................................................................................... 1<br />
Author ................................................................................. W.Turner, et. al. (see below)<br />
Date ................................................................................................................. 2011‐03‐29<br />
Status ............................................................................................... Approved for release<br />
Name Designation Affiliation Date Signature<br />
Additional Authors<br />
A. Faulkner, B. Stappers, S. Ransom, R. Weber, R. Eatough,M.Kramer<br />
Submitted by:<br />
W. Turner Signal Processing<br />
Domain Specialist<br />
SPDO 2011‐03‐29<br />
Approved by:<br />
P. Dewdney Project Engineer SPDO 2011‐03‐29
WP2‐040.030.010‐TD‐001<br />
Revision : 1<br />
DOCUMENT HISTORY<br />
Revision Date Of Issue Engineering Change<br />
Number<br />
Comments<br />
A ‐ ‐ First draft release for internal review<br />
B ‐ ‐<br />
C ‐ ‐<br />
1 29 th March 2011 ‐ First release<br />
DOCUMENT SOFTWARE<br />
Package Version Filename<br />
Wordprocessor MsWord Word 2007 01a‐WP2‐040.030.010‐TD‐001‐1_HighLevelDescr<br />
Block diagrams<br />
Other<br />
ORGANISATION DETAILS<br />
Name<br />
Physical/Postal<br />
Address<br />
SKA Program Development Office<br />
Jodrell Bank Centre for Astrophysics<br />
Alan Turing Building<br />
<strong>The</strong> University of Manchester<br />
Oxford Road<br />
Manchester, UK<br />
M13 9PL<br />
Fax. +44 (0)161 275 4049<br />
Website www.<strong>ska</strong>telescope.org<br />
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TABLE OF CONTENTS<br />
1 INTRODUCTION ............................................................................................. 7<br />
1.1 Purpose of the document ....................................................................................................... 8<br />
2 REFERENCES ................................................................................................ 9<br />
3 HIERARCHY ................................................................................................ 11<br />
3.1 Hierarchical Lifecycle ............................................................................................................ 11<br />
4 ELEMENT LEVEL: SIGNAL PROCESSING .............................................................. 12<br />
4.1 Environment .......................................................................................................................... 14<br />
4.2 Simulator ............................................................................................................................... 14<br />
4.3 Receptors .............................................................................................................................. 14<br />
4.4 VLBI ....................................................................................................................................... 15<br />
4.5 Power .................................................................................................................................... 15<br />
4.6 Cooling .................................................................................................................................. 15<br />
4.7 External Transient Triggers ................................................................................................... 15<br />
4.8 Time Reference ..................................................................................................................... 15<br />
4.9 Science Computing ................................................................................................................ 16<br />
4.10 Monitoring and Control ........................................................................................................ 16<br />
4.11 Stakeholders ......................................................................................................................... 16<br />
5 SUBSYSTEM ............................................................................................... 17<br />
6 RFI EXCISION ............................................................................................ 21<br />
7 CORRELATOR ............................................................................................. 24<br />
7.1 Delay Compensation Buffer .................................................................................................. 25<br />
7.2 Channeliser ........................................................................................................................... 25<br />
7.3 Corner Turn ........................................................................................................................... 28<br />
7.4 Full Stokes Correlator ............................................................................................................ 29<br />
7.4.1 Correlation Integration Period ...................................................................................... 29<br />
7.4.2 Correlator Processing Load ........................................................................................... 30<br />
8 CENTRAL BEAMFORMER ............................................................................... 32<br />
8.1 Buffer .................................................................................................................................... 33<br />
8.2 Voltage Storage ..................................................................................................................... 33<br />
8.3 Beamforming ........................................................................................................................ 33<br />
9 DE‐DISPERSION .......................................................................................... 35<br />
9.1 Incoherent Dedispersion ....................................................................................................... 35<br />
9.2 Delay and Sum Dedispersion ................................................................................................ 36<br />
9.3 Pre‐summing channels for large dispersion measures ......................................................... 36<br />
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9.4 Accumulating and differencing algorithm ............................................................................ 37<br />
9.5 De‐dispersion over multiple sample intervals ...................................................................... 37<br />
9.6 Taylor tree based algorithms ................................................................................................ 37<br />
9.7 Frequency Partitioning .......................................................................................................... 38<br />
9.8 Coherent de‐dispersion ........................................................................................................ 39<br />
9.9 Concept sizing ....................................................................................................................... 39<br />
10 PULSAR SEARCH ...................................................................................... 44<br />
10.1 Binary Search ........................................................................................................................ 44<br />
10.1.1 Matched Filter ............................................................................................................... 44<br />
10.1.2 Hough Transform .......................................................................................................... 46<br />
10.1.3 Stack Search .................................................................................................................. 46<br />
10.1.4 Phase Search ................................................................................................................. 46<br />
10.1.5 Coherence Recovery ..................................................................................................... 46<br />
10.1.6 Time Domain Resampling ............................................................................................. 47<br />
10.2 Time Domain Re‐Sampling .................................................................................................... 47<br />
10.3 FFT ......................................................................................................................................... 49<br />
10.4 Whitening and Normalisation ............................................................................................... 50<br />
10.5 Harmonic Sum ....................................................................................................................... 50<br />
10.6 Threshold Detection .............................................................................................................. 52<br />
10.7 Candidate Filtering ................................................................................................................ 52<br />
10.7.1 Artifcial Neural Nets ...................................................................................................... 53<br />
10.7.2 <strong>The</strong> Future ..................................................................................................................... 53<br />
10.7.3 Application to the SKA .................................................................................................. 53<br />
11 PULSAR TIMING ....................................................................................... 54<br />
11.1 Basic Parameters ................................................................................................................... 54<br />
11.2 Timing scenarios ................................................................................................................... 55<br />
11.3 Monitoring and Cadence: ..................................................................................................... 55<br />
11.4 Observing Frequency and Bandwidth ................................................................................... 56<br />
11.5 Collecting area, beams and integration time: ....................................................................... 56<br />
11.6 Forming the Beams: .............................................................................................................. 58<br />
11.7 Time Resolution and Frequency Resolution. ........................................................................ 58<br />
11.8 Data rates: ............................................................................................................................. 58<br />
11.9 Processing the Beams ........................................................................................................... 59<br />
11.9.1 (Coherent) De‐dispersion: ............................................................................................. 59<br />
LIST OF FIGURES<br />
Figure 1 Heirarchical Development ...................................................................................................... 12<br />
Figure 2: Signal Processing Functional Context Diagram ...................................................................... 13<br />
Figure 3 Signal Processing Definition .................................................................................................... 17<br />
Figure 4 A model of the u‐v plane for the SKA ...................................................................................... 18<br />
Figure 5 Beamforming .......................................................................................................................... 18<br />
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Figure 6 Internal Block Diagram of SKA1 Signal Processing .................................................................. 20<br />
Figure 7 Correlator Definition ............................................................................................................... 24<br />
Figure 8 Adjacent Channels Multiband Filter ....................................................................................... 28<br />
Figure 9 4‐Channel Taylor Tree De‐disperser ....................................................................................... 38<br />
Figure 10 Dispersion measure, DM, for pulsars at different galactic latitudes. ................................... 41<br />
Figure 11 Binary Pulsar Search Algorithms ........................................................................................... 44<br />
LIST OF TABLES<br />
Table 1 RFI Mitigation options, pro’s and con’s. ................................................................................... 22<br />
Table 2 Technology Readiness Levels of RFI mitigation methods. ....................................................... 23<br />
Table 3 DM Diagonal ............................................................................................................................. 40<br />
Table 4 Dedispersion Processing loads per beam ................................................................................. 42<br />
Table 5 Dedispersion Output Rate per beam ....................................................................................... 43<br />
Table 6 Number of trial Accelerations .................................................................................................. 48<br />
Table 7 Re‐sampling Processing Load per beam ................................................................................... 48<br />
Table 8 Time Re‐sampling output rates ................................................................................................ 49<br />
Table 9 FFT Processing Load per Beam ................................................................................................. 50<br />
Table 10 Harmonic Sum Processing Load for acceleration Processing per Beam ................................ 51<br />
Table 11 Harmonic Sum Output Rates per Beam ................................................................................. 52<br />
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LIST OF ABBREVIATIONS<br />
AA .................................. Aperture Array<br />
Ant. ................................ Antenna<br />
CoDR ............................. Conceptual Design Review<br />
DRM .............................. Design Reference Mission<br />
FLOPS ........................... Floating Point Operations per second<br />
FoV ................................ Field of View<br />
Ny .................................. Nyquist<br />
OH ................................. Over Head<br />
Ov .................................. Over sampling<br />
PAF ............................... Phased Array Feed<br />
PrepSKA........................ Preparatory Phase for the SKA<br />
RFI ................................. Radio Frequency Interference<br />
rms ................................ root mean square<br />
SEFD...........................System Equivalent Flux Density<br />
SKA ............................... <strong>Square</strong> <strong>Kilometre</strong> Array<br />
SKADS .......................... SKA Design Studies<br />
SPDO ............................ SKA Program Development Office<br />
SSFoM .......................... Survey Speed Figure of Merit<br />
TBD ............................... To be decided<br />
Wrt ................................. with respect to<br />
2011‐03‐29 Page 6 of 59
1 Introduction<br />
WP2‐040.030.010‐TD‐001<br />
Revision : 1<br />
<strong>The</strong> aim of this document is to present a <strong>high</strong> <strong>level</strong> functional breakdown of the Signal Processing<br />
aspects of the SKA telescope primarily for Phase 1, SKA1, but with consideration of scalability to<br />
Phase 2, SKA2, of the project. SKA Memo 125 [27] defines the main scientific goals and baseline<br />
technical concept for the SKA phase 1. This definition identifies the major science goals for SKA1:<br />
<br />
<br />
Study the history and role of neutral Hydrogen in the Universe from the dark ages to the<br />
present‐day<br />
Employ the detection and timing of binary pulsars and spin‐stable millisecond pulsars as<br />
probes of fundamental physics including<br />
o<br />
o<br />
o<br />
testing theories of gravity (including General Relativity and quantum gravity)<br />
to discover gravitational waves from cosmological sources<br />
to determine the equation of state of nuclear matter<br />
In addition, Memo 125 provides a baseline technical concept of SKA1 receptors including:<br />
<br />
<br />
A low‐frequency sparse aperture array with an A/Tsys of up to 2000 m 2 /K operating at<br />
frequencies between 70 and 450 MHz. <strong>The</strong> array will be centrally condensed but some of the<br />
collecting area will be in stations located out to a maximum baseline length of 100 km from<br />
the core<br />
A dish array with Aeff/Tsys of up to 1000 m 2 /K using approximately two hundred and fifty<br />
15‐metre antennas, employing an instrumentation package that will use single‐pixel feeds to<br />
