Data Concentrator - SVD data multiplexer with FPGA-based

Data ConcentratorSVD data multiplexer with FPGA-based tracking

Tracking-Meeting Bayrischzell

Jochen Dingfelder, Carlos Mariñas, Michael Schnellschnell@physik.uni-bonn.de

University of Bonn

July, 19th 2012

Michael Schnell (University of Bonn) Data Concentrator July, 19th 2012 1 / 21

Content

1 Motivation

2 Hardware Status

3 FPGA-based tracking

4 Simulation

Motivation

CopperSystem

DataConcentrator

optical links

Hardware Status

Content

1 Motivation

2 Hardware Status

4 Simulation

Hardware Status

Hardware Solution

• Advanced Mezzanine Card (AMC)• Redesign with 4 SFP connectors

(Zhen-An)→ 11 cards• Received during DEPFET meeting

in Seeon• Given back to Zhen-An for fixing

backplane problems• Start testing, when it returns

Hardware Status

Simplified Block Diagram

4:1Mux

Framer

11:1Mux

4:1Mux

Decoder

Scheduler &MMU

4 GB DDR 2Memory

Trackreconstruction

EthernetFrame

GPU ProtocolFramer

AmplitudeAnalysis

Collection

AMC "Datcon"

ATCAGPU Farm

Framer

AMC "Collector"

FPGA-based tracking

Content

1 Motivation

2 Hardware Status

4 Simulation

FPGA-based tracking

Data Flow Diagram Plan

General tracking module interconnection (can also be distributed)

Conformal

transformation

SVD strip-dataCoordinate

translator

transformation

creator

creation

Intercept

finder

FPGA-based tracking

Coordinate Translation

LUT for basic location lookup of eachladder

With strip ID, strip pitch in u-vdirection and DSP of FPGAdetermine precise position

Alignment constant for each ladder inu-v direction

Constant for sagging correction withLUT of a x2 function

FPGA-based tracking

SVD Clustering idea

+ Take center and size of cluster, saves space and resources− Additional type of data needed

FPGA-based tracking

General Testing Platform

Userlandtrack generation and strip ID calculation

Kerneltransmission to PCIe

over DMA map

PCIe 1xtransmission to FPGAand init processing

FPGAprocessing and

back transmission

Simulation

Content

1 Motivation

2 Hardware Status

4 Simulation

Simulation

Real 2D Hit

500 Background hits (∼ 1 percent occupancy)

5 generated tracks

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2

Simulation

Hough Space

Corresponding Hough Space:

-1.5 -1 -0.5 0 0.5 1 1.5

Simulation

FHT Example With Less Background

30 background hits and 2 tracks in Hough space

-1.5 -1 -0.5 0 0.5 1 1.5

Simulation

30 background hits and 2 tracks in Hough space with intercept regions

-1.5 -1 -0.5 0 0.5 1 1.5

Simulation

Zoom to one of the intercept regions

-1.28 -1.278 -1.276 -1.274 -1.272 -1.27 -1.268

Simulation

Definitions

A few later used definitions:

Efficiency:

ε := number of correct found trackstotal number of real tracks ε ∈ [0,1]

→ For all later shown plots: ε = 1!!

Purity:

p := number of found trackstotal number of real tracks p ≥ 0

→ p ≥ 1

Simulation

Track Purity With FPGA Algorithm Simulation

100 150 200 300 400 500

genera

Background Hits

1 generated Track2 generated Tracks3 generated Tracks4 generated Tracks5 generated Tracks

Simulation

Execution Time

Running on Core i7 2600 @ 3.8 GHz (with fixed affinity + turbo boost):

100 200 300 400 500 600 700 800 900 1000

CreateHough Trafo

Intercept FinderIntercept Finder (Vertex constrained)

Simulation

Visualization Software

For visualizationfull VXD (SVD,PXD) with activearea and stripand pixelstructure

Markingbackground,tracks, clusters...

Presentation

Simulation

Summary and Status

2D Simulation of the SVD (r-ϕ plane only), r-z plane in progress

Track reconstruction efficiency is high, but...tracks with Gaussian smearing only (2 strip pitches)

No multiple scattering, energy loss, magnetic fieldinhomogeneities...

