Spectral Analysis at the Limit – Applications in Radio Astronomy

Bruno Stuber Christian Monstein

Content1. Objectives and Technical Challenges2. Applications in Radio Astronomy 3. Summary and Conclusion

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Spectral Analysis at the Limit –

Applications in Radio Astronomy Digital Filterbank: 1-/2-Channel Mode using FPGAs

Bruno Stuber FHNW, Institute for AutomationChristian Monstein ETH Zurich, Institute for Astronomy

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FPGAFPGAFPGA

SpectrometerUnit

(Filterbank)

HOSTPC

RXSignals FPGA

Signal Spectra: Bandwidth Frequency Resolution «seamless» processing

System Overview:

Project

CTIContribution

Total [kFr]

CTI FHNW Project Partners FHNW

Filterbank 2014 457 360Industrial PartnerETH Zurich IAUni Bern IAP

IAIME

FFT 2 2008CoSpan

(50++) 50 Uni Bern IAP IAIME

FFT 1 2005ARGOS

292 240Industrial PartnerETH Zurich IAUni Bern IAP

IAIME

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The Line of Projects:

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1 Processing Unit: Field Programmable Gate Array

(FPGA)

Xilinx Virtex 6 (XC6VSX315T)

■ 393’600 Flip Flops

■ 1’344 Multipliers

■ 704 Block RAM each 36 kbit

- SRAM based FPGA

- 40 nm CMOS Process

- 12 Layer Cu Metal

- 1 V Core Voltage

Internal Clockrate: 200 MHz

The Signal Processing Units:

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A

D

Filter-Bank

(PolyphaseFilters)

OutputPro-

cessing

Accumu-lation 1

x(t)

fs

(3.2 GS/s )

32kFFT

DDR3RAM

Control-Inter-face

Data-Inter-face

WindowROM

FPGA

Data

Control

Accumu-lation 2

X

Single Channel Mode:

AD

Filter-bank

Accu3&4

x(t)

32kFFT

DDR3RAM

Control-Inter-face

Corr.ROM

Data-Inter-face

WindowROM

FPGA

Data

Control

y(t)

Filter-bank Output

Pro-cessing

Accu1&2

32kFFT

X

Y

AD

fs

(1.6 GS/s )

Dual Channel Mode:

Inside the FPGA: The «FFT» respectively the Filterbank Unit:

Mode-Switching«on the fly»

1 - Channel: (Input x Spectrum X)

Pxx X (Re, Im) P2xx

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2 - Channel: (Input x and y)

Pxx | Pyy X | Y P2xx | P2

yy

PX+Y | PX-Y (X+Y) | (X-Y) P2X+Y | P2

X-Y

PXY* Re2(PXY*) | Im2(PXY*)

Legend: Pxx = |X|2 : Power Spectrum |X|2 P2

xx : Square → Kurtosis-Analysis

PX+Y | PX-Y : Sum and Difference of SpectraPXY* : Cross-power Spectrum

Filterbank Output in 1-Channel- and 2-Channel-Mode:

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Front Panel Spectrometer

Bandwidth: 1600 | 2x800 MHz

Spectrum: 16’384 Bins

Update-Rate: every 10,2s | 20,4s

Multiplications/s :87,2 Milliards

FILTERBANK instead of FFT:

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Filterbank-Spectrum:Compute only every L-thDFT Bin N Bins

t

DC

Filterbank Frame: LN Samples

Scalar Product

fBin: 0 4 8 … (LN-1)

Bin: kL

4 Periods

f = 1/(LTF)

LTF

8 Periods

t

Filterbank Window

I II III IV

-5 -4 -3 -2 -1 -0.5 0 0.5 1 2 3 4 5-120

-100

-80

-60

-40

-20

0Selectivity DFT/ FFT | Window: Kaiser 9

dB

-5 -4 -3 -2 -1 -0.5 0 0.5 1 2 3 4 5-120

-100

-80

-60

-40

-20

0Selectivity Filterbank | Window: Def FT_1

Bin

dB

Filterbank

Selectivity Curve per Channel/ Bin:

«Standard» FFT

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Implementation: Technical Challenges

■ Architectur, Algorithms Filterbank instead of FFT, Channel Modes, …

VHDL–Design Scalable for different Target Hardwares ■

Timing: FPGA-Systemclock: 200 MHz !! ■

Matlab-Reference Bit-true VHDL Simulation Verification

IA: Bruno Stuber: Algorithms

Daniel Treyer: Matlab, Numerics

IME: Dino Zardet: Architectur, Verification

Michael Roth: VHDL Implementation

Stefan Brantschen: SW Interface

Optimal use of DSP-Slices on the FPGA ■

■ Fixed-Point Arithmetic Word Widths, Rounding, …

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…’’at the Limit’’ ???

The Signals:• Dynamic of the Input Signal

• Signal deep below the Noise Level Averaging, Measuring Differencies

• Short-term and Long-term Stability of the Equipment

The Technique:• Speed: Spectra processing «seamless»: 3,2 GS/s 97’600 Spectra/s

• Functionality: New Level achieved 1-Channel, 2-Channel Mode, …

• FPGA: Complexity and Speed Routing and Timing

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Spectrometer M0703A applications

• Antenna power in Radio Astronomy• Plan A: Gold mine in Uruguay• Plan B: Russian spy telescope in Latvia• Prototyping in Bleien AG

- Spectrum issue- 1/f noise, Allan Time- Solar bursts- Sky map

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Antenna power level in Radio Astronomy

Source Temperature Power

RFI due to FM, DVB-T, DAB-T -30.0 dBm

Solar radio burst 5000 Kelvin -114.7 dBm

Receiver noise 100 Kelvin -131.7 dBm

Cosmic microwave background 2.7 Kelvin -147.4 dBm

Baryonic oscillation, red shifted 21 cm line 5 µ Kelvin *) -205.7 dBm

Total dynamic range: 175.5 dB

*) requires at least 1 year on-source integration time

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Gold mine Castrillon in Minas Corrales, Uruguay BINGO - Baryon acoustic oscillations In Neutral Gas Observations

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RT-32 in Ventspils, Latvia (HIMap)

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Ex Soviet spy installation RT-32

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Offset mount of 8 dual polarization horns

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Bleien AG, SwitzerlandLeft: 5m parabolic dish, F/D=0.507Right: 7m parabolic dish, F/D=0.34

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Spectrum in Bleien

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Stability: 1/f noise, Allan Time

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High dynamic solar bursts

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High dynamic solar bursts

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High dynamic solar bursts

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Transit Radio Galaxy Cygnus A

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Transit Sagittarius A

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Sky Map

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ConclusionsSpectrometer is working …+ Input dynamic range improved (8 Bit → 12 Bit)+ Numerical artefacts reduced+ Functionality and modes significantly enhanced~ ADC input leveling not clear yet (rfi vs resolution)~ Stability analog-input over time

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Experts

Bruno Stuberwww.fhnw.ch/personen/bruno-stuberUniversity of Applied Sciences and Arts Northwestern Switzerland FHNW, Institute for Automationwww.fhnw.ch/technik/ia/

Christian Monstein www.astro.ethz.ch/people/person-detail.html?persid=86162ETH Zurich, Institute for Astronomywww.astro.ethz.ch/

Daniel Treyer FHNW, Institute for AutomationDino Zardet, Michael Roth FHNW, Institute of MicroelectronicsAxel Murk University of Bern, Institute of Applied Physics