provide <strong>high</strong> sensitivity and excellent polarisation characteristics over a frequency range of<br />
0.45‐3 GHz. <strong>The</strong> array will be centrally condensed but some of the elements will be colocated<br />
with the sparse aperture array stations out to a maximum baseline length of 100 km<br />
from the core.<br />
This Signal Processing High Level Description document is part of a document series generated to<br />
provide a top down and bottom up approach in support of the Signal Processing CoDR. This<br />
document set includes includes the following:<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
Signal Processing High Level Description<br />
Technology Roadmap<br />
Design Concept Descriptions<br />
Signal Processing Requirements<br />
Signal Processing Costs<br />
Signal Processing Risk Register<br />
Signal Processing Strategy to Proceed to the Next Phase<br />
Signal Processing Co DR Review Plan<br />
Software & Firmware Strategy<br />
2011‐03‐29 Page 7 of 59
WP2‐040.030.010‐TD‐001<br />
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<strong>The</strong> focus of this document is providing the <strong>high</strong> <strong>level</strong> logical architecture of the SKA <strong>signal</strong><br />
<strong>processing</strong>. This means identifying the structure and behaviour of the key functional blocks and their<br />
interfaces within the context of the SKA as a whole. It should be pointed out that the term ‘interface’<br />
is used as an abstract term as the aim of this document is not to specifically identify physical<br />
solutions but the logical functionality. However it is recognised that some aspects of the physical<br />
architecture need to be considered. For example, some physical aspects of the receptor technologies<br />
are likely to be imposed as constraints as part of the systems requirements.<br />
This document also flows down and develops the strategies identified in the Systems Engineering<br />
Management Plan (SEMP) as presented within the context of the <strong>signal</strong> <strong>processing</strong> domain. This<br />
includes the hierarchical approach and the iterated requirements driven design process.<br />
1.1 Purpose of the document<br />
<strong>The</strong> purposes of this document are as follows:<br />
• To present the context of Signal Processing within the SKA system hierarchy.<br />
<br />
To provide an overview of the Signal Processing life‐cycle.<br />
• To provide a system break down of the Signal <strong>processing</strong> capability in terms of identifying:<br />
o<br />
o<br />
o<br />
Where Interface Control Documents, ICD, are required.<br />
Function blocks<br />
To present an overview of the various algorithmic schemes that are being put forward<br />
for SKA <strong>signal</strong> <strong>processing</strong><br />
2011‐03‐29 Page 8 of 59
2 References<br />
WP2‐040.030.010‐TD‐001<br />
Revision : 1<br />
[1] SKA Science Case<br />
[2] <strong>The</strong> <strong>Square</strong> <strong>Kilometre</strong> Array Design Reference Mission: SKA‐mid and SKA‐Lo v 0.4<br />
[3] Science Operations Plan<br />
[4] System Interfaces<br />
[5] Environmental requirements (natural and induced)<br />
[6] SKA strategies and philosophies<br />
[7] Risk Register<br />
[8] Requirements Traceability<br />
[9] Logistic Engineering Management Plan (LEMP)<br />
[10] Risk Management Plan (RMP)<br />
[11] Document Handling Procedure<br />
[12] Project Dictionary<br />
[13] Strategy to proceed to the next phase<br />
[14] WP3 SKA array configuration report<br />
[15] WP3 SKA site RFI environment report<br />
[16] WP3 Troposphere measurement campaign report<br />
[17] SKA Science‐Technology Trade‐off Process (WP2‐005.010.030‐MP‐004)<br />
[18] A. Faulkner, et al., Aperture Arrays for the SKA: the SKADS White Paper, January 2010.<br />
[19] E. de Lera‐Acedo et al., System Noise Analysis of an Ultra Wide Band Aperture Array: SKADS<br />
Memo T28.<br />
[20] SKA Monitoring and Control Strategy WP2‐005.065.000‐R‐001 Issue Draft E<br />
[21] “<strong>The</strong> <strong>Square</strong> <strong>Kilometre</strong> Array”, Peter E. Dewdney, Peter J. Hall, Richard T. Schilizzi, and T.<br />
Joseph L. W. Lazio, Proceedings of the IEEE Vol. 97,No. 8, August 2009<br />
[22] Thompson, A. R., Moran, J. M., and Swenson, G. W. “Interferometry and Aperture Synthesis<br />
in Radio Astronomy” (second edition), Wiley, 1986.<br />
[23] System Engineering Management Plan (SEMP) WP2‐005.010.030‐MP‐001Reference 3<br />
[24] SKA System Requirement Specification (SRS)<br />
[25] SKA IP Policy Document<br />
[26] International Technology Roadmap for Semiconductors (ITRS), available at www.itrs.net.<br />
[27] A Concept Design for SKA Phase 1 (SKA1) SSEC SKA Phase 1 Sub‐committee,<br />
http://www.<strong>ska</strong>telescope.org/PDF/memos/125_Memo_Garrett.pdf<br />
[28] RFI Mitigation Implementation for Pulsar Radio Astronomy D. Ait‐Allal, R. Weber, C. Dumez‐<br />
Viou, I. Cognard, and G. <strong>The</strong>ureau<br />
[29] E.Serpedin, F. Panduru, I. Sari, and G.B. Giannakis, “Bibliography on cyclostationarity ” Signal<br />
Processing, vol. 85, pp. 2233‐2303, Dec. 2005.<br />
[30] R. Weber, P. Zarka, V. Ryabov, R. Feliachi, J. Grießmeier, L. Denis,V. Kozhyn, V. Vinogradov,<br />
and P. Ravier, “Data pre<strong>processing</strong> for decametre wavelength exoplanet detection: an<br />
example of cyclostationary rfi detector,” Eusipco, Poznan, Poland, 2007.<br />
[31] L. D'Addario, “Searching For Dispersed Transient Pulses With ASKAP”, SKA Memo 124,<br />
March 10, 2010.<br />
[32] R. Navarro, “Efficient Summing of ASKAP Beamformer Power Spectra over Multiple<br />
Dispersion Measures”, CRAFT memo, July 6, 2010.<br />
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[33] J. H. Taylor, “A Sensitive Method for Detecting Dispersed Radio Emission”, Astron.<br />
Astrophys. Suppl., issue 15, pp. 367‐369, 1974.<br />
[34] R. N. Manchester, A. G. Lyne, F. Camil, J. F. Bell, V. M. Kaspi, N. D'Amico, N. P. F. McKay, F.<br />
Crawford, I. H. Stairs, A. Possenti, M. Kramer, D. C. Sheppard, “<strong>The</strong> Parkes Multi‐Beam Pulsar<br />
Survey – I. Observing and Data Analysis Systems, Discovery and Timing of 100 Pulsars”, Mon.<br />
Not. R. Astron. Soc., issue 328, pp. 17‐35, 2001.<br />
[35] J.M. Cordes, M.A. McLaughlin, Searches for fast radio transients, <strong>The</strong> Astrophysical Journal<br />
(2003), pp. 1142.<br />
[36] G. M. Nita, D. E. Gary, Z. Liu, G. J. Hurford, & S. M. White, 2007, Radio Frequency<br />
Interference Excision Using Spectral‐Domain Statistics, PASP, 119, 805.<br />
[37] Burke‐Spolaor et al., Peryton Event, submitted .<br />
[38] Kramer et al., 2004, New Astr. Rev., 48, 993<br />
[39] Cordes et al., 2004, New Astr. Rev., 48, 1413<br />
[40] Lorimer & Kramer, 2005, Handbook of Pulsar Astronomy, CUP<br />
[41] Smits et al., 2009, A&A. 493. 1161<br />
[42] Smits et al., 2011, SKA Phase I Memo<br />
[43] R P Eatough, A Search for Relativistic Binary Pulsars in <strong>The</strong> Galactic Plane (PhD <strong>The</strong>sis)<br />
[44] T Colgate, N Clarke, Searching for Fast Transients with SKA Phase 1<br />
WP2‐040.030.010‐TD‐004 Rev B<br />
[45] SKA Science Working Group, <strong>The</strong> <strong>Square</strong> <strong>Kilometre</strong> Array Design Reference Mission: SKA<br />
Phase 1 Rev 1.3 2011.01.17<br />
2011‐03‐29 Page 10 of 59
3 Hierarchy<br />
WP2‐040.030.010‐TD‐001<br />
Revision : 1<br />
<strong>The</strong> SKA subsystem is of sufficient scale and complexity that the Systems Engineering Management<br />
plan has defined multiple layers of hierarchy:<br />
L8: SKA User<br />
L7: System<br />
L6: Element<br />
L5: Sub‐System<br />
L4: Assembly<br />
L3: Sub‐Assembly<br />
L2: Component<br />
L1: Part<br />
Although not explicitly stated in the SEMP, the hierarchical approach has the advantage of breaking<br />
down the complexity of the system. Each layer is only concerned about its own functionality and its<br />
interface to the immediately adjacent layers.<br />
Within the hierarchical scheme, Signal Processing is defined at the element <strong>level</strong> deriving its<br />
requirements directly from a subset of System <strong>level</strong> requirements. In turn, the sub‐system <strong>level</strong><br />
allows the Signal Processing element to be partitioned further into Level 5 functionality. Introducing<br />
these layers of hierarchy ensures that the complexity of the system is broken down such that<br />
individual layers only have to deal with their relevant perspective of the system.<br />
3.1 Hierarchical Lifecycle<br />
Figure 1 shows how the hierarchical nature of the system translates into its development life cycle.<br />
Each <strong>level</strong> in the hierarchy has its own <strong>level</strong> of requirements that drive the architectural design for<br />
that <strong>level</strong>. <strong>The</strong>se requirements are derived as a result of partitioning the architecture from the next<br />
<strong>high</strong>er <strong>level</strong> in the hierarchical structure. <strong>The</strong>re is also a feedback to the requirements at the next<br />
<strong>level</strong> up to allow any potential issues with the requirements to be identified. This feedback scheme<br />
may ultimately ripple up the hierarchy to the SKA User <strong>level</strong>. In this case, the scope of the SKA<br />
telescope may need to be renegotiated.<br />
As part of the life‐cycle, the hierarchy is also imposed on the installation and setting to work of the<br />
system. <strong>The</strong> requirements at each <strong>level</strong> are to be verifiable allowing integration to be performed<br />
from the Part <strong>level</strong> upwards ultimately resulting in a fully validated system.<br />
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SKA User<br />
User<br />
Requirement<br />
Feedback<br />
Program<br />
Engineering<br />
Installation<br />
& Validation<br />
Operations<br />
Support<br />
Telescope<br />
System<br />
System<br />
Requirement<br />
System<br />
Architectural<br />
Design<br />
Feedback<br />
Product<br />
Engineering<br />
Installation<br />
&<br />
Verification<br />
Integrated<br />
System<br />
Element<br />
Element<br />
Requirement<br />
Partition<br />
Element<br />
Architectural<br />
Design<br />
Feedback<br />
Product<br />
Engineering<br />
Installation<br />
&<br />
Verification<br />
Integrated<br />
Element<br />
Sub-system<br />
Sub-system<br />
Requirement<br />
Partition<br />
Sub-System<br />
Architectural<br />
Design<br />
Feedback<br />
Product<br />
Engineering<br />
Installation<br />
&<br />
Verification<br />
Integrated<br />
Sub-System<br />
Assembly<br />
Sub-Assembly<br />
Assembly<br />
Requirement<br />
Sub-<br />
Assembly<br />
Requirement<br />
Partition<br />
Partition<br />
Assembly<br />
Architectural<br />
Design<br />
Feedback<br />
Sub-Assy<br />
Architectural<br />
Design<br />
Product<br />
Engineering<br />
Product<br />
Engineering<br />
Installation<br />
&<br />
Verification<br />
Installation<br />
&<br />
Verification<br />
Integrated<br />
Assembly<br />
Integrated<br />
Sub-<br />
Assembly<br />
Component<br />
Component<br />
Specification<br />
Component<br />
Design Build<br />
& Test<br />
Components<br />
Part<br />
Part<br />
Specification<br />
Figure 1 Heirarchical Development<br />
4 Element Level: Signal Processing<br />
This document presents a functional model of the <strong>signal</strong> <strong>processing</strong> domain based on the Structure<br />
and Behaviour diagrams defined by the SysML general‐purpose graphical Modelling language<br />
supplemented by supporting text. At this stage, the language is being used purely as a means of<br />
providing formalised diagrams for the document and these have not been entered into a modelling<br />
tool.<br />
<strong>The</strong> language allows a model of the system to be presented in a hierarchical manner with the ability<br />
to drill down through the hierarchy whilst keeping the complexity of individual diagrams to a<br />
reasonable <strong>level</strong>. This document treats the Signal Processing as a standalone model which can be<br />
integrated into a larger system model. Consequently the <strong>signal</strong> <strong>processing</strong> <strong>description</strong> starts by<br />
providing the context at the element (see Figure 1) <strong>level</strong> prior to moving down through the system<br />
hierarchy layers. For this SysML block definition diagram the SYSMOD profile notations for actors has<br />
been used.<br />
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bdd [package] Context [Signal <strong>processing</strong> context]<br />
0..*<br />
Environment<br />
Engineer<br />
Maintainer<br />
Monitoring &<br />
Control<br />
Operator<br />
Simulator<br />
Scientist<br />
0..*<br />
Digitised<br />
RF + RFI<br />
«System»<br />
Signal Processing<br />
Processed Data<br />
Receptors<br />
Science<br />
Computing<br />
0..*<br />
1..*<br />
VLBI<br />
Power<br />
Cooling<br />
External<br />
Transient<br />
Triggers<br />
Time<br />
Reference<br />
Figure 2: Signal Processing Functional Context Diagram<br />
<strong>The</strong> aim of the diagram is to identify the complete set of external and user systems that interface to<br />
the Signal Processing domain at both phase 1 and phase 2 of the project. External systems are<br />
treated as black boxes and are represented by a 3‐D box in the diagram. User systems provide a<br />
mechanism for user interaction and typically include keyboards displays etc. <strong>The</strong> User System is also<br />
presented as a 3‐D box in the diagram but is in association with a ‘stick‐man’ symbol representing<br />
the actor.<br />
<strong>The</strong> lines connecting blocks within the diagram represent associations between the blocks. Within<br />
the Figure 2 context, these associations are largely based on flows between the blocks. Flows are not<br />
limited to data exchange but can include physical entities such as fluids or electrical current. <strong>The</strong><br />
flows don’t have to be atomic: for example the receptors provide a flow of digitised RF data<br />
combined with RFI Data.<br />
<strong>The</strong> multiplicity of an item is provided at the ends of the association lines. For example there are<br />
zero to any number of External Transient Triggers or Simulators and 1 to any number of Time<br />
References. Where a multiplicity isn’t provided it is to be assumed to be unity.<br />
Each interface will require an Interface Control Documentation set; this will include one or more:<br />
o<br />
o<br />
Data Exchange Specifications<br />
Physical Interface Specifications<br />
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This document limits its coverage to logical interfaces. However, physical implementation options<br />
for the key interfaces are provided within the Design Concept Description documents.<br />
A brief <strong>description</strong> of each interface is provided below with an indication of whether applicable to<br />
phase 1, phase 2 or both. Detail of the interfaces and the first drafts of their Interface Control<br />
Documents will be developed as part of the development phase of the Signal Processing leading up<br />
to the Sub‐System Requirement Review, SRR. <strong>The</strong>se will present the initial requirements for both the<br />
physical aspects, data flow and meta data flow across each interface.<br />
4.1 Environment<br />
Overall environmental conditions for the telescope including temperature, humidity, shock,<br />
vibration, particle and wildlife ingress.<br />
For the Signal Processing the environment is to a greater extent controlled by the equipment<br />
housing. For the Phase 1 of the project this is provided by the Correlator Room in the Central<br />
Processing facility. At Phase 2, dish station beamforming is that is in close proximity to the Stations.<br />
Proposed Correlator Room requirements are provided within the Signal Processing Requirements<br />
document.<br />
<strong>The</strong> interface to the environment is applicable at both phase 1 and phase 2 of the project.<br />
4.2 Simulator<br />
Stimulators may be required to support development of Signal Processing equipment and provide<br />
preliminary testing prior to shipment to the Signal Processing facility.<br />
<strong>The</strong> interface to simulators is applicable at both phase 1 and phase 2 of the project.<br />
4.3 Receptors<br />
<strong>The</strong> RF <strong>signal</strong> is the wanted <strong>signal</strong> from the astronomical source being observed. <strong>The</strong> Design<br />
Reference Mission [2] defines the performance envelope for the telescope.<br />
RF Interference represents any external contaminating RF <strong>signal</strong>. This is site dependent and is<br />
detailed in WP3 SKA site RFI environment report [15].<br />
Interface to 50 Sparse Aperture Arrays and 250 Dishes equipped with Single Pixel Feeds will be<br />
implemented at Phase 1 as detailed in SKA memo 125.<br />
Phase 2 will extend the capability of the telescope by increasing the number of Sparse Aperture<br />
