Derivation of the frequency mismatch probability in linear FMCW radar based on target distribution

In LFMCW (linear frequency modulated continuous wave) radar, there is a nonzero probability for mismatches to occur under certain conditions. This probability strongly depends on the modulation employed as well as on the distribution of targets in the radar's field of view, i.e. the application of the radar sensor. Hence to reduce mismatches in a given application, an effective approach is to carefully design the modulation used. Instead of utilizing extensive simulations, we derive the distribution of mismatches analytically, solely based on the modulation parameters and a given distribution of targets. Based on that mismatch distribution, an application-specific optimization of the modulation is feasible.