Local positioning systems (LPS) are not only of increasing interest for industrial and commercial applications, but are also required for crisis management to keep track of first responders at all times, both for security and for logistic reasons. In such systems, frequency-modulated continuous wave (FMCW) radar is widely used. However, the properties of the radio channel for the application in crisis scenarios are very difficult to predict. Therefore, the FMCW principle is going to be investigated with regard to different channels. Especially the impact of heavy multipath environments on the concept is modeled and simulated. Furthermore, a detection algorithm is proposed to cope with fading radio channels and the impact of different Fast Fourier Transform (FFT) windows is discussed.