Arrays and dishes to nominally 250 and 3000 respectively. In addition, there is the potential inclusion<br />
of<br />
o<br />
o<br />
Wide Band single pixel Feeds<br />
Dense Aperture Arrays<br />
o<br />
Phased array Single Pixel Feeds<br />
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4.4 VLBI<br />
<strong>The</strong> VLBI Data Interface Specification Release 1.0 ratified 26 th June 2009 specifies the standardized<br />
transport‐independent VLBI data‐interchange format that is suitable for all types of VLBI data<br />
transfer, including real‐time and near‐real‐time e‐VLBI well as disk‐file storage.<br />
http://www.vlbi.org/vsi/docs/VDIF%20specification%20Release%201.0%20ratified.pdf<br />
<strong>The</strong> complementary physical interface specification is currently being written.<br />
Although the VDIF specification makes no mention of data‐transport protocol, it has been developed<br />
with an awareness of expected methods of data transport, including network transport using various<br />
standard protocols, as well as physical or electronic transport of standard disk files.<br />
VLBI interface is not applicable to phase 1 of the project.<br />
4.5 Power<br />
External power to the system is dealt with in the Power section of the Strategies and Philosophies<br />
document [6].<br />
<strong>The</strong> interface to the power distribution is applicable at both phase 1 and phase2 of the project<br />
4.6 Cooling<br />
<strong>The</strong> strategy for dealing with cooling for the SKA telescope is detailed in the Cooling section of the<br />
Strategies and Philosophies document [6].<br />
<strong>The</strong> interface to the cooling is applicable at both phase 1 and phase2 of the project<br />
4.7 External Transient Triggers<br />
<strong>The</strong> SKA telescope is to provide the facility for receiving external transient triggers. <strong>The</strong> interface is<br />
to utilise the SkyAlert service (http://www.skyalert.org/ ) (TBC) which collects and distributes<br />
astronomical events in near‐real time and distributes the resultant data in accordance to the<br />
provisional standard VOevent (http://www.ivoa.net/Documents/REC/VOE/VOEvent‐20061101.html<br />
). <strong>The</strong> transient events include but are not limited to supernovae, gamma‐ray bursts, micro‐lensing .<br />
Transient detection triggers may also be generated internal to the SKA telescope if these are<br />
external to the Signal Processing, they are to be included as part of the External Transient Trigger<br />
interface.<br />
<strong>The</strong> interface for transient triggering isn’t part of phase1 of the project<br />
4.8 Time Reference<br />
It is anticipated that this will be satellite GPS and is detailed in the Timing and Synchronisation<br />
section of the SKA Strategies and Philosophies document [6].<br />
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<strong>The</strong> interface to the Time Reference is applicable at both phase 1 and phase2 of the project<br />
4.9 Science Computing<br />
<strong>The</strong> Science Computing provides data and meta‐data reduction to a format desired by the end user<br />
scientist from raw u‐v plane or non imaging data.<br />
<strong>The</strong> interface to the Science Computing is applicable at both phase 1 and phase2 of the project<br />
4.10 Monitoring and Control<br />
Monitoring includes output from the telescope to the operator. This will provide information on the<br />
health status and the configuration of the telescope and is detailed in the Monitoring and Control<br />
Strategies and Philosophies document [20].<br />
External operator control of the telescope is detailed in the Science Operations Plan [3] and the<br />
Monitoring and Control Strategies and Philosophies document [20] .<br />
<strong>The</strong> interface to the Science Computing is applicable at both phase 1 and phase2 of the project<br />
4.11 Stakeholders<br />
Within the context of Signal Processing the Stakeholders are the external systems or humans that<br />
interact with Signal Processing equipment. <strong>The</strong> term ‘interact’ is used to indicate an associated<br />
change of state or the behavioural aspects of the system. <strong>The</strong> interactions of the Stakeholders are<br />
to be captured using Use Cases which are to be captured as part of the Requirements set.<br />
<strong>The</strong> Signal Processing Stakeholders include (but may not be limited to):<br />
• Scientists<br />
<strong>The</strong> Scientist defines and then submits a plan that details the <strong>high</strong> <strong>level</strong> usage of the telescope<br />
required for performing observations that support science experiments.<br />
• Operators<br />
<strong>The</strong> Operator is normally a Staff Astronomer or an Engineer that controls the SKA Telescope during<br />
science experiments or engineering experiments.<br />
• Maintainers<br />
<strong>The</strong> Maintainer is a technical person that is skilled and qualified prior to receiving SKA Telescope<br />
Technical Training and is responsible for Corrective and Preventive Maintenance and for the<br />
telescope.<br />
<strong>The</strong> Maintainer is also involved during telescope task execution. <strong>The</strong> maintainer monitors the system<br />
health displays regularly during task execution and could, when required, takes manual control of<br />
resources for the purposes of testing and diagnosis. (This authorisation needs to be delegated by the<br />
operator).<br />
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• Engineer<br />
<strong>The</strong> Engineer is part of the multi‐disciplined SKA design team and is responsible for design<br />
commissioning, verification and incremental upgrade of the telescope.<br />
<strong>The</strong> interface to the Signal Processing stakeholders is applicable at both phase 1 and phase2 of the<br />
project.<br />
5 Subsystem<br />
Having presented the Signal <strong>processing</strong> as a black box with a definition of its external interfaces in<br />
section 4, a definition of the Signal Processing internal functionality is now presented.<br />
bdd [block] system [Signal <strong>processing</strong> definitions]<br />
«block»<br />
Signal Processing<br />
1..* 1..*<br />
1..*<br />
1..*<br />
«block»<br />
Correlator<br />
«block»<br />
Non-Imaging<br />
Computing<br />
«block»<br />
Beamforming<br />
«block»<br />
RFI Excision<br />
Figure 3 Signal Processing Definition<br />
Figure 3 provides a SysML graphical representation of the logical subsystem types that make up the<br />
Signal Processing element<br />
<br />
<br />
<br />
<br />
RFI Mitigation<br />
Correlator<br />
Beamforming<br />
Non‐Imaging Computing<br />
RFI Mitigation functionality is cross cutting across the whole of the SKA telescope with different<br />
strategies applied at different points in the system for different observation modes. It’s functionality<br />
within the Signal Processing cross‐cuts that of Correlation, Non‐Imaging and Beamforming. Section<br />
6 provides an overview of the RFI Mitigation strategies applicable to the Signal Processing.<br />
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Correlation is the first step in combining the receptors as part of imaging. <strong>The</strong> correlator provides<br />
cross correlation between each pair of receptors (known as a baseline) sharing the same frequency<br />
range and pointing. <strong>The</strong> correlator performs what is known as Full Stokes correlation which provides<br />
cross correlation for the four combinations of the two polarisations from receptors. <strong>The</strong> distance<br />
between the receptors (baseline length) determines the resolution of the image and the number of<br />
baselines the number of points within the image. <strong>The</strong> correlator produces what is known as the u‐v<br />
plane which is the Fourier Transform of the final image. <strong>The</strong> Science Computing provides the inverse<br />
transform to create the final image. A snap shot of the u‐v plane for the SKA is shown in Figure 4<br />
Figure 4 A model of the u‐v plane for the SKA<br />
Due to the rotation of the Earth with respect to the point being imaged, each point within the u‐v<br />
plane moves in an elipse as a function of time. This is used to fill in the gaps between the individual<br />
points. However, there are a couple of aspects that need to be considered for correlation that<br />
potentially impact on the image quality. <strong>The</strong>se relate to the effect of smearing as a result of sampling<br />
theorem in terms of bandwidth and the amount of integration that can be implemented on the cross<br />
correlation products [22]. Section 7 provides a functional breakdown and sizing of the <strong>processing</strong><br />
associated with Correlation including details of the bandwidth and integration rate limits required.<br />
Beamforming allows the field of view available to the telescope to be expanded by combining<br />
receptors into arrays to allow directional reception of <strong>signal</strong>s.<br />
Incoming <strong>signal</strong><br />
Elements<br />
+ + + + + + + + + + + + + + + + + + + + + + + + Beam<br />
C0I0+ C1I1+ C2I2+ C3I3+ C4I4+ C5I5 + C6I6+ C7I7+ C8I8+ C9I9+ C10I10+ C11I11+ C12I12+ C13I13+ C14I14+ C15I15+ C16I16+ C17I17+ C18I18+ C19I19+ C20I20+ C21I21+ C22I22+ C23I23<br />
C 0 I 0 + C 1 I 1 + C 2 I 2 + C 3 I 3 + C 4 I 4 + C 5 I 5 +......<br />
Figure 5 Beamforming<br />
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<strong>The</strong> formation of beams is achieved by introducing geometric delays for each receptor and summing<br />
across all receptors in the array Figure 1. By the manipulation of the individual delays the direction<br />
of the beam can be steered and even multiple beams generated. A useful approximation to<br />
introducing time delays is phase delay; however, this is only applicable if the bandwidth time<br />
product is much less than unity. <strong>The</strong> use of phase delay techniques reduces the beamforming to<br />
multiplying each data stream from a receptor by a complex coefficient prior to adding the data.<br />
For the SKA1 beamforming within the Signal <strong>processing</strong> domain is limited to Central beamforming.<br />
This forms beams across dishes and/or AA_low beams within the central 5km diameter core.<br />
Further details are provided in section 8<br />
Non‐Imaging Processing is a term used for:<br />
<br />
<br />
<br />
Pulsar search<br />
Pulsar Timing<br />
Transients detection<br />
At present only Pulsar Search and Timing is part of the SKA with transient detection being SKA2.<br />
However aspects of transient detection require consideration as part of the extensibility of SKA1.<br />
Common to all three of these is De‐dispersion which refers to the process of correcting frequency<br />
dependent time delays introduced as a result of the properties of the Inter‐Galactic medium through<br />
which the received <strong>signal</strong>s are likely to have propagated through. Several techniques have been<br />
developed to provide this <strong>processing</strong> and these are detailed in section 9.<br />
Pulsar searching and more specifically the techniques developed for the detection of binary pulsar<br />
systems is detailed in section 10.<br />
Pulsar Timing is detailed in section 11<br />
Having identified the types of <strong>processing</strong> included as part of the <strong>signal</strong> <strong>processing</strong> domain, it is<br />
informative to provide a diagram illustrating some lower <strong>level</strong> detail and how individual blocks<br />
logically relate to each other.<br />
Figure 6 provides an Internal Block Diagram the Signal Processing. This is a representative logical<br />
implementation and may develop with the definition phase of the project as lower architectural<br />
issues are identified.<br />
Details of the lower <strong>level</strong> blocks will be covered in the remaining sections of this document.<br />
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ibd [block] system [Signal Processing IBD]]<br />
ibd [block] system [Correlator CentralBeamformer IBD]]<br />
RF + RFI Dish<br />
RF + RFI AA_low<br />
«block»<br />
:Delay<br />
Compensation<br />
Buffer Dish<br />
«block»<br />
:Delay<br />
Compensation<br />
Buffer SAA<br />
«block»<br />
:Coarse<br />
Channelisation<br />
«block»<br />
:RFI Mitigation<br />
«block»<br />
:Fine<br />
Channelisation<br />
& Fractional Bit<br />
Rotation<br />
0..1<br />
«block»<br />
:Corner Turn<br />
«block»<br />
:Stokes<br />
Correlation<br />
«block»<br />
:Integration<br />
Science<br />
Computing<br />
C&M<br />
«block»<br />
:Coefficient<br />
Generation<br />
«block»<br />
:Central<br />
Beamforming<br />
RFI<br />
Database<br />
Time Reference<br />
«block»<br />
: I I 2<br />
ibd [block] system [Non Imaging Processing IBD]]<br />
ibd [block] system [Pulsar Survey IBD]]<br />
«block»<br />
:DeDispersion<br />
«block»<br />
:Binary Search<br />
«block»<br />
:Harmonic Sum<br />
«block»<br />
:Whitening&<br />
Normalisation<br />
«block»<br />
:Candidate<br />
Selection<br />
Science<br />
Computing<br />
ibd [block] system [Pulsar Timing]]<br />
«block»<br />
:Coherent<br />
DeDispersion<br />
«block»<br />
:Folding<br />
Science<br />
Computing<br />
«block»<br />
:Pulse arrival<br />
Time Prediction<br />
Ephemeris<br />
& PolyCo.<br />
Figure 6 Internal Block Diagram of SKA1 Signal Processing<br />
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<strong>The</strong> effectiveness of mitigation is limited by the estimation and detection accuracies of the <strong>signal</strong>s<br />
involved. Different astronomical observing modes may require different interference mitigation<br />
techniques and approaches. Examples of these modes are spectral line observations, polarisation<br />
measurements, synthesis imaging, and pulsar research.<br />
<strong>The</strong>re are many ways to define categories for interference, such as narrow band or wide band, fixed<br />
or moving sources, categories based on statistical properties (e.g. spatial and temporal coherence)<br />
or based on modulation type, distinctions based on the amount of a‐priori information of the<br />
transmitter or on differences in spatial properties or polarisation, categories based on field strength,<br />
power and temporal spectral occupancy, and categories of overlapping <strong>signal</strong> parameter domains.<br />
Clearly, a great diversity of approaches is possible, and in choosing an optimal approach the<br />
following should be considered:<br />
<br />
<br />
Depending on the interference properties, the architecture of the radio telescope and the type<br />
of observation, the same RFI mitigation technique can be useless or very efficient.<br />
Efficiency is generally linked with specificity. <strong>The</strong> more a priori information on the RFI can be<br />
exploited, the better will be the RFI mitigation algorithm.<br />
In other words, it is impossible to define one single approach which will cover all current and future<br />
scenarios. <strong>The</strong> consequence is that several (as far as possible “orthogonal”) methods have to be<br />
implemented such that they can be used in conjunction. For exotic or unexpected scenarios, the<br />
radio telescope architecture should be flexible enough to allow reallocation of <strong>signal</strong> <strong>processing</strong><br />
resources to RFI mitigation.<br />
<strong>The</strong> RFI challenge in the SKA candidate sites in Australia and South Africa may not be so great. Under<br />
this assumption, one basic or recurrent scenario could be to carefully design the analogue parts,<br />
taking RFI threats into consideration, but to limit the digital measures to “flagging". In that case, the<br />
digital <strong>signal</strong> <strong>processing</strong> resources could be fully dedicated to regular <strong>signal</strong> <strong>processing</strong> tasks most of<br />
the time and could be partially re‐used (scheduled) for observations facing specific RFI issues.<br />
In particular, it would be worthwhile to continuously monitor the quality of the data. Given the<br />
extreme sensitivity of the SKA telescope, this task has to be a by product of the radio telescope itself<br />
(i.e. an auxiliary antenna will not be sensitive enough). So, it would be interesting to implement<br />
some detection methods (to be defined) as regular <strong>signal</strong> <strong>processing</strong> tasks at station <strong>level</strong> and core<br />
<strong>level</strong>. <strong>The</strong> results could be linked to a kind of RFI statistics database or could be attached to the data<br />
for flagging.<br />
Table 1 shows a table describing what class of RFI mitigation techniques could be applied at the<br />
different <strong>level</strong>s of the SKA <strong>signal</strong> flow, from antenna <strong>level</strong> to core <strong>level</strong>. In addition, this table<br />
provides some pro's and con's, assuming that the corresponding implementation will be done in the<br />
