Considerations on barycentric referencing for Noema    
(MT Oct2011) Rev 08/13

The earth motion causes an annual  ~200ppm pk-pk  Doppler "shift" which is traditionally corrected for by shifting the LO1.
Actually Doppler effect can be considered  a "shift" only when applied to a CW signal. For a wide band signal the width also is expanded or compressed in the same proportion, the difference may reach 0.8 MHz  across a 4 GHz IF baseband, and this can be a few tens of spectrometer channels. For a several-month observation, it is desirable that the channels keep integrating in a fixed source-referenced  frequency frame, whilst the instrument performs the appropriate on-line corrections according to the current Earth situation.
Adjusting the correlator clock has the effect of expanding/compressing its channelization grid and can be used to correct for this effect in the hardware. A few years ago G.Paubert called this technique "barycentric referencing" because the Earth/Moon/Sun center of mass is to be considered. On the PdB interferometer this has some consequences :

1:On the Walsh cycle generator

Since the integration time is defined in the correlator by a fixed number of clock cycles, the basic  (31 msec) dump time is expected to vary by +/- 100 ppm. Preserving the orthogonality of the Walsh sequences  requires that encoding and decoding are perfectly synchronous, so the LO1 Walsh generator  must also derive from the same barycentric clock, and its sequence initialized by the same 1PPS.

2: On the computer transfer

As a consequence, the 1-second correlator data dumps will no longer be triggered by the 1PPS events, but by a slowly drifting barycentric 1PPS-B. The time difference between the two can reach  0.1 sec after 1000 seconds.  At any time, but preferably at the start of a scan, the computer should request the barycentric reference generator to align its "1PPS-B"  on the UTC 1PPS  in order to avoid transfer jams.

 3: On the LO1 and LO2 ('s)

All the LOs in the receiving chain should be locked to the barycentric reference. Offsetting the master 5 MHz would be the simplest solution. But high performance frequency synthesizers (e.g. Rohde Und Schwarz) happen to (disdainfully)  reject  any external reference frequency which is offset by as much as 100ppm.  So  an exception has to be made for the LO1. It will have to be connected to the fixed reference 5 MHz and be Doppler-corrected by software, as traditionnally. Note that the 100MHz and 0.5 MHz are part of the LO1 elaboration scheme and they are also locked to the fixed 5 MHz.

 4: On the delay system

The delay effectively elaborated by the digital hardware is proportional to the correlator clock period, which has been adjusted after the radial velocity of the Earth. The geometrical delay is independent of it. The difference may reach 1 nsec. A simple software scaling is necessary before sending the delay value to the hardware.

Fig.1 : Connexions of the future backends elements to implement barycentric referencing.

Performance of the barycentric generator
It generates two references, named 128 MHz-B and 1PPS-B,  which are more appropriate for the new systems than the vintage pair 5MHz,1PPS.
Since the 128 MHz is multiplied up to only ~10GHz , its spectral quality does not need to be outstanding. A good VCXO is sufficient to achieve it.
Its settling time (PLL  bandwith) is a concern only when the source is changed (e.g. jump to calibrator). It just needs to be smaller than the antenna motion time. Anything smaller than10 seconds is OK, 1 second is probably a convenient value.  All the PLL's which are locked  on the 128 MHz (and there will be many) are a lot faster, so they will not be subject to cycle skipping. If zero correction is sent (or no software present), the system works exactly as on classic fixed clocks . This mode is useful for VLBI where Doppler is taken into account in the correlator.

Refreshing rate of the Doppler parameters

Three actions are available for tracking,
a) Change the synthesizer frequency. This is almost immediate and can take place any time (TBD :without affecting the data ?)
b) Change the barycentric generator frequency. Has a ~1 second settling time, during which the Walsh orthogonality might be altered.
c) Request an alignment of the 1PPS-B  on UTC, operation that causes a 1-second loss of data. The computer sends to the barycentric generator a command to align the 1pps-B on UTC. At the same time it starts counting the 32pps-B events sent by the counter and fetches the corresponding Walsh function values.  When the drift relative to UTC reaches some value (e.g.0.1 sec), or when some pre-defined time has elapsed, the computer may re-iterate alignment.

The (rough) tables below suggest that the annual motion sets the maximum size of the correction, but it is the diurnal motion that determines its refreshing rate.

The rule of thumb is that  a change is needed whenever the frequency drift reaches one tenth of the smallest spectral channel. This leads to a synthesizer refresh every four scans at maximum. The barycentric generator can stay unchanged for one hour. A good policy is probably to have it refreshed and aligned at the same time, once every 20 minutes or so.