gums, I discussed a constant signal of lowered power with pseudorandom noise, PRN, modulation. (I did not state it in exactly those sorts of terms. I tried to phrase it so non-EEs could dig what I said.) GPS is a good example. And I'd postulate a chipping rate (PRN bit rate) around 1/10th to 1/2 the nominal 37.5 kHz. Once doing that I'd use crystal control even if it's a "floor sweeping" crystal with very wide tolerance. (200 parts per million.) You'd have to acquire time and frequency, of course. The acquisition problem may indicate a lower chipping rate. (And my jargon may be a tad out of date. Those are the terms we used in the department at Rockwell where I did this sort of stuff for over a decade.)
{^_^}