digital domain. However, it appears that their impact on both the image residual and the calibration<br />
effectiveness is not fully understood yet, especially in the case of spatial filtering techniques and<br />
many of the paetric techniques. Besides, none of the techniques have been applied in very large<br />
scale telescope arrays.<br />
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Signal Path Method Pro’s Con’s<br />
Antenna<br />
beam‐formers<br />
(e.g. PAF)<br />
varying spatial filtering,<br />
including sidelobe<br />
canceller<br />
reduce strong RFI enables<br />
the use of less ADC bits /<br />
lessens LNA req.<br />
fluctuating beam may<br />
impair calibration<br />
fixed spatial filtering<br />
reduce strong RFI enables<br />
the use of less ADC bits<br />
/lessens LNA req.<br />
difficult; needs careful<br />
calibration<br />
[excision]<br />
lower SP load at output<br />
station beamformers<br />
‐<br />
Station<br />
beamformers<br />
fixed spatial filter<br />
very cheap; reduce data<br />
transport rate to central site<br />
more complex operation;<br />
connection with central<br />
systems<br />
varying spatial filters,<br />
sidelobe canceller<br />
somewhat better<br />
suppression than fixed;<br />
tracking possibilities<br />
may be costly; changing<br />
sidelobes may impair<br />
calibration<br />
excision (assuming no<br />
subband filtering is<br />
done yet)<br />
low SP load unless booking<br />
is done on excised samples;<br />
fast transients<br />
bookkeeping very costly;<br />
impairing gain estimate<br />
otherwise<br />
parametric techniques<br />
(assuming wide bands)<br />
can be used in combination<br />
with other methods<br />
may be costly<br />
Precorrelation<br />
Interstation sidelobe<br />
cancelling/ spatial<br />
filtering, moving sources<br />
may be applicable at shorter<br />
timescales than at location<br />
of correlator output<br />
influences UVW data<br />
points; may impair<br />
calibration<br />
Correlation excision can be done at short<br />
timescales and short<br />
bandwidths; common<br />
practice<br />
may be complex; may be<br />
time consuming<br />
Table 1 RFI Mitigation options, pro’s and con’s.<br />
In Table 2, an estimate of the degree of maturity of the different RFI mitigation approaches is<br />
presented. Two evaluation scales are proposed, one based on current experimentations within<br />
existing radio telescopes (i.e. small/medium size radio telescopes) and another one based on the<br />
requirement for a large scale radio telescope such as envisioned in the SKA project. In that case, the<br />
different <strong>level</strong>s have been associated to some fundamental steps in the SKA design process, which<br />
are:<br />
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RFI Mitigation Algorithms TRL Justification<br />
a. Excision 6 Post Correlation Narrowband Flagging –TRL 9<br />
Pre Correlation Narrowband Excision –TRL 8<br />
Pre Correlation Broadband Excision –TRL 8<br />
b. Detection 6 Power Detection – TRL9<br />
Analysis based on analysis of the pdf‐ TRL 7<br />
Higher Order Statistics detection e.g. Kurtosis – TRL 9<br />
Cyclo Stationary Detection – TRL7<br />
Multiple Antenna Detection subspace techniques – TRL7<br />
c. Spectral Filtering 5 Band Selection – TRL9<br />
Notch Filtering out of band – TRL9<br />
Notch Filtering in band TRL 1<br />
Cyclostationary Spectral Filtering – TRL3 ‐7<br />
d. Spatial Filtering 5 Spatial filtering at (phased array) station <strong>level</strong> – TRL7<br />
Pre‐correlation spatial filtering – TRL7<br />
Post Correlation filtering using closure phases – TRL3‐8<br />
Spatial filtering using reference antennas – TRL7<br />
Spatial Filtering using cyclostationary – TRL3<br />
e. Single Channel<br />
Filtering<br />
f. Miscellaneous<br />
Techniques<br />
5 Subtraction of estimated RFI waveform – TRL7<br />
Parametric RFI estimation and subtraction – TRL3‐7<br />
3 Polarisation based RFI Mitigation – TRL1<br />
Fringe rotation Techniques – TRL3<br />
RFI suppression by delay smearing – TRL3<br />
Imaging and post‐correlationRFI removal using clean and<br />
beamforming techniques – TRL3<br />
Estimating RFI correlation matrix using cyclo‐stationary<br />
techniques – TRL3<br />
Table 2 Technology Readiness Levels of RFI mitigation methods.<br />
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As part of forming the coherently de‐dispersed data, methods of RFI excision can be applied. <strong>The</strong>re<br />
are a number of possible mechanisms by which RFI rejection might occur and it may be that until<br />
data from the pathfinders are in place that it isn’t known what will be necessary.<br />
At present it is assumed that RFI mitigation is based on the flagging of frequency channels that are<br />
suspected of being contaminated. <strong>The</strong> flagging is based on two strategies:<br />
<br />
<br />
<br />
<strong>The</strong> use of historic data provided via an RFI data base<br />
Threshold detection based on the auto correlation of individual frequency channels<br />
Detections within the Signal Processing chain can potentially in feed to the RFI data base.<br />
A basic algorithm would be that a mask of known frequencies which correspond to RFI, such a list<br />
might be made up from previous observations. Such an algorithm would be at a relatively low<br />
computational load and may be built into the channelization or de‐dispersion step by blanking<br />
channels.<br />
7 Correlator<br />
bdd [block] system [Correlator & Central Beamformer definitions]<br />
«block»<br />
Correlator<br />
«block»<br />
RFI Mitigation<br />
«block»<br />
Channeliser<br />
«block»<br />
Full Stokes<br />
Correlator<br />
«block»<br />
Central<br />
Beamformer<br />
«block»<br />
Delay<br />
Compensation<br />
Buffer<br />
«block»<br />
CornerTurn<br />
«block»<br />
Monitor&<br />
Control<br />
«block»<br />
Channeliser<br />
Coarse<br />
«block»<br />
Channeliser<br />
Fine<br />
Figure 7 Correlator Definition<br />
This section provides details on the functional breakdown of the correlator in accordance with Figure<br />
7 and provides <strong>processing</strong> sizing and bandwidth estimates.<br />
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7.1 Delay Compensation Buffer<br />
Digital data received at the channeliser is compensated with respect to <strong>signal</strong> propagation delay by<br />
use of a data buffer. This buffer may also form a storage area for test data in off line test<br />
diagnostics. This delay compensation is only time sample accurate for the received <strong>signal</strong>.<br />
<strong>The</strong> propagation delay is a function of the communication path length which as a first approximation<br />
is taken as the base‐line length which is nominally 200km and over 3000km for SKA1 and SKA2<br />
respectively. In reality the communication path will not be point to point and as a result will be<br />
greater than the baseline length.<br />
Assuming the <strong>signal</strong> propagates at the speed of light in optical cable (2 x 10 8 m/s ‐1 ) , the buffer depth<br />
will need to compensate for 1ms and 15ms delay for baselines of 200km and 3000km respectively.<br />
For SKA phase 1 dishes:<br />
_ 250 <br />
200 10<br />
2 10 1 10 2 4 <br />
~ 2 <br />
For SKA phase 1 Sparse Aperture Arrays:<br />
_ 50 <br />
200 10<br />
2 10 480 0.35 10 2 4 <br />
~ 67 <br />
This assumes that all baselines require the same amount of storage as the maximum leading to an<br />
over estimate in the memory requirement. Only storing data applicable to the delay for each<br />
baseline can reduce the memory requirements but at the expense of complexity of the memory<br />
management. A potential compromise could be to use a few block ranges of baseline length with<br />
associated delays. <strong>The</strong> effectiveness is quite <strong>high</strong> due the <strong>high</strong> percentage of antenna within the<br />
core.<br />
7.2 Channeliser<br />
Channelization refers to the process of splitting the received RF base banded <strong>signal</strong> into a contiguous<br />
set of narrow frequency channels. This section specifically describes the process in association with<br />
imaging. <strong>The</strong>re are four reasons why channelization is required:<br />
<br />
<br />
<br />
<br />
To facilitate the approximation of phase shift to time delay for digital domain beam‐forming<br />
To provide the frequency resolution appropriate to the time resolution for Non‐Imaging<br />
computing<br />
To minimise the radial smearing of U‐V data.<br />
To minimise the impact of RFI<br />
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<strong>The</strong> first of these requires that the worst case bandwidth time product of the incident wave‐front<br />
across the collection (station) of receptors used to digitally form beams using phase shifting<br />
techniques is much less than unity.<br />
It should be noted that the requirements of channelization for Non‐Imaging Processing differ from<br />
those associated with imaging <strong>processing</strong>. <strong>The</strong> frequency resolution, ∆ν, of the channeliser<br />
corresponds to the required time resolution of 50us for pulsar sear and .2us to 1 us pulsar timing:<br />
∆ <br />
1<br />
<br />
20 , 1 5 <br />
For Sparse Aperture Arrays some channelization will be implemented at the array as part of the<br />
station beamforming process.<br />
When considering the overall SKA, the radial smearing of U‐V data is detailed in Thompson, Moran<br />
and Swenson’s Interferometry and Synthesis in Radio Astronomy, the relative amplitude, R a ,<br />
produced for a bandwidth ∆ν at an observation frequency ν o , is approximated by the expression:<br />
<strong>The</strong> radius, , of the Field of View is proportional to <br />
the antenna diameter in metres.<br />
where is the wavelength and d<br />
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And the synthetic beam radius, , is proportional to<br />
baseline.<br />
<br />
<br />
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where D max is the maximum<br />
<br />
∆ <br />
0.939 1<br />
2<br />
1 <br />
<br />
<br />
An accepted simplification is:<br />
∆ <br />
<br />
<br />
~ 1 10 <br />
<br />
<br />
Consequently the frequency cell width required is inversely proportional to the maximum baseline<br />
for a given observation frequency and amplitude smearing.<br />
For dishes with less than 2 percent smearing over a 200 km baseline:<br />
∆ 3 10<br />
0.939 1<br />
.98 1 15<br />
200000 <br />
∆ 49 <br />
For Sparse AAs with less than 2 percent smearing over a 200 km baseline:<br />
∆ 3 10<br />
0.939 1 180<br />
1 <br />
.98 200000 <br />
∆ 590 <br />
In both case this is less stringent than the frequency resolution requirement of 2kHz identified for<br />
the DRM Chapter 11: Tracking Galaxy Evolution over Cosmic Time using H1 Absorption.<br />
Recently, channelisation is typically implemented using the Multiband Filtering techniques based on<br />
an FFT architecture, though hierarchical FIR filtering has also been used on the WIDAR correlator.<br />
<strong>The</strong> disadvantage of the Multiband filter technique is the leakage between frequency channels.<br />
However this can be resolved by oversampling techniques as demonstrated on the ASKAP path<br />
finder project. In this case, the channelization is split into two stages: coarse channels before beamforming<br />
and fine channels after beam‐forming. A <strong>description</strong> of the technique is provided in ALMA<br />
Memo 447. <strong>The</strong> <strong>processing</strong> load per antenna feed per polarisation is dependent on the quality of the<br />
multiband filter response, the FFT size and the amount of up‐sampling applied. It can be shown the<br />
number of taps in the form of a FIR filter is proportional to the ratio of the original sample frequency<br />
over the filter transition band (Crochiere, R E and Rabiner, L R: Optimum FIR Digital Implementations<br />
for Decimation , Interpolation and Narrowband Filtering. Ballanger, M G: Computation Rate and<br />
Storage Estimation in Multirate Digital Filtering with Half‐Band Filters)<br />
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<br />
. <br />
∆<br />
where 2 < k < 4 depending on the amount of pass‐band and stop‐band ripple that is acceptable and<br />
f old is the pre‐decimated sample rate.<br />
Figure 8 shows two adjacent channels of the multiband filter that has been up‐sampled to provide<br />
separation between frequency channels.<br />
Figure 8 Adjacent Channels Multiband Filter<br />
<strong>The</strong> up‐sampling is achieved by overlapping the incoming data to provide a channel frequency<br />
separation of f s . <strong>The</strong> channel width is f and the width of the frequency channel at half the rejection<br />
amplitude is f so .<br />
<strong>The</strong> up‐sampling is achieved by overlapping the incoming data stream by a factor that is a ratio of<br />
two integer values p and q such that:<br />
<br />
<br />
<br />
<br />
Where N overlap is the number of samples that are overlapped.<br />
<strong>The</strong> <strong>processing</strong> load for the channelization is therefore:<br />
1 2 2 <br />
Typically the channelizer will be implemented in two or more sequential stages: course through to<br />
fine. <strong>The</strong> finer resolution channelizer is implemented on each of the time series emerging from the<br />
up‐stream up‐sampled coarser channelizer .<br />
7.3 Corner Turn<br />
<strong>The</strong> data produced by the channeliser is a streamed set of frequency channels for each receptor.<br />
However, the cross correlation process used in the full Stokes Correlator may require (depending on<br />
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architecture) the data be reordered such that a set of data from all receptors for each frequency<br />
channel is provided.<br />
7.4 Full Stokes Correlator<br />
Full Stokes Correlation is provided by the correlator to provide a set of U‐V plane points for each<br />
frequency channel and beam direction.<br />
<strong>The</strong> number of correlations<br />
<br />
1<br />
2<br />
<br />
<br />
Where N ant is the number of stations, N Beams is the number of beams generated per station and N chan<br />
is the number of frequency channels generated by the channelizer.<br />
<strong>The</strong> correlator <strong>processing</strong> load, C, is independent of the number of frequency channels, N Chan as the<br />
correlation rate is inversely proportional to the number of channels.<br />
2<br />
16 Ω<br />
<br />
1.2 180 2<br />
<strong>The</strong> resultant correlation data can be integrated to reduce bit rate. <strong>The</strong> maximum integration period<br />
is determined by the acceptable <strong>level</strong> of smearing of U‐V data due to the rotation period of the Earth<br />
against the sky.<br />
7.4.1 Correlation Integration Period<br />
From [22], the relative amplitude produced for an integration period, τ a , is approximated by the<br />
expression:<br />
1 1 2<br />
3 0.8326 <br />
<br />
2<br />
1 2 1 2 0 <br />
<br />
Identifying the term (l 1 2 + m 1 2 sin 2 δ 0 ) as the radius squared of the maximum field of view the<br />
equation can be rearranged to provide the maximum integration time, τ a , in terms of a desired<br />
smearing constraint on R a<br />
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<br />
31 <br />
0.8326 <br />
<br />
1<br />
<br />
<strong>The</strong> radius, , of the Field of View is proportional to .<br />
And the synthetic beam radius, , is proportional to<br />
<br />
<br />
.<br />
<strong>The</strong> Earth’s rotation, ω e = 7.92 x 10 ‐5 radians per second<br />
31 <br />
0.8326 <br />
<br />
<br />
<br />
<br />
31 0.98<br />
0.8326 7.92 10 15<br />
200 10 <br />
<strong>The</strong> output rate of the correlator is to be minimised to limit the load on the Imaging Computing. This<br />
is achieved by integrating the Correlation results. However, integration has the effect of smearing<br />
the data and reducing the amplitude from the peak response to a point source due to the effects of<br />
the Earth’s rotation through the fringes.<br />
Currently the DRM calls for less than 2 percent smearing which corresponds to > 0.98<br />
<br />
<br />
<br />
32 ∆<br />
<strong>The</strong> upper frequency taken to calculate the integration time is either the maximum capability of the<br />
receptor or the upper frequency of the Science requirement depending on which is the lower. On<br />
this basis, more than one receptor technology may be required to provide the required frequency<br />
coverage.<br />
In the more general case, the frequency coverage of individual technologies may differ from the<br />
values quoted and may even provide overlaps in frequency across technologies. This provides the<br />
option of correlation across receptor technologies which are likely to have differing sample rates. In<br />
this case, interpolation of the data streams is required to provide sample <strong>level</strong> time alignment for<br />
