Modeling and numerical simulation of sawtooth FMCW

Sawtooth FMCW is widely used in ranging systems because of the high ranging precision. Combining features of modulo function, which is periodic and discontinuous, the analytical expressions of frequency and phase of sawtooth FMCW were deduced to express them in multi-FM-period, and the discontinuousness at boundary between FM periods. The mathematics modeling and simulations were realized. The correctness of analytical expressions was proven analytically by deduction of differential and integral relationships between frequency and phase. The result of numerical simulation also shows that frequency and phase expressions have relationships of differential and integral, which are the corrective expressions for frequency and phase. And the expressions could correctly describe the discontinuousness of sawtooth FMCW at boundary between FM periods. The expressions for frequency and phase of Sawtooth FMCW in multi-FM-period can serve as a base for further research of ranging process involving sawtooth FMCW.