The document discusses the advancements in spectral analysis for radio astronomy using FPGA-based filterbank technology. It highlights the technical challenges, improvements in bandwidth and frequency resolution, and outlines applications for various radio astronomy projects. Key conclusions indicate enhancements in dynamic range and functionality, alongside ongoing concerns about stability and input leveling.

1. Spectral Analysis at the Limit –
Applications in Radio Astronomy
Bruno Stuber Christian Monstein

2. Content
1. Objectives and Technical Challenges
2. Applications in Radio Astronomy
3. Summary and Conclusion
17. March 2015 2
Spectral Analysis at the Limit –
Applications in Radio Astronomy
Digital Filterbank: 1-/2-Channel Mode using FPGAs
Bruno Stuber FHNW, Institute for Automation
Christian Monstein ETH Zurich, Institute for Astronomy

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FPGAFPGA
FPGA
Spectrometer
Unit
(Filterbank)
HOST
PC
RX
Signals
FPGA
Signal Spectra:
 Bandwidth 
 Frequency Resolution 
 «seamless» processing
System Overview:


4. Project
CTI
Contribution
Total [kFr]
CTI
FHNW
Project Partners FHNW
Filterbank 2014 457 360
Industrial Partner
ETH Zurich IA
Uni Bern IAP
IA
IME
FFT 2 2008
CoSpan
(50++) 50 Uni Bern IAP
IA
IME
FFT 1 2005
ARGOS
292 240
Industrial Partner
ETH Zurich IA
Uni Bern IAP
IA
IME
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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
(Polyphase
Filters)
Output
Pro-
cessing
Accumu-
lation 1
x(t)
fs
(3.2 GS/s )
32k
FFT
DDR3
RAM
Control-
Inter-
face
Data-
Inter-
face
Window
ROM
FPGA
Data
Control
Accumu-
lation 2
X
Single Channel Mode:
A
D
Filter-
bank
Accu
3&4
x(t)
32k
FFT
DDR3
RAM
Control-
Inter-
face
Corr.
ROM
Data-
Inter-
face
Window
ROM
FPGA
Data
Control
y(t)
Filter-
bank Output
Pro-
cessing
Accu
1&2
32k
FFT
X
Y
A
D
fs
(1.6 GS/s )
Dual Channel Mode:
Inside the FPGA: The «FFT» respectively the Filterbank Unit:
Mode-Switching
«on the fly»

7. 1 - Channel: (Input x  Spectrum X)
Pxx X (Re, Im) P2
xx
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2 - Channel: (Input x and y)
Pxx | Pyy X | Y P2
xx | P2
yy
PX+Y | PX-Y (X+Y) | (X-Y) P2
X+Y | P2
X-Y
PXY* Re2(PXY*) | Im2(PXY*)
Legend:
Pxx = |X|2 : Power Spectrum |X|2
P2
xx : Square → Kurtosis-Analysis
PX+Y | PX-Y : Sum and Difference of Spectra
PXY* : 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 10,2s | 20,4s
Multiplications/s :
87,2 Milliards

9. FILTERBANK instead of FFT:
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Filterbank-Spectrum:
Compute only every L-th
DFT Bin
 N Bins
t
DC
Filterbank Frame: LN Samples
Scalar Product
f
Bin: 0 4 8 … (LN-1)
Bin: kL
4 Periods
f = 1/(LTF)
LTF
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
0
Selectivity 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
0
Selectivity Filterbank | Window: Def FT_1
Bin
dB
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 SimulationVerification
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, Switzerland
Left: 5m parabolic dish, F/D=0.507
Right: 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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Conclusions
Spectrometer 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 Stuber
www.fhnw.ch/personen/bruno-stuber
University of Applied Sciences and Arts Northwestern Switzerland FHNW,
Institute for Automation
www.fhnw.ch/technik/ia/
Christian Monstein
www.astro.ethz.ch/people/person-detail.html?persid=86162
ETH Zurich, Institute for Astronomy
www.astro.ethz.ch/
Daniel Treyer FHNW, Institute for Automation
Dino Zardet, Michael Roth FHNW, Institute of Microelectronics
Axel Murk University of Bern, Institute of Applied Physics