the correlation process. Further work is required to identify the associated <strong>processing</strong> load and<br />
evaluate the merits of correlating across receptor types.<br />
7.4.2 Correlator Processing Load<br />
<strong>The</strong> correlator is full Stokes with a <strong>processing</strong> load proportional to the square of the number of<br />
antennas, N a and <strong>signal</strong> bandwidth, BW. Nominally, the load is independent of the number of<br />
frequency channels<br />
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<br />
1<br />
2<br />
4 <br />
/<br />
For dishes SKA phase 1<br />
<br />
250 250 1<br />
2<br />
4 2.55 10 2 8 ~ 8 <br />
/<br />
For Sparse Aperture Array<br />
<br />
50 50 1<br />
1440 4 380 10 2<br />
2<br />
8 ~ 42 /<br />
<strong>The</strong> memory requirements for the Correlator output are potentially significant with the<br />
compounded effect of the number of baselines, the number of channels N chan and number of beams<br />
N beams<br />
1<br />
2<br />
<br />
For SKA phase 1 dishes<br />
<br />
250 250 1<br />
2<br />
1 10<br />
1 10 1 4 <br />
~ 125 <br />
For SKA phase 1 Aperture Arrays<br />
<br />
50 50 1<br />
2<br />
<br />
380 10<br />
1 10 480 4 <br />
~ 1 <br />
As mentioned previously the number of channels increases with baseline length. Only storing the<br />
required number of channels for each baseline can reduce the memory requirements but at the<br />
expense of complexity of the memory management. A potential compromise could be to use a few<br />
block ranges of baseline length with associated numbers of channels. <strong>The</strong> effectiveness is quite <strong>high</strong><br />
due the <strong>high</strong> percentage of antenna within the core.<br />
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8 Central Beamformer<br />
At present it is assumed that there will be thirty five 180 metre diameter AA_Low arrays in the<br />
central 5 km core and 175 15 metre diameter dishes and these will be used for phase 1 Pulsar<br />
Searching .<br />
<strong>The</strong> following frequency ranges are being considered for SKA1<br />
AA_Low:<br />
Dish 1 :<br />
Dish 2 :<br />
Dish 3 :<br />
350 – 450 MHz.<br />
450MHz – 1 GHz<br />
1GHz – 2 GHz<br />
2GHz – 3 GHz<br />
In general, the Field of View of diameter D at wavelength, λ, is:<br />
180<br />
1.2 <br />
4 <br />
<strong>The</strong> SKA1 DRM [45] requires a 36,000 deg 2 surveys to be completed within two years. Assuming the<br />
survey is made up of individual 600 second observations and that only 200 days of the 2 years are<br />
used for different observations(to allow time for repeat observations and calibration), then 1.25<br />
deg 2 are required per observation.<br />
Consequently, the number of beams from a 180m diameter station to fill the required 1.25 square<br />
degrees for pulsar <strong>processing</strong> at the upper frequency of 450MHz is:<br />
<br />
1.25<br />
180<br />
1.2 <br />
4 <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
180<br />
1.2 <br />
4 <br />
1.25<br />
3 10 <br />
450 10 180 <br />
25 <br />
This does not include any over‐lapping of beams that may be required.<br />
<strong>The</strong> total data rate from N SAA aperture arrays with bandwidth B SAA is:<br />
2 2 <br />
35 25 450 350 10 2 2 4 1 /<br />
<strong>The</strong> total data rate from N dish dishes with instantaneous bandwidth B dish is:<br />
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8.1 Buffer<br />
2 2 <br />
_ 175 1000 450 10 2 2 4 1.5 /<br />
_ 175 2000 1000 10 2 2 4 2.8 /<br />
_ 175 3000 2000 10 2 2 4 2.8 /<br />
A buffer is provided to compensate for the time of arrival of data arriving from the Sparse Aperture<br />
Arrays. <strong>The</strong> maximum difference in time of arrival for phase 1, t tr , is the time for optical <strong>signal</strong>s to<br />
travel 2.5 km which is of the order of 8.3 us.<br />
<strong>The</strong> minimum memory requirement for AA_low is then:<br />
For dishes:<br />
480 2 2 <br />
225 <br />
2 2 <br />
25 <br />
8.2 Voltage Storage<br />
<strong>The</strong> incoming data rate from the AA_Low Arrays for 1.25 square degrees FoV has been shown to be<br />
of the order of 1 T bits per second for phase 1 and dishes up to 2.8 T bits/s. <strong>The</strong> observation time<br />
T obs is of the order of 600 seconds.<br />
Consequently, to store an observation’s worth of receptor data requires at least 210 T Bytes of disk<br />
storage. This does not include the overhead for metadata which is assumed to be of the order of<br />
10%<br />
8.3 Beamforming<br />
Beam‐forming allows individual receptor elements to be combined in such a way that the resultant<br />
beam can be steered. To maintain optimum sensitivity beam‐forming should ideally be performed<br />
coherently either by introducing finely controlled time delays or – under narrowband conditions –<br />
phase delays.<br />
Central beam‐forming for SKA1 is used to form beams across dishes or AA_Low station beam sets to<br />
meet the requirements of the pulsar survey and timing chapters of the DRM including the survey<br />
“on‐sky” time.<br />
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Smits et al [41] show that beam‐forming is more efficient if implemented hierarchically using subarrays<br />
and the number of operations for the beam‐forming is N osb :<br />
2 _ 2<br />
<br />
<br />
<br />
where B is the Bandwidth and ξ is a factor to allow for the possible extension of the FoV by the use<br />
of PAFs which takes the value of one for single pixel feeds.<br />
For aperture arrays the <strong>processing</strong> load is given by:<br />
1.25 <br />
<br />
180 2 <br />
2<br />
2<br />
Receptor Bandwidth G Hz N osb N beams<br />
Dish<br />
2GHz to 3GHz<br />
Dish 1 GHz to 2GHz 6 x 10 15 operations 111,111*<br />
Dish 0.45 to 1GHz 3 x 10 15 operations 111,111**<br />
AA_low 0.35 to 0.45 GHz 8 x 10 13 operations 18,981<br />
* Dish FoV less than 1.25 deg 2<br />
**Dish FoV more than 1.25 deg 2<br />
Smits also suggests that the second stage of hierarchical beam‐forming might be incoherent to<br />
reduce the number of beams required. However this reduces sensitivity by a factor of<br />
<br />
Beam‐former Output rate:<br />
∆ 2 _<br />
<strong>The</strong> number of bits at the beam‐former output to ensure there is no clipping is 14 which assumes for<br />
each beam a single 4 bit multiply (array data and coefficient) followed by 35 accumulates into a 14<br />
bit accumulator.<br />
.<br />
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9 De‐Dispersion<br />
bdd [block] system [DeDispersion definitions]<br />
«block»<br />
DeDispersion<br />
«block»<br />
Coherent<br />
«block»<br />
Incoherent<br />
«block»<br />
Delay & Sum<br />
«block»<br />
Accumulation<br />
& Difference<br />
«block»<br />
Taylor Tree<br />
«block»<br />
PreSumming<br />
«block»<br />
Multiple<br />
Sample<br />
Period<br />
«block»<br />
Frequency<br />
Partitioning<br />
9.1 Incoherent Dedispersion<br />
Incoherent de‐dispersion involves <strong>processing</strong> the received <strong>signal</strong> after it has been detected, that is<br />
after it has been channelized into its spectral components (via a filterbank) and after the <strong>signal</strong>s<br />
from each of its channels have been converted to intensity‐like quantities via a square‐law detector.<br />
At this point, <strong>processing</strong> is deemed to be incoherent since the resulting <strong>signal</strong>s do not contain any<br />
phase information.<br />
Incoherent de‐dispersion corrects for dispersion by advancing the spectral components of the <strong>signal</strong><br />
by the dispersive delays predicted for an assumed dispersion measure. As lower frequencies are<br />
dispersed more than <strong>high</strong>er frequencies, this is achieved by delaying the <strong>high</strong>er frequency<br />
components so that they coincide with the expected arrival time of the lowest frequency<br />
component. <strong>The</strong> re‐aligned <strong>signal</strong> components are then summed together to produce a de‐dispersed<br />
version of the input <strong>signal</strong> for the assumed DM.<br />
Delays and sums are common digital <strong>signal</strong> <strong>processing</strong> operations. In digital de‐dispersion systems,<br />
where each <strong>signal</strong> channel consists of a digitised stream of samples, significant delays can be applied<br />
to individual channels by storing samples within memory. <strong>The</strong> storage forms a frequency time array<br />
from which samples can be retrieved and summed using digital accumulators.<br />
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9.2 Delay and Sum Dedispersion<br />
A delay‐and‐sum approach to de‐dispersion, described in [31], involves summing the frequency‐time<br />
samples for each of the assumed dispersion measures in turn, completing the sums for all dispersion<br />
measures within one sample interval, then advancing the frequency‐time array by a sample interval<br />
and commencing the next round of additions. This procedure suffers from the following memory<br />
bandwidth inefficiencies:<br />
a. Some samples are needed in the sums for different dispersion measures and are read<br />
from memory multiple times within a sample interval.<br />
b. <strong>The</strong> samples needed for de‐dispersion are distributed in small clumps through‐out the<br />
frequency‐time array. This inefficiency is particular to SDRAM technology which relies on<br />
burst accesses to contiguous memory locations in order to achieve <strong>high</strong> access bandwidths.<br />
By itself the delay‐and‐sum algorithm scales poorly with the number of <strong>signal</strong>s being de‐dispersed<br />
and with finer time and frequency resolutions. For more scalable systems, additional and/or<br />
alternative techniques are necessary to overcome these inefficiencies.<br />
9.3 Pre‐summing channels for large dispersion measures<br />
With delay‐and‐sum de‐dispersion, summations for large DMs consume a greater proportion of<br />
memory bandwidth than those for small DMs, because they are dispersed across a greater number<br />
of samples in the memory's frequency‐time array. For large DMs, most of the array samples that<br />
need to be summed occupy successive time intervals within common frequency channels. This latter<br />
fact can be exploited by summing the samples before storing them to memory so that fewer<br />
samples need to be read back from memory for de‐dispersion.<br />
One such scheme involves several <strong>level</strong>s of sample integrations, with separate frequency‐time arrays<br />
for each integration <strong>level</strong>. <strong>The</strong> lowest integration <strong>level</strong>, <strong>level</strong> 0, is used to de‐disperse the lowest<br />
group of DMs using the delay‐and‐sum algorithm described earlier. For <strong>level</strong> 1, every pair of samples<br />
are summed and the summed samples are stored to the frequency‐time array for <strong>level</strong> 1. <strong>The</strong> <strong>level</strong> 1<br />
frequency‐time array is used to de‐disperse the next group of larger DMs. Likewise, every pair of<br />
<strong>level</strong> 1 samples are summed and stored to the frequency‐time array for <strong>level</strong> 2, which is used to dedisperse<br />
the next group of larger DMs; and so it goes on for the <strong>high</strong>er <strong>level</strong>s.<br />
Note that the sample times of the <strong>level</strong> i samples become twice the sample times of the <strong>level</strong> i‐1<br />
samples, thus de‐dispersions at <strong>high</strong>er <strong>level</strong>s are performed at courser and courser time resolutions.<br />
Generally, this reduces the <strong>signal</strong>‐to‐noise ratio of the de‐dispersed <strong>signal</strong>s, but courser time<br />
resolutions have less of an impact on the SNR of more <strong>high</strong>ly dispersed <strong>signal</strong>s, because they are<br />
more temporally dispersed and scattered [35], so the reduction in SNR can be controlled by careful<br />
selection of the DMs for each <strong>level</strong>. Using this pre‐summing technique with only 4 <strong>level</strong>s, while<br />
maintaining more than 90% of the SNR, the memory bandwidth can be reduced by a factor of 5.<br />
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9.4 Accumulating and differencing algorithm<br />
Another scheme devised to reduce the memory bandwidth by pre‐summing the samples is<br />
documented in [39]. In this scheme, the de‐disperser maintains an accumulator at its input for each<br />
frequency channel. <strong>The</strong> accumulators continuously sum the samples that the de‐disperser receives<br />
every sample interval for the corresponding channels, and the accumulators are allowed to<br />
wraparound when they overflow. Rather than storing the received samples to memory, the dedisperser<br />
captures the state of each accumulator to memory once every sample interval.<br />
To determine the sum of the samples for a given DM within a frequency channel, the de‐disperser<br />
need only read two values from memory: the accumulated value one sample before the start of the<br />
pulse dispersed within that channel, and the accumulated value at the end of the pulse dispersed<br />
within that channel. <strong>The</strong> de‐disperser reads these two values and differences them, thus reducing<br />
the sum of potentially many samples to a difference of just two accumulator values per channel. <strong>The</strong><br />
number of bits per accumulator is necessarily larger than the number of bits per sample and<br />
therefore more memory is required to store the accumulations, but depending on the range of DMs<br />
searched, significant memory bandwidth can be saved using this approach.<br />
For low DMs where pulses are dispersed across less than two samples per frequency channel, this<br />
method actually increases the amount of <strong>processing</strong> and memory bandwidth needed, since it always<br />
retrieves and differences two accumulations per channel, whereas only one or two samples per<br />
channel would need to be retrieved from memory using the delay‐and‐sum approach. Greater<br />
optimization is therefore achievable by reserving this method for <strong>high</strong>er DM values.<br />
9.5 De‐dispersion over multiple sample intervals<br />
<strong>The</strong> schemes described so far perform de‐dispersion operations for each DM independently, one<br />
after another, without taking advantage of the fact that most samples are needed in the dedispersion<br />
calculations for other DMs. Also, for a given DM, they calculate each successive value of<br />
the dedispersed <strong>signal</strong> independently, without taking advantage of the fact that most samples are<br />
needed in the calculations for several successive de‐dispersion values.<br />
Within a period of multiple sample intervals, each sample is retrieved from memory only once and is<br />
reused across an array of parallel accumulators – one accumulator per DM per sample interval<br />
within the period. This technique improves memory efficiency by using larger period sizes, but at the<br />
expense of larger arrays of accumulators and greater latency (proportional to the size of the period).<br />
9.6 Taylor tree based algorithms<br />
<strong>The</strong> de‐dispersion algorithms described to this point involve many redundant operations in that they<br />
add the same samples multiple times for different DMs. Taylor tree de‐dispersion [33] reduces<br />
<strong>processing</strong> by avoiding redundant additions performed within a sample interval across all DMs.<br />
A Taylor tree consists of a network of delay and sum elements inter‐connecting N inputs with N<br />
outputs. Figure 9 illustrates a four‐channel Taylor tree (N = 4) with delay elements represented by<br />
their Z‐transform. Each input, in, represents a channel of the dispersed <strong>signal</strong>, with iN‐1 being the<br />
channel of <strong>high</strong>est frequency. Each output, on, represents a de‐dispersed version of the <strong>signal</strong>, with<br />
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o0 having a DM of 0, and oN‐1 having the largest DM. <strong>The</strong> appealing feature of this structure is that<br />
the number of addition operations is equal to Nlog2N (whereas N2 additions are required when<br />
redundant additions are not avoided).<br />
Figure 9 4‐Channel Taylor Tree De‐disperser<br />
One of the shortcomings of Taylor trees is that they implement linear approximations to dispersion<br />
(not proportional to the inverse‐square of the frequency) which are less accurate for lower<br />
frequencies and wider bandwidths. However, [34] suggests that the input <strong>signal</strong> channels can be<br />
“linearized” by inserting redundant null channels between the existing channels. In effect, this<br />
spreads the <strong>signal</strong> out in frequency, with more spreading at lower frequencies so that the dispersion<br />
is linear before it is de‐dispersed through the Taylor tree.<br />
Another shortcoming of Taylor trees is that they search linear ranges of DMs from zero to the<br />
