We have recently proposed a stochastic microwave-based measurement approach for the loading state of the catalysts used in automotive aftertreatment systems. In this approach, the interior of the catalyst housing acts as a wireless channel between two end devices of a communications system. It was shown that, depending on the transmission channel characteristics, the properties of the catalyst such as its state can be inferred from the properties of some random function such as the received time response (a random function of time) or its Fourier transform, the received spectrum (a random function of frequency). This publication presents results on the resolution of the measurement method when the normalized cross-correlation function between the received spectra with respectively unloaded and loaded catalyst is used as random function. In particular, we have investigated the influence of the transmit signal power. Measurements and signal evaluation were performed for diesel particulate filter (DPF) with different soot loads probed with an ultra wideband (UWB) system and subsequent processing of the waveform in the frequency domain.