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