The Unambiguous Distance in a Phase-based Ranging System with Hopping Frequencies

It is a challenge to specify unambiguous distance (UD) in a phase-based ranging system with hopping frequencies (PRSHF). In this letter, we propose to characterize the UD in a PRSHF by the probability that it takes on its maximum value. We obtain a very simple and elegant expression of the probability with growth estimation techniques from analytic number theory. It is revealed that the UD in a PRSHF usually takes on the maximum value with as few as 10 frequencies in measurement, almost independent of the specific distribution of available bandwidth.