A Solution to the Wrapped Phase Problem by Dual Subcarrier-Modulated Chirps

Abstract

It is well-known that the phase of the beat signal in frequency modulated continuous wave (FMCW) radar contains information about the range. However, $2\pi $ phase wrapping limits the maximum unambiguous range to an unrealistically short distance. As a result, phase has not been widely used as a means for range finding. In this work, we propose a dual-frequency chirp waveform formed by modulating a baseband chirp onto two subcarriers, combing them then following by main carrier modulation. This approach means that each subcarrier creates its own beat signal represented by rotating phasors. Each phase angle carries information about the delay but is subject to phase wrap very quickly. The obvious solution is to limit delay by choosing a working range of unrealistically short distances. However, it can be shown that the phase differences between the two phasors could be worked out in such a way as to cancel phase wrap. A waveform design parameter in the form of the spread-delay product is identified that when properly chosen will mitigate phase wrap before it occurs. The spread-delay term is the product of subcarrier frequency spacing and the expected delay. There are no restrictions on choosing the spacing; hence, the waveform can be tuned to match all expected delays. Simulations are run to show that the concept works for both short ranges, as in automotive radar, and long-range surveillance such as air traffic control.