TOW 2007: Correlator Theory
Kerry Kingham - U.S. Naval Observatory
Roger Cappallo – Haystack Observatory
Mike Titus - Haystack Observatory
Outline
• Basic idea of how the correlator works
• Description of the Arcane (and Archaic) “Fringe Plot”
• Some idea of how problems affect the results
What Does a Correlator Do(and how does it do it)?
Why Correlate?
• If we had a high snr, we could just difference the arrival times (e.g. pulse)
• Unfortunately, quasar signals are ~103 weaker than the noise in our best receiving systems
• The correlater allows us to magically pull this weak signal out of the noise and measure its delay (and rate) between two sites
Cross-correlation of weak signals
• Let s(t) be a weak astronomical signal, and n1(t) and n2(t) be noise signals at sites 1 & 2
Correlation of weak signals (cont’d)
• Product of signals is:
(s + n1) (s + n2) = s2 + n1s + n2s + n1n2
Summed Correlation Components
Correlation Hardware
• If done at the original RF, a delay model by itself would produce the correct Doppler shift
• Since we process at baseband, we need to have separate delay and phase models
Correlator Channel
Bandwidth Synthesis
• We measure delay by observing phase differences at different frequencies
• For a given delay, the higher the frequency, the greater the change in phase:
frequency
phase(rot)
No good!
Optimizing Coherence
• In addition to the linear phase change due to frequency, there is a contribution to each channel’s phase from the instrumentation
• e.g. the filters in each VC have slightly different delays
• The phase cal subsystem injects tones into the front end every MHz with the same phase (at the start of each second).
• The correlator detects each tone, and adjusts the phase of the corresponding channel.
Phase-cal aligns the channels:
The Fringe Plot!
(How a Mark IV Correlator person sees the results of correlation)
Top of the Plot in 3D!(Kashima style)
The Correlator as Spectrum Analyzer
• The correlator cross-correlates at many “lags”in the time domain
• If we have it autocorrelate (Gc to Gc rather than Gc to Ap) we get an autocorrelation function in delay (time).
• If we Fourier Transform the autocorrelation function in delay we transform the time function into a frequency function!
• We can turn the Correlator into a large, expensive, not very portable spectrum analyzer
Correlator as Spectrometer (cont)
Phase Cal as Test Tone
• Phase cal tones are injected early in the signal path
• They are excellent test signals as well as alignment tools
• At both the station and at the correlator, Pcal tones can be used as probes to investigate problems in the VLBI system
Analyzing Pcal Tones at the Correlator: Internal Spurious
Signals
• Generated inside the VLBI System
• If at 1 Mhz or multiple and locked to the Maser, it can affect the phase cal amplitudes and phases
• Reflections of the Pcal tones are a common source of these signals
Signal Locked to Maser
Spurious Signal in Phase Cal
Reflected Signal
Reflected Signal
Spurious Signal amplitude > Phase Cal amplitude
Channel SpectraShowing Internal (?) RFI Signals
External Signals
• Not locked to maser
• Not necessarily at p-cal frequencies
• May be Time Dependent
• May be dependent on telescope direction
Early ScanRFI in “d” channel
A Few Minutes LaterNo RFI in “d” channel
Channel SpectraGood Channel (note p-cals):
First Case: Bad RFI Second Case: Not so Bad RFI
Very External Signals
• Direct Digital Audio Broadcast Satellites
– “XM” & “Sirius” over North America
– Proposed service for Europe
“XM” Signals in N.A. Stations
References
• http://ivscc.gsfc.nasa.gov/publications/gm2000/whitney2
• http://ivscc.gsfc.nasa.gov/publications/gm2004/kondo
• http://www.nrao.edu/php/sigpath/StaticHTML/correlator.ph
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• http://www.cv.nrao.edu/vlbabook
End of Correlator Theory
Hardware and Software Structure
...of current Mark IV correlator