“diagonal” DM, i.e. the DM at which the dispersion gradient is one channel per sample interval. [34]<br />
suggests ways of extending the range of DMs searched by using an array of Taylor trees of equal size.<br />
<strong>The</strong> first tree in the array operates on the input channel samples to give a range of N dedispersions<br />
from a DM of zero to the diagonal DM. <strong>The</strong> second tree operates on a linearly delayed version of the<br />
input, where each channel is delayed in proportion to its channel number: channel 0 has no delay,<br />
and channel N‐1 is delayed by (N‐1) sample intervals. Thus the second tree produces another N DMs<br />
from the diagonal DM to twice the diagonal DM. For the third tree, the channel samples are<br />
summed in pairs and delayed as described above to give another N DMs from twice the diagonal DM<br />
to four times the diagonal DM; and so on. In this way the DM step size becomes exponentially larger<br />
in steps of N DMs.<br />
9.7 Frequency Partitioning<br />
Frequency partitioning is another technique that can be used to reduce the overall <strong>processing</strong><br />
required for de‐dispersion. <strong>The</strong> technique has been used in the Taylor tree de‐dispersion system<br />
described in [34] and Section 7.5.2 describes how it can be used with the delay‐and‐sum algorithm.<br />
<strong>The</strong> concept is simply to partition the channels into sub‐bands and to de‐disperse each frequency<br />
sub‐band individually. Better <strong>processing</strong> efficiency can be realised by virtue of the smaller frequency<br />
sub‐bands being less (and more linearly) dispersed. A second, coarser stage of dedispersion is<br />
needed to combine the de‐dispersed streams for each frequency sub‐band.<br />
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9.8 Coherent de‐dispersion<br />
An analysis in [35] shows that incoherent de‐dispersion can never completely remove the effects of<br />
dispersion from a <strong>signal</strong>, even if the dispersion measure is precisely known, because it only removes<br />
the inter‐channel effects of dispersion; it does not remove the dispersion that occurs within each<br />
finite width frequency channel. Coherent de‐dispersion on the other hand can (in theory) completely<br />
remove the effects of dispersion from a <strong>signal</strong>, given that the dispersion measure is known.<br />
Coherent de‐dispersion involves <strong>processing</strong> the received <strong>signal</strong> before it has been detected such that<br />
the <strong>signal</strong> maintains its phase information. Dispersion represents a rotation of the <strong>signal</strong>'s phase in<br />
proportion to the inverse‐square of the frequency, and coherent de‐dispersion therefore involves<br />
rewinding the dispersive phase rotation. Essentially, this is a de‐convolution procedure in which the<br />
convolution function (the impulse response of the dispersive medium) has the form of a “chirp”<br />
pulse.<br />
Algorithms for performing coherent de‐dispersion using dedicated hardware require further<br />
investigation.<br />
9.9 Concept sizing<br />
<strong>The</strong> SKA beams need to be buffered in channelized form for the length of an observation in order to<br />
be de‐dispersed at various dispersion measures and to resample for alternative accelerations. A<br />
typical search observation time T obs would be of the order 10 minutes long with the number of<br />
samples accumulating to twice this value for optimising the subsequent FFTs.<br />
<strong>The</strong> corresponding DM max for the frequency channel width, ∆ν, to restrict smearing to one time<br />
sample:<br />
∆ 1<br />
<br />
20<br />
<br />
3<br />
<br />
8.3 10 3 ∆<br />
Larger DMs will temporally smear over a larger time frame which leads to the concept of the<br />
diagonal DM. This involves dropping the time resolution used in de‐dispersion in quantum factors of<br />
2 as a function of DM whilst maintain the same frequency resolution.<br />
This relationship is correct if only interstellar dispersion is relevant, but interstellar scattering alters<br />
(reduces) the number of trial values needed. For large DMs the pulse broadening from scattering<br />
dominates the time resolution and so a coarser grid of DM values can be used as DM gets larger.<br />
<strong>The</strong> number of dispersion measures for a frequency band ranging from f min to f max in GHz and a<br />
sample time, t samp , in microseconds:<br />
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<br />
4150 max max 1 1 2<br />
1 2<br />
<br />
<br />
<br />
Table 3 provides details of the number of dispersion measures for both frequency ranges available<br />
from the dish and for the top 100 MHz of the sparse array for phase 1 of the SKA. <strong>The</strong> table assumes<br />
a DM diagonal where time resolution is traded against the maximum dispersion measure. To obtain<br />
<strong>high</strong> dispersion measure and <strong>high</strong> time resolution requires <strong>high</strong>er frequencies.<br />
This relationship is correct if only interstellar dispersion is relevant, but interstellar scattering alters<br />
(reduces) the number of trial values needed. For large DMs the pulse broadening from scattering<br />
dominates the time resolution and so a coarser grid of DM values can be used as DM gets larger.<br />
tsamp<br />
us<br />
DM max<br />
Dish<br />
2 – 3<br />
GHz<br />
N DM<br />
Dish<br />
2 – 3<br />
GHz<br />
DM max<br />
Dish<br />
1 – 2<br />
GHz<br />
N DM<br />
Dish<br />
1 – 2<br />
GHz<br />
DM max<br />
Dish<br />
.45 – 1<br />
GHz<br />
N DM<br />
Dish<br />
.45 – 1<br />
GHz<br />
DM max<br />
Sparse AA<br />
.35 ‐ 45<br />
GHz<br />
N DM<br />
Sparse<br />
AA<br />
.35 ‐ .45<br />
GHz<br />
50 2400 27,778 300 18,700 27 8,972 13 3,457<br />
100 4800 13,889 600 9,350 54 4,486 26 1,728<br />
200 1,200 9,350 108 4,486 52 1,728<br />
400 2,400 9,350 216 4,486 103 1,728<br />
800 4,800 9,350 432 4,486 207 1,728<br />
1,600 9,375 864 4,486 413 1,728<br />
Table 3 DM Diagonal<br />
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Figure 10 Dispersion measure, DM, for pulsars at different galactic latitudes. 1<br />
<strong>The</strong> Dispersion measure as a function of galactic Latitude is shown in Figure 1 which provides a<br />
graphical indication of the amount of sky that requires <strong>high</strong> dispersion measure searching. It can be<br />
envisaged that the Sparse AAs could be used to search off the galactic centre where the dispersion<br />
measures are not so <strong>high</strong> and the dishes used (possibly simultaneously) for the galactic centre.<br />
To estimate roughly the <strong>processing</strong> load, a hybrid version of Taylor tree dispersion is considered<br />
within the limitations detailed in section 9.6. <strong>The</strong> basic Taylor Tree structure is shown in Figure 9 for<br />
a 4 channel implementation. This structure is adapted to take advantage of the diagonal DM<br />
methodology where time resolution is traded against Dispersion Measure.<br />
Assuming zero padding of the number of frequency channels to the number of dispersion measures,<br />
the <strong>processing</strong> load per second for each element along the DM diagonal using a Taylor tree is<br />
Nd_ops:<br />
_ <br />
1<br />
<br />
1 (adapted from B. Klein (MPIfR) unpublished] and taken from Tools of Radio Astronomy: Wilson,<br />
Rohlfs and Huttemeister)<br />
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tsamp<br />
us<br />
N DM<br />
N D_ops<br />
(G MACs)<br />
N DM<br />
N D_ops<br />
(G MACs)<br />
N DM<br />
N D_ops<br />
(G MACs)<br />
N DM<br />
N D_ops<br />
(G MACs)<br />
Dish<br />
Dish<br />
Dish<br />
Dish<br />
Dish<br />
Dish<br />
Sparse AA<br />
Sparse AA<br />
2 – 3<br />
GHz<br />
2 – 3<br />
GHz<br />
1 – 2<br />
GHz<br />
1 – 2<br />
GHz<br />
.45 – 1<br />
GHz<br />
.45 – 1<br />
GHz<br />
.35 ‐ 45<br />
GHz<br />
.35 ‐ .45<br />
GHz<br />
50 27,778 8.2 18,700 5.3 8,972 2.4 3,457 0.8<br />
100 13,889 1.9 9,350 1.2 4,486 0.5 1,728 0.2<br />
200 9,350 0.6 4,486 0.3 1,728 0.09<br />
400 9,350 0.3 4,486 0.1 1,728 0.05<br />
800 9,350 0.2 4,486 0.07 1,728 0.02<br />
1,600 4,486 0.03 1,728 0.01<br />
Table 4 Dedispersion Processing loads per beam<br />
<strong>The</strong> total <strong>processing</strong> load :<br />
__ ~ 21 <br />
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In addition there are also delay elements per diagonal DM element, N dly which for large DM<br />
approximates to:<br />
~ <br />
<br />
4<br />
<br />
4 <br />
Ignoring any zero padded channels, the output rate, G dps is:<br />
<br />
1<br />
<br />
<br />
tsamp<br />
us<br />
N DM<br />
G dps<br />
(M bit/s)<br />
N DM<br />
G dps<br />
(M bit/s)<br />
N DM<br />
G dps<br />
(M bit/s)<br />
N DM<br />
G dps<br />
(M bit/s)<br />
Dish<br />
Dish<br />
Dish<br />
Dish<br />
Dish<br />
Dish<br />
Sparse AA<br />
Sparse AA<br />
2 – 3<br />
GHz<br />
2 – 3<br />
GHz<br />
1 – 2<br />
GHz<br />
1 – 2<br />
GHz<br />
.45 – 1<br />
GHz<br />
.45 – 1<br />
GHz<br />
.35 ‐ 45<br />
GHz<br />
.35 ‐ .45<br />
GHz<br />
50 27,778 556 18,700 375 8,972 179 3,457 69<br />
100 13,889 139 9,350 94 4,486 45 1,728 17<br />
200 9,350 47 4,486 22 1,728 9<br />
400 9,350 23 4,486 11 1,728 4<br />
800 9,350 12 4,486 6 1,728 2<br />
1,600 4,486 3 1,728 1<br />
Table 5 Dedispersion Output Rate per beam 2<br />
2 Assumes data is truncated to 4 bits<br />
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10 Pulsar Search<br />
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SKA Memo 125 provides has identified two major science goals that are to drive the technical<br />
specifications for the SKA1. One of these is:<br />
‘Detecting and timing binary pulsars and spin‐stable millisecond pulsars in order to test theories of<br />
gravity (including General Relativity and quantum gravity), to discover gravitational waves from<br />
cosmological sources, and to determine the equation of state of nuclear matter.’<br />
10.1 Binary Search<br />
<strong>The</strong> detection of binary pulsar systems as part of a pulsar search requires algorithms that are<br />
capable of compensating for loss of sensitivity caused by the pulsar’s elliptical orbital motion as a<br />
result of the Doppler component.<br />
Ralph Eatough’s 2009 PhD thesis [43] provides an overview of the common time and frequency<br />
domain techniques that have been developed to compensate for the effects of pulsar orbital motion<br />
and are represented in Figure 11. Non binary systems can be considered as a special case where the<br />
Doppler component is zero.<br />
bdd [block] system [Binary search definitions]<br />
«block»<br />
Binary Search<br />
«block»<br />
Matched<br />
Filter<br />
«block»<br />
Stack Search<br />
«block»<br />
Coherence<br />
Recovery<br />
«block»<br />
Hough<br />
Transform<br />
«block»<br />
Phase<br />
Search<br />
«block»<br />
Time Domain<br />
Resampling<br />
Figure 11 Binary Pulsar Search Algorithms<br />
A brief overview of each technique is provided in the following sections.<br />
10.1.1 Matched Filter<br />
An alternative method of conducting "constant acceleration" searches uses complex matched<br />
filtering in the Fourier domain as opposed to re‐sampling of the de‐dispersed time series. <strong>The</strong> local<br />
(meaning only those near the Fourier frequency of interest) complex Fourier amplitudes from the<br />
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FFT of a time series are convolved with analytically computed templates to generate optimally<br />
sampled two‐dimensional portions of the frequency‐frequency derivative (or f‐fdot) plane. <strong>The</strong><br />
templates may be thought of as digital filters whose lengths represent how many Fourier bins a<br />
<strong>signal</strong> linearly drifts during an observation. <strong>The</strong> number of bins drifted is a parameter typically called<br />
'z', which can be directly related to acceleration 'a' via:<br />
<br />
<br />
where T is the observation duration, f is the pulsar spin frequency (or harmonic of its spin<br />
frequency), and c is the speed of light. Since the templates only depend on 'z' (and not on the spin<br />
frequency) they may be pre‐computed and stored. A range of them will efficiently generate<br />
horizontal slices in the f‐fdot plane via the FFT convolution theorem. N independent fdot (or 'z')<br />
slices in an f/fdot plane of length 'M' Fourier bins (where M is typically
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One disadvantage to Fourier‐domain acceleration searching is that harmonic summing is signicantly<br />
more complicated than for time‐domain re‐sampling. This is because two‐dimensional portions of<br />
the f‐fdot plane must be summed as opposed to one‐dimensional portions of the simple powerspectrum.<br />
If the full f‐fdot plane can be computed and kept in memory, which may very well be<br />
possible for large‐scale surveys with the SKA (where time series are likely to be 5‐20 min in<br />
duration), the harmonic summing calculations and book‐keeping will be dramatically simplified.<br />
<strong>The</strong> reference for Fourier domain acceleration searching is Ransom, Eikenberry & Middleditch 2002,<br />
AJ, 124, 1788.<br />
10.1.2 Hough Transform<br />
<strong>The</strong> original Hough algorithm developed by Paul Hough in the 1960s maps a straight line y = ax + b in<br />
the (x, y) plane into (a, b) parameter space where it becomes a point. Consequently a point in (x, y)<br />
space can be represented as a line of form b = y − ax in parameter space. Many points arranged in a<br />
preferred direction in the (x, y) plane would appear as lines in the (a, b) plane that converge at a<br />
particular a and b that parameterize the line. <strong>The</strong> principle can be extended to almost any functional<br />
form in the (x, y) plane although this results in <strong>high</strong>er dimensional parameter spaces. <strong>The</strong> method<br />
has been used in the PhD thesis of Aulbert (2005) to search for sinusoidal tracks left by binary<br />
pulsars in dynamic power spectra.<br />
10.1.3 Stack Search<br />
A stack search works by simply chopping the time series up into a number of smaller segments<br />
(Wood et al., 1991). Each segment is then Fourier transformed and the segments are summed<br />
together with various offsets corresponding to different frequency drift rates i.e. different<br />
acceleration trials. Typically, only linear offsets (constant accelerations) are applied but, since the<br />
algorithm is efficient there is no reason why quadratic and even cubic frequency offsets could not be<br />
searched. <strong>The</strong> configuration of summed spectra with the binary candidate showing <strong>high</strong>est SNR<br />
should be given by the correct acceleration trial. Unfortunately, by splitting the time series into<br />
segments and operating on them separately the phase information of the observation is lost and the<br />
spectra are summed incoherently. This results in a 30% reduction in SNR compared to the<br />
equivalent spectral SNR of the solitary pulsar (Faulkner, 2004).<br />
10.1.4 Phase Search<br />
<strong>The</strong> phase search implemented in Scott Ransom’s software Presto2 essentially performs a number of<br />
short DFTs over different parts of the fluctuation spectrum. For very short period binaries where the<br />
observation length covers at least one orbit, the phase modulation search can be applied (Jouteux et<br />
al., 2002, Ransom et al., 2003). <strong>The</strong> effect of these very short orbital periods is to create sidebands in<br />
the Fourier power spectrum. DFTs are used to sum any sidebands (collecting the power). Both the<br />
orbital and pulsar periods can be found using this method.<br />
10.1.5 Coherence Recovery<br />
This frequency domain technique (Ransom et al., 2002) involves taking an FFT of the time series to<br />
generate the power spectrum with the pulse smeared over a number of spectral bins. <strong>The</strong> functional<br />
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form of the smearing is known so it is possible to collect the power back into one frequency bin by<br />
using a filter that is the complex conjugate of the smearing function. <strong>The</strong> filter is applied over all<br />
frequencies in the spectrum to look for periodicities corresponding to particular constant<br />
accelerations. <strong>The</strong> method is in principle computationally efficient as an FFT of the entire time series<br />
only needs to be performed once.<br />
10.1.6 Time Domain Resampling<br />
In the time domain the equivalent technique is time domain resampling. Here the time samples are<br />
transformed into a frame inertial with respect to the pulsar, but instead of a search to find the exact<br />
form of v(t) a constant acceleration is assumed, i.e. v(t) = a0t. A time interval in the observers frame<br />
t can then be transformed into the pulsar frame τ by simple application of the Doppler formula,<br />
