On the Unambiguous Distance of Multicarrier Phase Ranging With Random Hopped Frequencies

Multicarrier phase ranging (MCPR) technique has been widely used in radio navigation, telemetry, radar, and many other fields. In an MCPR system, unique range estimation can be obtained within only the so-called unambiguous distance (UD) because of phase ambiguity. As a metric gauging, the measurable distance of an MCPR system, the UD has been well studied under two common configurations: the linearly spaced frequencies and the proportionally spaced frequencies. In this paper, we propose to apply the frequency hopping (FH) waveform to the MCPR systems for an enhanced antijamming capability, which has been a key criterion in military and other mission critical applications. It is, however, difficult to define the UD with randomly spaced frequencies (RSF) led by the FH waveform. Under the RSF configuration, the UD becomes a random variable. We try to depict its statistical property with a deterministic value and find that the upper bound of the random UD plays an important role. We prove that, without phase noise, the UD can reach its upper bound with a large probability when only a dozen of carriers are employed, as long as the hop set of FH waveform is large enough. Simulations further show that even in the presence of phase noise and multipath fading scenarios the UD under the RSF configuration can also achieve its upper bound asymptotically if the number of carriers is moderately increased from a dozen to several dozens. Our paper uncovers the feasibility of applying the FH waveform to the MCPR systems.