→ Switch to the basf2 framework

• Done, but only with local coordinates of sensors.

• Hough transformation only feasible with up to 1 − 2 percentoccupancy

Simulation

Thank you for your attention!

Backup Technical Specifications

Technical Specification on I/O

Input:Up to 42 (32)optical-fibre links

1.5 Gbps max

On average110 Mbpsexpected

Dynamicbandwidth

Output:6.25 Gbps overbackplane orSFP+

440 Mbpsaverage datarate

Dynamicbandwidth

→ Total: 4.6 Gbps ≈ 550 MiB/s

Backup Idea

Tracking Options

Hough Transformation to findstraight and arc tracks (afterconformal transformation)

Can be fast and efficientimplemented in the FPGA overFast Hough Transformation (FHT)

First 2D resulsts of the next slides

Open for other algorithm, likesector-neighbour finding cellularautomaton or Kalman-Filter -1

0 0.5 1 1.5 2

0 0.5 1 1.5 2 2.5 3 3.5 4

Houghtransformation

Backup FPGA Implementation

Trigonometric Functions and Memory Requirements

Need trigonometric functions like sine and cosine e.g. forcoordinate transformation

CORDIC: Basic Lookup table for nodes and a shift-addimplementation of approximation functionPure LUT: Large Lookup table for every value (high memoryrequirements)

FPGAs’ DSPs used as Multiplier/Divider unit.

Block Memory needed to translate strip IDs into coordinates andROI creation

Backup FPGA Implementation

Status of the Different Blocks in Simulations

4:1Mux

Framer

11:1Mux

4:1Mux

Decoder

Scheduler &MMU

4 GB DDR 2Memory

Trackreconstruction

EthernetFrame

GPU ProtocolFramer

AmplitudeAnalysis

Collection

AMC "Datcon"

ATCAGPU Farm

Framer

AMC "Collector"

Backup Multiplexer Theory

Multiplexing

Three general types of multiplexing:Frequency Division Multiplexing (FDM)

Time Division Multiplexing (TDM)

Statistical Multiplexing

Because of dynamic bandwidth “Statistical Multiplexing” would bemost suitable

Demultiplexing is trivial, if only multiplexing of 32 bit words isensured

Backup Multiplexer Theory

Aurora overview

Xilinx Aurora protocol as physical link layer over GTP

Takes care of every “low level” operation like clock correction,symbol decoding and 8B/10B Encoding

Easy data transmission/framing over locallink

Error detection and initialization

Status wires for channel and lanes

Lane: One communication lineChannel: Concentration of one or more lanes

Backup Hough-Transformation

Simple Hough Trafo in 2D with straight tracks

Hits in 2 D

Want to find straight tracks i : yi = m · xi + a in this mess

→ Go to Hough-Space: a = −m · xi + yi

0 0.5 1 1.5 2 2.5 3 3.5 4

xMichael Schnell (University of Bonn) Data Concentrator July, 19th 2012 22 / 21

Hough-Space

0 0.5 1 1.5 2

Find interception of 5 Tracks around zero!

Found 2: y1 = 0.6 · x ; y2 = 1.5 · xMichael Schnell (University of Bonn) Data Concentrator July, 19th 2012 21 / 21

With tracks

Found 2:y1 = 0.6 · xy2 = 1.5 · x

0 0.5 1 1.5 2 2.5 3 3.5 4

tr 1tr 2

Coordinate Transformation

This is bad for tracks close or parallel to y-axes (m = inf.)!

Make a coordinate transformation like: r = x · cos(Φ) + y · sin(Φ)

0 0.5 1 1.5 2

trackr

Implementation in FPGA?

Use Fast Hough Transformation!

Divide and Conquer type algorithm

0 0.5 1 1.5 2

Implementation in FPGA 2

Vary with minimum and maximum size of a unit area the tolerance

Efficient and highly parallelisable, a sector for each unit

0 0.5 1 1.5 2

Also support of different shapes

One more to go...

0 0.5 1 1.5 2

Error comes for “free”

Done... finally

0 0.5 1 1.5 2

Data Concentrator - SVD data multiplexer with FPGA-based

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