1 <br />
<br />
1 <br />
<br />
<strong>The</strong> constant τ0 is chosen such that τ = tsamp at the midpoint of the observation (e.g. Camilo et al.,<br />
2000). New samples are computed from a linear interpolation over the original time series<br />
(Middleditch & Kristian, 1984). Following resampling the time series is then searched with the<br />
standard FFT techniques.<br />
10.2 Time Domain Re‐Sampling<br />
This section takes the Time Domain Re‐Sampling binary search case identified as one of the options<br />
in section 10.1.6 and provides a ball park estimation of the <strong>processing</strong> loads and data rates. This is<br />
not meant to represent a preference for the algorithm. <strong>The</strong> development phase will investigate and<br />
model each of the algorithms in more detail to determine which is optimal for the SKA.<br />
Assuming constant acceleration for the re‐sampling and that the maximum pulse smearing is t samp .<br />
<strong>The</strong>n, for samples lying exactly between acceleration trials,<br />
<br />
2<br />
<br />
Substituting t = T/2 and letting allows the acceleration step size to be calculated<br />
8 <br />
<br />
8 3 10 <br />
600 <br />
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Assuming that the time series for the lowest DM is decimated by a factor of 2, the following table<br />
details the number of trail accelerations as a function of sample time:<br />
t samp us δa ms ‐2 N acc<br />
100 (50) 0.66 (0.33) 303<br />
100 0.66 303<br />
200 1.3 152<br />
400 2.7 76<br />
800 5.3 38<br />
1,600 10.6 19<br />
<strong>The</strong> <strong>processing</strong> load at each time resolution:<br />
Assuming N ops_dm = 2<br />
Table 6 Number of trial Accelerations 3<br />
_ <br />
1<br />
<br />
_<br />
tsamp<br />
us<br />
N DM<br />
N D_ops<br />
(G Macs)<br />
N DM<br />
N D_ops<br />
(G Macs)<br />
N DM<br />
N D_ops<br />
(G Macs)<br />
N DM<br />
N D_ops<br />
(G Macs)<br />
Dish<br />
Dish<br />
Dish<br />
Dish<br />
Dish<br />
Dish<br />
Sparse AA<br />
Sparse AA<br />
2 – 3<br />
GHz<br />
2 – 3<br />
GHz<br />
1 – 2<br />
GHz<br />
1 – 2<br />
GHz<br />
.45 – 1<br />
GHz<br />
.45 – 1<br />
GHz<br />
.35 ‐ 45<br />
GHz<br />
.35 ‐ .45<br />
GHz<br />
100 (50) 27,778 337 18,700 227 8,972 109 3,457 42<br />
100 13,889 84 9,350 57 4,486 27 1,728 11<br />
200 9,350 14 4,486 7 1,728 3<br />
400 9,350 4 4,486 2 1,728 0.7<br />
800 9,350 0.9 4,486 0.4 1,728 0.2<br />
1,600 0.2 4,486 0.1 1,728 0.04<br />
Table 7 Re‐sampling Processing Load per beam 4<br />
3 Assumes + 100ms -2 acceleration range<br />
4 Assumes Nacc of Table 6<br />
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<strong>The</strong> output rate, G rsps is:<br />
<br />
1<br />
<br />
<br />
tsamp<br />
us<br />
N DM<br />
G rsps<br />
(G bit/s)<br />
N DM<br />
G rsps<br />
(G bit/s)<br />
N DM<br />
G rsps<br />
(G bit/s)<br />
N DM<br />
G rsps<br />
(G bit/s)<br />
Dish<br />
Dish<br />
Dish<br />
Dish<br />
Dish<br />
Dish<br />
Sparse AA<br />
Sparse AA<br />
2 – 3<br />
GHz<br />
2 – 3<br />
GHz<br />
1 – 2<br />
GHz<br />
1 – 2<br />
GHz<br />
.45 – 1<br />
GHz<br />
.45 – 1<br />
GHz<br />
.35 ‐ 45<br />
GHz<br />
.35 ‐ .45<br />
GHz<br />
50 27,778 168 18,700 114 8,972 54 3,457 21<br />
100 13,889 42 9,350 28 4,486 14 1,728 5<br />
200 9,350 7 4,486 3 1,728 1<br />
400 9,350 2 4,486 0.9 1,728 0.3<br />
800 9,350 0.4 4,486 0.2 1,728 0.08<br />
1,600 4,486 0.05 1,728 0.02<br />
10.3 FFT<br />
<strong>The</strong> <strong>processing</strong> load at each time resolution:<br />
Table 8 Time Re‐sampling output rates<br />
_ 5 <br />
<br />
<br />
<br />
1<br />
<br />
t samp<br />
us<br />
N dm<br />
N dm<br />
N dm<br />
N dm<br />
N acc T obs N rs_ops<br />
(G Macs)<br />
N rs_ops<br />
(G Macs)<br />
N rs_ops<br />
(G Macs)<br />
N rs_ops<br />
(G Macs)<br />
Dish<br />
Dish<br />
Dish<br />
Sparse AA<br />
Dish<br />
Dish<br />
Dish<br />
SparseAA<br />
2 ‐ 3<br />
GHz<br />
1 ‐ 2<br />
GHz<br />
0.45‐1<br />
GHz<br />
.35‐.45<br />
GHz<br />
2 – 3 GHz<br />
1‐2 GHz<br />
.45 ‐ 1<br />
GHz<br />
.35 ‐ .45<br />
GHz<br />
100 27,778 18,700 8,972 3,457 303 600 3960 2670 1280 493<br />
100 13,889 9,350 4,486 1,728 303 600 948 640 306 118<br />
200 9,350 4,486 1,728 152 600 153 73 28<br />
400 9,350 4,486 1,728 76 600 37 18 7<br />
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t samp<br />
us<br />
N dm<br />
N dm<br />
N dm<br />
N dm<br />
N acc T obs N rs_ops<br />
(G Macs)<br />
N rs_ops<br />
(G Macs)<br />
N rs_ops<br />
(G Macs)<br />
N rs_ops<br />
(G Macs)<br />
Dish<br />
Dish<br />
Dish<br />
Sparse AA<br />
Dish<br />
Dish<br />
Dish<br />
SparseAA<br />
2 ‐ 3<br />
GHz<br />
1 ‐ 2<br />
GHz<br />
0.45‐1<br />
GHz<br />
.35‐.45<br />
GHz<br />
2 – 3 GHz<br />
1‐2 GHz<br />
.45 ‐ 1<br />
GHz<br />
.35 ‐ .45<br />
GHz<br />
800 9,350 4,486 1,728 38 600 9 4 2<br />
1600 4,486 1,728 19 600 1 0.4<br />
<strong>The</strong> output rate, G fftps is:<br />
This is the same as the Input rate<br />
10.4 Whitening and Normalisation<br />
Table 9 FFT Processing Load per Beam<br />
<br />
<br />
1<br />
<br />
<br />
According to Kramer and Lorimer [40]‘fluctuations in the receiver and/or data acquisition systems<br />
often manifest themselves via a significant low‐frequency or red noise component when viewed in<br />
the Fourier domain’. It is standard practice to whiten and normalise the spectrum prior to any<br />
detection <strong>processing</strong>.<br />
10.5 Harmonic Sum<br />
Harmonic summing provides a gain in sensitivity over that provided by a single harmonic analysis.<br />
<strong>The</strong> energy in the harmonics is a function of the duty cycle of the pulsar pulse.<br />
32 harmonics is required for slow and un‐accelerated pulsars and 8 harmonics are optimal for milli<br />
second pulsars and acceleration searches. This is because the accuracy of the "linear" acceleration<br />
approximation is proportional to 1/f. So the <strong>high</strong>er harmonics see more and more non‐ linear<br />
effects and therefore contribute less and less to the accumulated <strong>signal</strong> to noise ratio. In fact,<br />
historically, in most cases, binary pulsars have been detected in only 3 harmonics. <strong>The</strong> exact<br />
boundary between the use of 32 and 8 harmonics is still to be determined.<br />
For estimating the <strong>processing</strong> load it is assumed that summing of up to 8 harmonics for acceleration<br />
<strong>processing</strong> and is provided by the <strong>processing</strong> chain for each beam, dispersion measure and<br />
acceleration trial.<br />
This is implemented by stretching the power spectrum, in the frequency dimension, across an<br />
observation by factors of two. To cover 8 harmonics requires this process to occur 3 times.<br />
Consequently, the <strong>processing</strong> load, Ghs :<br />
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1<br />
<br />
<br />
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t samp<br />
us<br />
N dm<br />
N dm<br />
N dm<br />
N dm<br />
N acc T obs N hs<br />
(G Macs)<br />
N hs<br />
(G Macs)<br />
N hs<br />
(G Macs)<br />
N hs<br />
(G Macs)<br />
Dish<br />
Dish<br />
Dish<br />
Sparse AA<br />
Dish<br />
Dish<br />
Dish<br />
SparseAA<br />
2 ‐ 3<br />
GHz<br />
1 ‐ 2<br />
GHz<br />
0.45‐1<br />
GHz<br />
.35‐.45<br />
GHz<br />
2 – 3 GHz<br />
1‐2 GHz<br />
.45 ‐ 1<br />
GHz<br />
.35 ‐ .45<br />
GHz<br />
100 27,778 18,700 8,972 3,457 303 600 3234 2184 1044 402<br />
100 13,889 9,350 4,486 1,728 303 600 810 545 261 101<br />
200 9,350 4,486 1,728 152 600 137 65 25<br />
400 9,350 4,486 1,728 76 600 34 16 7<br />
800 9,350 4,486 1,728 38 600 8 4 2<br />
1600 4,486 1,728 19 600 1.2 0.4<br />
Table 10 Harmonic Sum Processing Load for acceleration Processing per Beam<br />
<br />
<br />
<br />
1<br />
<br />
4 <br />
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tsamp<br />
us<br />
N DM<br />
G rsps<br />
(G bit/s)<br />
N DM<br />
G rsps<br />
(G bit/s)<br />
N DM<br />
G rsps<br />
(G bit/s)<br />
N DM<br />
G rsps<br />
(G bit/s)<br />
Dish<br />
Dish<br />
Dish<br />
Dish<br />
Dish<br />
Dish<br />
Sparse AA<br />
Sparse AA<br />
2 – 3<br />
GHz<br />
2 – 3<br />
GHz<br />
1 – 2<br />
GHz<br />
1 – 2<br />
GHz<br />
.45 – 1<br />
GHz<br />
.45 – 1<br />
GHz<br />
.35 ‐ 45<br />
GHz<br />
.35 ‐ .45<br />
GHz<br />
50 27,778 168 18,700 114 8,972 54 3,457 21<br />
100 13,889 42 9,350 28 4,486 14 1,728 5<br />
200 9,350 7 4,486 3 1,728 1<br />
400 9,350 2 4,486 0.9 1,728 0.3<br />
800 9,350 0.4 4,486 0.2 1,728 0.08<br />
1,600 4,486 0.05 1,728 0.02<br />
Table 11 Harmonic Sum Output Rates per Beam<br />
10.6 Threshold Detection<br />
15 /<br />
<strong>The</strong> resultant data from the harmonic sum is searched for power components that exceed a<br />
threshold determined by the acceptable false alarm rate. <strong>The</strong> threshold <strong>level</strong> is determined by:<br />
/ <br />
4<br />
1 4<br />
Where N samp is the number of samples of the spectrum<br />
10.7 Candidate Filtering<br />
Large all sky surveys for radio pulsars produce extremely large numbers of candidate pulsars. As<br />
discussed in Eatough et al (2010)[43] the most recent Parkes Mutli‐beam Survey re<strong>processing</strong><br />
resulted in more than 8 million candidates. While tools have been established which allow for more<br />
efficient selection of which of these candidates to view have been established these typically only<br />
reduce the number of candidates by about an order of magnitude. This still leaves a significant<br />
problem as even 1 million candidates requires years of effort to view.<br />
<strong>The</strong> location of both phases of the SKA in predominantly radio quiet regions will decrease the<br />
influence of interfering <strong>signal</strong>s on the number of candidates. Moreover the multi‐beam nature of the<br />
telescopes will also provide a very effective anti‐coincidence filter, which should also reduce<br />
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spurious detections. However, the number of candidates produced in surveys with the SKA will still<br />
greatly out strip those produced by any previous survey. This is mainly due to the extreme<br />
sensitivity, the amount of sky that will be surveyed, the <strong>high</strong> time resolution, large number of<br />
dispersion measures and acceleration trials.<br />
It is also more than likely that the <strong>processing</strong> of the pulsar survey data will be happening in real time<br />
and so further <strong>processing</strong> of data to try and confirm candidates may not be possible. So robust<br />
methods to identify candidates in the data sets will be required to ensure that confirmation<br />
observations are effient and if possible only the data sets from only the best candidates are kept for<br />
further inspection.<br />
10.7.1 Artifcial Neural Nets<br />
Recently Eatough et al (2010) and Bates et al (2011) have introduced the idea of using Artificial<br />
Neural Nets for the selection of candidates for subsequent viewing. <strong>The</strong>se algorithms were applied<br />
to a re<strong>processing</strong> of the Parkes Multi‐beam Survey and the new High Time Resolution Survey with<br />
Parkes. <strong>The</strong> basis of the neural net approach to sorting pulsar candidates is to try to describe the<br />
plots which are viewed by eye, and use the natural pattern recognition of humans, with a set of<br />
numbers, or scores, which can be used to identify common traits of pulsars. A set of known pulsars<br />
and a set of "not‐pulsars" are used to train the neutral net, the resultant "net" is then applied to a<br />
validation set to determine how well it is doing.<br />
Eatough et al established that about 92% of all known pulsars in a sample of some 2.5 million<br />
candidates and Bates et al extended this work and applied it to a larger set of known pulsars and<br />
added more scores but found a total recovery rate of about 85% for pulsars with periods longer than<br />
about 100 milliseconds. <strong>The</strong>y find that there is a clear relationship with the pulse duty cycle and the<br />
ability to recover the pulsar and so further improvement of these techniques is possible. It should be<br />
pointed out that applying the neural net reduces the number of candidates that need to be viewed<br />
by more than an order of magnitude and has already helped discover a few 10's of pulsars.<br />
10.7.2 <strong>The</strong> Future<br />
Further investigation of the appropriate scoring scheme for identifying pulsars is currently<br />
underway. In particular improving the performance of the nets for the detection of millisecond<br />
pulsars will be essential. It is important to note that the <strong>high</strong>er time resolution of the HTRU survey<br />
over the PMB surveys has already improved the response to MSPs. Another area of active research is<br />
which neural net algorithms provide the best performance. At present relatively simple and old<br />
algorithms have been tried and there are efforts on going to improve this. It will also be important to<br />
investigate the performance of these nets to finding radio transients. We have started on applying<br />
them to the RRAT sources, but so far with less success than for radio pulsars, but this likely reflects<br />
the usefulness of the scores being used.<br />
10.7.3 Application to the SKA<br />
<strong>The</strong> large number of candidate sources that will be revealed in the SKA pulsar and fast transient<br />
surveys will be a vital aspect of the whole <strong>processing</strong> and observing effort. To minimise follow up<br />
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observations robust candidates need to be identified, but it is also vital that the number of<br />
candidates to be viewed manually be greatly reduced.<br />
While the application of Neural Nets to pulsar searches is still in it's infancy it has shown great<br />
promise. Moreover it doesn't add a significant <strong>processing</strong> load to the overall pulsar <strong>processing</strong> <strong>signal</strong><br />
chain. On existing 2.6 GHz CPUs it takes just a few seconds to produce the necessary scores for each<br />
candidate. If there are less than a few tens of candidates per beam this means that it always takes<br />
much less than the <strong>processing</strong> time to find the candidate, than to generate scores. Once these<br />
scores have been accumulated, running the Neural Net on a few thousand potential candidates also<br />
takes just a few minutes on a single core 2.6 GHz CPU.<br />
<strong>The</strong> use of some kind of system for reducing the number of pulsar and fast transient candidates that<br />
need to be viewed manually will be essential in the SKA era. <strong>The</strong>se algorithms need not add<br />
significantly to the overall <strong>processing</strong> load and will greatly improve the observing efficiency by<br />
reducing the number of false positives. <strong>The</strong>y will also significantly decrease any data products that<br />
need to be archived. Development work is still required in determining the best possible set of<br />
scores, algorithms and training methods for the pulsars and especially for the transients.<br />
11 Pulsar Timing<br />
One of the key goals of the SKA in both phase 1 and 2 will be to perform <strong>high</strong> precision timing of<br />
known pulsars in order to test theories of gravity and to detect and study a gravitational wave<br />
background. An important aspect of this pulsar timing is the initial, post‐discovery, timing of pulsars<br />
discovered with the SKA in the Galactic Census observations of phase 1 and 2. It is not until this<br />
initial timing solution is hand that we can make an initial assessment of whether a pulsar is<br />
interesting or not. For the majority of the pulsars discovered in the survey, modest timing precision<br />
is required, while for the <strong>high</strong> precision timing of a much smaller number of pulsars, such as the<br />
millisecond pulsars and those in binaries, the <strong>high</strong>est demands in time and frequency resolution,<br />
calibration, collecting area and cadence will be set.<br />
This section of the document describes the technical and operational requirements for achieving the<br />
stated headline and key science of the SKA in Phase I and II. It does not address the issue of<br />
polarization calibration which is addressed elsewhere.<br />
11.1 Basic Parameters<br />
<strong>The</strong> basic functional requirements for a timing programme with the SKA is described in this section<br />
of the document. It consists of three possible parts, all of which required for the headline science:<br />
Phase 1<br />
Phase 2<br />
<br />
Galactic Centre<br />
<strong>The</strong> optimal timing parameters are <strong>high</strong>ly source dependent, i.e. they depend on whether the pulsar<br />
is a young, normal pulsar (compared to an old millisecond pulsar), the flux density and pulse jitter of<br />
