Backend electronics for
radioastronomy
G. Comoretto
Data processing of a
radioastronomic signal
Receiver (
front

end
)
Separates the two polarizations
Amplifies the signal by ~10
8
Limits the band to a few GHz
Translates the sky frequency to a more manageable
range
The resulting signal is then processed by a
back end
Electric field E(t)
Power density S(f)
to
backend
Data processing of a
radioastronomic signal
Measure S as a function of time, frequency, polarization
status, baseline
Total power
Polarimetry
Spectroscopy
Interferometry
Pulsar (search and timing)
Record the instantaneous field E(t) for further
processing
VLBI/ Remote interferometry
Radio science
Composite of the above (e.g. spectropolarimetric
interferometry)
Signal conversion
IF output may be too wide
Difficulties of building wideband backends
Necessity of having several spectral points across
the IF bandwidth (e.g. for Faraday rotation)
Interest in a specific spectral region (e.g. line
spectroscopy)
Necessity to avoid contaminated portion of the IF
band
Baseband converters (BBC): select a portion of the IF
bandwidth and convert it to frequencies near zero
Each BBC followed by a specific backend (total power,
polarimeter, spectrometer, VLBI channel....)
Simplest observable: total integrated flux over the
receiver bandwidth
Filter: selects the frequency band of interest
Square law detector: diode (simpler, wideband) or
analog multiplier (more accurate, expensive, band
limited)
Integrator: sets integration time: time resolution vs.
ADC speed
ADC: converts to digital. Integrator & ADC are often
implemented as a voltage

to

frequency converter &
counter
Total power
Sensitivity:
t
= integration time
D
f
= bandwidth or frequency resolution
S
= total (receiver dominated) noise
For modern receivers, 1/f gain noise dominant for t > 1

10 s
need for accurate calibration & noise subtraction
Added mark
Correlating receiver
On

the fly mapping
Wobbling optics
Total power
Polarimetry
Dual polarization receiver:
vertical/horizontal or
left/right
Cross products give
remaining Stokes
parameters
Instrumental polarization:
30dB = 0.1%
Bandwidth limited by
avaliable analog multipliers
Need for coarse
spectroscopic resolution
(Faraday rotation)
Spectroscopy
Acousto

optic spectrometer:
signal converted to acoustic waves in a crystal
diffraction pattern of a laser beam focussed on a CCD
amplitude of diffracted light proportional to S(f)
Large bandwidth, limited (1000 points) resolution
Rough, compact design
All parameters (band, resolution) determined by
physical design => not adjustable
AOS Array for Herschel

HiFi
LiNb cell with 4 acoustic channels
Instantaneous band: 4x1.1 GHz (4
–
8 GHz)
Resolution : 1 MHz
Spectroscopy
–
Digital
correlator
Digital spectrometers:
Bandwidth determined by sampling frequency
Max BW technologically limited, currently to few 100MHz
Reducing sampling frequency decreases BW = > increased
resolution
Autocorrelation spectrometers (XF)
Compute autocorrelation function:
Fourier transform to obtain S(f)
Frequency resolution:
Signal quantized to few bits (typ. 2)
Complexity proportional to N. of spectral points
Spectroscopy
–
FFT
spectrometer
FFT spectrometers:
Compute spectrum of finite segment of data
Square to obtain power and integrate in time
Complexity proportional to log
2
(N) => N
large
Requires multi

bit (typ. 16

18 bit) arithmetic
Easy to implement in modern, fast FPGA, with HW
multipliers
Slower than correlator, but keeping pace
Polarimetric capabilities with almost no extra cost
Spectroscopy
–
FFT
spectrometer
Poly

phase structure: multiply (longer) data segment
with windowing function => very good control of filter
shape
Very high dynamic range (10
6

10
9
) => RFI control
Interferometry
Visibility function: <E
1
(t)*E
2
(t+
t
)>
Computed at distant or remote location: need for
physical transport of the radio signal
Directly connected interferometers
Connected interferometers with digital samplers
at the antennas and digital data link
E

VLBI: time

tagged data over fast commercial
(IP) link
Conventional VLBI: data recorded on magnetic
media
Accurate phase and timing control
Interferometry
Visibility computed on dedicated correlator or FFT
processor
Conventional correlator scales as (number of
antennas)
2
FFT (FX) scales as N
Must compensate varying geometric delay:
Varying sampler clock
Memory based buffer, delay
by integer samples
Phase correction in the
frequency domain
Due to frequency conversion,
varying delay causes
“fringe frequency” in the correlation
ALMA correlator (1 quadrant)
Digital vs. Analog Backend
All backend functions can be performed on a digital
signal representation
Current programmable logic devices allow to implement
complex functions on a single chip
Digital system advantages:
predictable performances
–
easy calibration
high rejection of unwanted signals

RFI
Better performances, filter shapes etc.
Easy interface with digital equipments
Example of a general

purpose full digital
backend
Digital vs. Software
Backend
Software backends (e.g. SW correlator) becoming
possible
e.g Blue Chip IBM supercomputer viable as LOFAR
correlator
Most Radio Science processing done on software
Computing requirements scale as a power of the BW
Dedicated programmable logic still convenient
1 FPGA: 50

500 MegaOPS, ~16 FPGA/board
MarkIV correlator (in FX architecture): 1.7 TeraOPS
EVLA Correlator: 240 TeraOPS
Digital Backend: Examples
ALMA Digital filterbank:
2 GHz IF input
32x62.5 MHz
independently tunable
BBC
General purpose board,
can be configured to
implement 16 FFT
spectropolarimeters @
125 MHz BW each
Digital Backend: Examples
VLBI dBBC:
1 GHz IF input
250 MHz output bandwidth
Directly interfaces with E

VLBI
BEE2 Berkeley system
1 GHz IF input
General purpose board, with library of
predefined components
System design and validation using MATLAB
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