Mathematical Modeling of FMCW Radar: Sounding Signal Simulation

The paper presents models of changes in the instantaneous frequency, instantaneous phase, and the signal itself at any instant of time for a complex broadband two-way infinite continuous signal of an FMCW (Frequency Modulated Continuous Wave) radar with linear frequency modulation (LFM), the law of variation of which has the shape of an equilateral triangle. The proposed models are simple to implement and can be helpful in further discrete-time modeling of the operation of FMCW radar and any processes therein. In this case, obtaining a complex broadband signal from time analysis is possible, rather than performing complex analytical calculations. The models consider various propagation options, including the case of a signal radiated by a moving transmitter, propagating towards a moving target, reflecting from it, and returning to the moving receiver. The ability to determine individual signal values at arbitrary moments over an infinite time interval allows us to take into account not only the Doppler effect, as a change of individual oscillation frequency associated with the movement of the radar and target, but also changes in the shape and duration of a complex signal, as well as the spectral shift and change of its width. The models make it possible to simulate changes in the speed of clocks in the transmitter and receiver due to changes in their ADC and DAC sampling rates.