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the source and whether the pulsar is in a binary orbit. Moreover, timing observations of newly<br />
discovered pulsars have to be done with a different cadence than known pulsars timed for specific<br />
experiments, such as gravitational wave detection or tests of theories of gravity.<br />
Indeed, the specifics of pulsar timing make the requirements different from most other pulsar timing<br />
projects; in particular as a large Field‐of‐View will not compensate for a reduced sensitivity. This is in<br />
particular the case for studying the fast binary pulsars, where sufficient sensitivity must be available<br />
to ``resolve'' the orbit with appropriate time‐of‐arrival (TOA) measurements that cover the orbit in<br />
small enough intervals. Hence, it is important to collect enough flux density for having a precisely<br />
measured TOA with an integration time as short as possible. On the other hand, while raw<br />
sensitivity (collecting area and bandwidth) is extremely important, it is not the only criterion that<br />
determines the observing requirements. See further below<br />
11.2 Timing scenarios<br />
Three different scenarios are considered PhaseI/PhaseII/Galactic Centre<br />
Pulsars to be timed (point sources): 5000/25000/50<br />
Single Obs Duration:<br />
> 120 s / many hours<br />
Integration/Pointing from monthly (1000's of sources), biweekly<br />
(~100 sources), daily for few hours (for fast binary<br />
systems)/daily<br />
Number of Stations:<br />
variable (multi‐beaming, sub‐arraying, full array)/full array<br />
Collecting area, A/T: >1000 m 2 K ‐1 / >10,000 m 2 K ‐1 / 5,000 ‐ 10,000 m2 K ‐1<br />
Diameter of Stations:<br />
Size of Core:<br />
Frequency:<br />
Bandwidth:<br />
Sampling Time:<br />
non‐critical, array assumed to be phased up/whole array<br />
non‐critical, array assumed to be phased up<br />
500 ‐ 3000 MHz / 10 ‐ 15 GHz<br />
>20%, ideally 500‐3000 instantaneously / 4 GHz<br />
0.2 us /1us<br />
11.3 Monitoring and Cadence:<br />
Pulsar timing requires the regular observations of pulse arrival times with <strong>high</strong> precision. <strong>The</strong> latter<br />
scales, to first order, with <strong>signal</strong>‐to‐noise ratio which is larger at lower frequencies due to the steep<br />
spectrum of pulsars. For normal timing observations of known pulsars monthly or bi‐weekly<br />
observations are sufficient. However, if the pulsar is in a binary orbit, dense coverage of all orbital<br />
phases is required. For orbits of a few hours, this can be achieved in a single session while pulsars<br />
with orbital periods of days, weeks or months need to be covered in appropriate intervals. For new<br />
pulsars, a 'timing solution' needs to be obtained first. This usually requires dense observations at the<br />
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start with increasing intervals between the observations (i.e. from minutes to hours, days and<br />
weeks). Obtaining a full timing solution also requires coverage over a year (in order to break a<br />
correlation between the pulsar position and the pulsar spin down). Solving a pulsar and obtaining a<br />
full solution can be shortened if the position of the pulsar can be measured at the beginning using<br />
imaging over large baselines to arcsec precision.<br />
11.4 Observing Frequency and Bandwidth<br />
<strong>The</strong> optimal observing frequency for <strong>high</strong> precision timing is usually between 1‐3 GHz, as a<br />
compromise that takes into account the steep spectrum of pulsars and the effects of the interstellar<br />
weather which become reduced at <strong>high</strong> frequencies. <strong>The</strong> ionized interstellar medium (ISM) disperses<br />
the <strong>signal</strong> and the ISM's inhomogeneities lead to a scattering of the <strong>signal</strong> via multi‐path<br />
propagation. While the former can be accounted for with optimal de‐dispersion techniques, the<br />
latter usually cannot but the effects scale inversely with frequency with about the fourth power.<br />
Moreover, the turbulent properties of the ISM mean that the effective dispersion and scattering<br />
properties vary on a number of timescales, so that they should be determined with quasisimultaneous<br />
multi‐frequency or wide bandwidth observations. Large bandwidth also reduces the<br />
impact of interstellar scintillation which can cause the brightness of a point source like pulsars to<br />
vary significantly. <strong>The</strong> ISM effects are in particular severe for pulsars in the Galactic plane. For the<br />
Galactic Centre region, timing (and searching) will have to be conducted at 10 GHz or even <strong>high</strong>er.<br />
Here, however, the size of the region to be studied and monitored is small and localized. In contrast,<br />
pulsar <strong>signal</strong>s from sources outside the Galactic plane suffer less from ISM effects, so that for timing<br />
observations between 500‐1000 MHz may be sufficient.<br />
Memo 130 assumes for Phase I frequency coverage of 0.45‐1 GHz and 1‐2 GHz for dishes with Single<br />
Pixel Feeds and 70‐450 MHz with aperture arrays. In this case, <strong>high</strong> precision timing for pulsars in the<br />
plane would be conducted with dishes between 1‐2 GHz, while the bulk of the sources will be timed<br />
between 0.45‐1 GHz with dishes or at 70‐450 MHz with aperture arrays. Typically, a bandwidth of<br />
20% of the centre frequency is demanded for timing observations. For <strong>high</strong> precision measurements,<br />
a larger fractional bandwidth is <strong>high</strong>ly desirable, in particular to combat ISM effects. A simultaneous<br />
coverage of frequencies between 0.4 and 3 GHz would also eliminate the need to re‐observe the<br />
same source at multiple frequencies to account for interstellar weather. Given Memo 130, a larger<br />
fraction bandwidth (~500 MHz at low frequencies, ~1 GHz above 1 GHz) would be available,<br />
although it would split the SKA in sub‐arrays to achieve simultaneous coverage of larger frequency<br />
ranges.<br />
11.5 Collecting area, beams and integration time:<br />
<strong>The</strong> time needed to achieve a precise TOA depends on two main factors:<br />
minimum <strong>signal</strong>‐to‐noise‐ratio (S/N~10 for normal pulsar timing, S/N >~100‐1000 for precision<br />
timing) and pulse jitter. <strong>The</strong> integration time for weak pulsars will be limited by the radiometer<br />
equation, while for strong pulsars a sufficient number of pulses need to be added before a stable<br />
pulse profile is reached, regardless of the S/N (e.g. Liu et al. 2011). In the latter case, a few thousand<br />
pulses should be added. For typical periods of millisecond pulsars, a few minutes of observing time<br />
will be sufficient. For <strong>high</strong> precision timing of millisecond pulsars, the maximum time (for achieving a<br />
fixed S/N and sufficient number of added pulses) is to be used.<br />
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Smits et al (2009) [41] demonstrated that the number of pulses located in a single FoV (and hence<br />
could be timed simultaneously) is small and presented an algorithm to optimize the observing time.<br />
<strong>The</strong>y concluded that the larger number of beams with full sensitivity available with aperture arrays<br />
would reduce the needed observing time dramatically compared with a solution that uses subarraying<br />
of dishes. This is caused by the much denser concentration of pulsars in the Galactic plane<br />
which would have to be observed at <strong>high</strong>er frequencies and hence dishes with smaller FoV.<br />
It is important to note that for many of the pulsars it is not possible to trade FoV for sensitivity, as a<br />
large instantaneous sensitivity is required to obtain a TOA for pulsars in short binary orbits. Only<br />
then can a TOA be measured in sufficiently short intervals that allow us to resolve the orbit. As these<br />
systems are usually more isotropically distributed they will also not greatly benefit from wider FoVs.<br />
Estimating the required collecting area is difficult, as it strongly depends on the flux density of the<br />
most exciting pulsars to be discovered. However, we can use our known population to give an<br />
estimate. In general, there we will be two types of experiment that require the <strong>high</strong>est precision,<br />
namely the test of theories of gravity by monitoring the motion of a relativistic binary in a fast orbit<br />
with finely sampled TOAs, and the monitoring for pulsars in a pulsar timing array to detect<br />
gravitational waves. As some of us have shown in Liu et al. (2011), given sufficient calibration, this<br />
translates into sensitivity of the telescope. Using the best relativistic laboratory to date as a<br />
guideline, the double pulsar, we currently need a 100‐m telescope with about 30% fractional<br />
bandwidth to obtain a precise TOA in 30 sec to resolve the 147‐min binary orbit. Placing the 1.6‐mJy<br />
(1400 MHz) at a distance of the Galactic Centre (rather than in the true distance of only 1 kpc) we<br />
need an A/T of 26,000 m 2 K ‐1 to do a similar experiment for a new source half‐way through the<br />
Galaxy. An increase in bandwidth will help reducing this requirement, and the hope that 1‐2 min<br />
TOAs may be sufficient to resolve the orbit, we estimate that we need a minimum of about an A/T of<br />
10,0000 m 2 K ‐1 (1‐2 GHz) to time a newly discovered pulsar with the full SKA. Performing the GR‐test<br />
Phase I headline science as outlined in Kramer & Stappers (2010) requires at least 1,000 m 2 K‐1. We<br />
note that finding and timing a pulsar orbiting SGR A* to study its space‐time will need to be done at<br />
a frequency of 10 GHz or <strong>high</strong>er, which requires significant A/T to compensate for the steep<br />
spectrum of pulsars. In general, however, the timing precision can be less than needed for the other<br />
experiment, so that we estimate that a collecting area of about 5,000‐10,000 m 2 K ‐1 is needed to<br />
extract the science.<br />
<strong>The</strong> other experiment, the detection of gravitational waves (GWs) with Phase I and the study of the<br />
GWs with Phase II, requires <strong>high</strong>‐sensitivity observations of known millisecond pulsars. <strong>The</strong> goal is to<br />
increase the sample of pulsars timed with a precision better than 100 ns to about 100 or more<br />
(compared to the ~5 today). Following the results and simulations presented by Smits et al. (2011),<br />
this seems possible with a similar sensitivity as needed for the gravity tests described above.<br />
<strong>The</strong> collecting area of the SKA is distributed sparsely. Here we assume that the full SKA can be<br />
phased up to form multiple tied array beams. <strong>The</strong> usefulness of a wide FoV and many beams for<br />
pulsar timing has been demonstrated by Smits et al. (2009). Here, we mostly gain for timing pulsars<br />
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in the Galactic plane where the density is large. Increasing the FoV to 200 deg^2 or more, also makes<br />
timing the pulsars off the plane vastly more efficient. For timing pulsars in the Galactic plane, it is<br />
<strong>high</strong>ly beneficial that the upper frequency range of the Aperture Arrays is about 1 GHz and that<br />
more than 50% of the total collecting SKA area can be phased up. Using the strategy of Smits et al.,<br />
a maximum FoV of 250 deg 2 for AA and 20 deg 2 for dishes (with PFA), as well as assuming that<br />
sufficient beams can be produced to pixelize these FoVs, it would take up to 6 days to obtain a single<br />
timing point for 14 000 pulsars to be discovered in the surveys. Obtaining one <strong>high</strong>‐precision timing<br />
point it will take up to 3 days with dishes and only 14 hours for timing with AA.<br />
In SKA Phase 1 the smaller field of view will influence how many pulsars will be in each field of view.<br />
<strong>The</strong>re will of course also be less pulsars but not in the same proportion. Simulations for SKA phase 1<br />
show for a FoV of 2.1 deg 2 , we will get a maximum of 15 pulsars in the FoV.<br />
For a FoV of 30 deg 2 , there will be 200 pulsars at most. So in order to be as efficient as possible we<br />
would need of the order of 50 beams for the timing, as these will be needed for the AAs, and will<br />
greatly improve the efficiency of the timing.<br />
11.6 Forming the Beams:<br />
In order to achieve the maximum sensitivity the station/dish beams from each of the dishes/stations<br />
in as much of the array as possible need to be added coherently. To form the coherent sum requires<br />
that the phase relationship between the <strong>signal</strong>s for each beam from each dish station be known<br />
precisely. It is important to note that phase calibration also requires that there is a known phase<br />
relationship between the time and frequency references at each of the stations. To obtain phase<br />
corrections will require the regular observation of calibration point sources and a decomposition<br />
analysis. <strong>The</strong>se phases will then need to be applied to the data from each of the stations along with<br />
the geometric corrections to point each of the tied‐array beams in the correct direction.<br />
<strong>The</strong> output product for all beams should be complex channelized data so that it is possible to<br />
perform coherent de‐dispersion on all beams. While this is strictly necessary only for the <strong>high</strong><br />
precision timing objects, it simplifies the pipeline, should be technically achievable for a sufficient<br />
number of beams and will also improve timing precision at lower frequencies. Moreover it will have<br />
application to other areas of pulsar science such as single pulse and polarization studies.<br />
11.7 Time Resolution and Frequency Resolution.<br />
We assume a maximum time resolution of 0.2 us for the final data product. <strong>The</strong> ability to fully record<br />
the complex channelized data at <strong>high</strong> time resolution over the entire available bandwidths for a<br />
reduced number of beams will also be required.<br />
11.8 Data rates:<br />
<strong>The</strong> data rate can be defined in terms of the Nyquist sampling of the baseband data as there will be<br />
no averaging of the data before it is transported back to the main computing centre even if there is<br />
channelisation. Assuming that the data is sampled at 4 bits, and that we need only transport data of<br />
about 50 beams (we obtain a data then we have a rate of 30 Gbytes/s. <strong>The</strong> exact number of required<br />
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beams can be traded against observing time, as it will simply take longer to go through the list.<br />
However, that is only possible up to a point where other observations or sufficient sampling is not<br />
possible anymore. We consider 50 beams at the lowest possible limit but recommend more to<br />
reduce the impact on other science areas.<br />
We note that it is at the beamforming stage where it will be crucial that information about the<br />
quality of the station data, either through station calibration, or checks done once the data arrive a<br />
central <strong>processing</strong> facility, to determine that the data from all the station are providing data of<br />
sufficient quality. <strong>The</strong> exact algorithm for determining this quality and how to adjust data when<br />
stations drop in or out will need to be developed especially if changes are occurring on relatively<br />
short timescales, that is shorter than a typical observation duration.<br />
11.9 Processing the Beams<br />
When all of the beams (one per pulsar to be timed) have been formed it is necessary to perform a<br />
number of steps which are common to all of them. <strong>The</strong>se include to coherently de‐dispersing the<br />
data (thereby also forming all Stokes parameters), interference rejection, polarisation calibration<br />
and folding.<br />
11.9.1 (Coherent) De‐dispersion:<br />
To correct for the dispersive delay due to the interstellar medium requires that the frequency<br />
dependent phase shift of the <strong>signal</strong> applied by the ISM is unwrapped again in a process known as<br />
coherent de‐dispersion (e.g. Lorimer & Kramer 2005). This process requires complex channelized<br />
data for each beam. In contrast to search observations, the dispersion measure for pulsars to be<br />
timed is known and the result of the discovery process. Improvements to the dispersion measure<br />
precision will be obtained in an off‐line analysis process.<br />
This process includes the Fourier‐Transform of the complex data into the frequency domain, this<br />
process may not be necessary if the data are already delivered as complex channelized data. <strong>The</strong><br />
data is then multiplied with the inverse ISM filter function plus tapering and the re‐transformation<br />
into the time domain.<br />
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