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:    = integration time    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 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 ( ) => RFI control

Interferometry Visibility function: 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: 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 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