Time and Synchronization for OVRO LWA352
Creators: name: D'Addario, Larry R.
Publisher: name: California Institute of Technology
Year: 2020

description: For many reasons, it is desirable for the outputs of a telescope to be labeled with the
times of the observations; we call this time tagging. It requires some sort of clock, along with a
mechanism for assigning clock readings to telescope outputs. If generating the outputs involves
combining multiple signals, as in a radio telescope array, and especially if that processing is
distributed across multiple devices, there is also a need to synchronize the timing among the
signals. That is, we want to ensure that the time tag assigned to an output applies in the same
way to all signals, not just one of them or an average of them.
These two objectives, time tagging and synchronization, usually have very different
requirements for accuracy and precision. For example, for a telescope that generates outputs
every few seconds, time tagging with a precision of 1 s may be sufficient. But if it is combining
signals in a band near 1 GHz, synchronization precision must be << 1 ns. For time tagging, but
not for synchronization, there may be an additional requirement for accuracy with respect to an
external measure of time, such as UTC; the basic requirement is with respect to time on a local
clock ("telescope time"). Some telescope designs have conflated these three requirements –
synchronization precision, time tagging precision with respect to telescope time, and time
tagging accuracy with respect to external time – and attempted to accomplish all with a common
implementation, concentrating on the last item to the detriment of the others.
When multiple devices must know something about time, the timing information must be
distributed to them from the telescope clock. The information is distributed using timing signals.
Any timing signal can be described by two fundamental parameters, its accuracy and it
ambiguity. For example, we could use a 10 MHz tone as a timing signal. If its signal-to-noise
ratio is such a receiver can measure its phase to .01 cycle, then it has an accuracy of 1 ns; and,
since each cycle is indistinguishable from the next, it has an ambiguity of 100 ns. Or consider
transmitting periodic pulses at a rate of 1 per second (1 PPS, which is a traditional choice in
radio astronomy, introduced in VLBI practice more than 50 years ago). If its SNR is such that a
receiver can measure the rising edge to 10 ns, then that is its accuracy; its ambiguity is 1 s. Or
consider transmitting a 64b number that is proportional to time with its LSB representing 1 ns.
Its ambiguity is 584 years. In principle its accuracy is 1 ns, but in practice it is difficult to build a
digital receiver that can measure the number's arrival time to 1 ns, and to build a digital network
whose latency is stable and known to 1 ns. The point is that there are practical limits to the
ambiguity-to-accuracy ratio that can be achieved with a single signal. To achieve a higher ratio,
multiple timing signals can be used in a hierarchy. A fast signal is used to obtain the required
accuracy, but with low ambiguity; a slower signal then has just enough accuracy to resolve the
ambiguity of the fast signal, but larger ambiguity. We continue in this way with additional
signals until the desired ambiguity is achieved, retaining the first signal's accuracy. The key is
that each signal must resolve the ambiguity of its predecessor, and of course all signals must be
consistent with each other (all derived from the same clock). Some telescopes have been
designed with fast and slow timing signals but without paying attention to these principles.
description: Accepted Version - memo14.pdf