Outline

1

Online Trigger Implementation

• Outline
• general architecture
• tracklet matching algorithm
• track reconstruction
• hardware implementation
• status of implementation

Jan de Cuveland V. Lindenstruth, R.
Schneider Kirchhoff Institute of
Physics University of Heidelberg Chair of
Computer Science / Computer Engineering Prof. Dr.
Volker Lindenstruth URL www.ti.uni-hd.de mail
cuveland_at_kip.uni-heidelberg.de
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Global Tracking Unit (GTU)

• Online Trigger Architecture
• local tracking units (MCMs) on detector perform
  straight line fits
• readout network with 1080 optical links (2 per
  detector)
• "tracklet" (32-bit word)
• Y position
• slope
• Z position (padrow number)
• charge
• central point of processing Global Tracking Unit
  (GTU)

• GTU architecture
• tracklets from detectors on different planes are
  matched to tracks
• matching is performed on per-module basis no
  inter-module matching.
• built of FPGAs
• 1 (large) FPGA chip per module (12 links), 90
  FPGAs
• timing is critical
• 1.4 µs total processing time
• much to be done in parallel
• problem 3-dimensional matching of tracklets

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Tracklet Matching in Z

• matching required in 3 coordinates
• z position
• y position
• deflection (dy/dx slope)
• simultaneous fitting of all coordinates hard to
  realize
• Z coordinate can be handled separately
• only few different values for Z
• Z coordinate is needed only for matching, not for
  reconstruction of pt
• tracklets arrive sorted in Z

• particles may traverse several (up to 3) padrow
  numbers, due to
• not fully projective geometry
• vertex position distribution

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Tracklet Matching in Z

• solution
• assign tracklets to logical channels
• max. 3 padrows per track ? 3 channels needed
• process the 3 channels in parallel
• perform Y and deflection matching for each
  subchannel
• from simulation max. 8 tracklets per plane per
  subchannel

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Tracklet Matching in Y

• project tracklets to virtual plane in the middle
  of each module
• for each Z-subchannel
• sort tracklets in ascending order of Y
• apply sliding window matching algorithm
• matching condition difference in projected Y
  position lt 11.6 mm
• from simulation max. 2 tracks inside window per
  plane per Z-channel

6
Tracklet Matching in Deflection

• convert tracklet slope into deflection angle
  against vertex direction
• deflection is only relevant if tracklets match in
  Y position
• deflection matching condition
• deflection angle difference lt 3.0
• a track is found, if ? 4 tracklets from different
  detectors inside sameY window match also in
  deflection angle

• Matching algorithm summary
• find matches in z coordinate (padrow number)
• find matches in projected y coordinate
• find matches in deflection angle

7
pt Reconstruction

• linear fit of unprojected Y positions of
  tracklets
• approximates circle segment
• from line parameters A and B, pt can be
  calculated using only additions and
  multiplications

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GTU Architecture Overview
input unit (plane 5)
input unit (plane 4)
input unit (plane 3)
input unit (plane 2)
input unit (plane 1)
input unit (plane 0)
z-ch. 2 sorter
z-ch. 1 sorter
z-ch. 0 sorter
z-ch. 2 sorter
z-ch. 1 sorter
z-ch. 0 sorter
z-ch. 2 sorter
z-ch. 1 sorter
z-ch. 0 sorter
z-ch. 2 sorter
z-ch. 1 sorter
z-ch. 0 sorter
z-ch. 2 sorter
z-ch. 1 sorter
z-ch. 0 sorter
z-ch. 2 sorter
z-ch. 1 sorter
z-ch. 0 sorter
matcher z-ch 2
matcher z-ch 1
matcher z-ch 0
matching unit seedline 3
matching unit seedline 2
matching unit seedline 1
matching unit seedline 3
matching unit seedline 2
matching unit seedline 1
matching unit seedline 3
matching unit seedline 2
matching unit seedline 1
merger uniquifier
pt reconstruction unit
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Input Unit

• What is done in the input units?
• Each unit
• receives all tracklets from one plane via 2 links
• merges tracklets from both links in order of
  ascending Z position
• saves all tracklet information into memories for
  later processing
• projects Y position to middle plane
• calculates deflection angle from slope and Y
  position

10
Z-Channel Sorting Unit

• What is done in the z-channel sorting units?
• Each unit
• represents one logical channel (per plane)
• selects tracklets that belong to this channel and
  assigns them a subchannel index
• sorts tracklets with same subchannel index in
  ascending order of Y

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Matching Unit

• What is done in the matching units?
• Each unit
• applies sliding window algorithm for a constant
  seed plane
• saves sorted tracklets into memories
• always looks at two consecutive tracklets in each
  plane
• compares them (sequentially) to tracklets in seed
  plane
• compares also deflection angle if a potential
  match has been found

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GTU Architecture Overview
input unit (plane 5)
input unit (plane 4)
input unit (plane 3)
input unit (plane 2)
input unit (plane 1)
input unit (plane 0)
z-ch. 2 sorter
z-ch. 1 sorter
z-ch. 0 sorter
z-ch. 2 sorter
z-ch. 1 sorter
z-ch. 0 sorter
z-ch. 2 sorter
z-ch. 1 sorter
z-ch. 0 sorter
z-ch. 2 sorter
z-ch. 1 sorter
z-ch. 0 sorter
z-ch. 2 sorter
z-ch. 1 sorter
z-ch. 0 sorter
z-ch. 2 sorter
z-ch. 1 sorter
z-ch. 0 sorter
matcher z-ch 2
matcher z-ch 1
matcher z-ch 0
matching unit seedline 3
matching unit seedline 2
matching unit seedline 1
matching unit seedline 3
matching unit seedline 2
matching unit seedline 1
matching unit seedline 3
matching unit seedline 2
matching unit seedline 1
merger uniquifier
pt reconstruction unit
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Status

• Extensive simulation with AliRoot data has been
  done...
• to prove applicability of sliding window
  algorithm
• to investigate to what extend math operations can
  be simplified
• do without trigonometric functions, divisions
• approximate calculations with look-up tables
• to determine necessary bit widths and buffer
  depths for hardware implementation
• Implementation
• architectural concept has been developed
• important parts have been implemented in VHDL