Spectrogram analysis of multipath fading channels

The analysis of the Doppler power spectral density (PSD) of measured and simulated data is an important topic in the area of mobile radio channel modelling. In this paper, we estimate the Doppler PSD of multipath fading channels by using the concept of the spectrogram. The spectrogram is a spectral representation that gives insight into how the distribution of the spectral density of a signal changes over time. The multipath fading channel is modelled by a sum-of-cisoids (SOC) process. A closed-form solution is presented for the spectrogram and the corresponding time-dependent autocorrelation function (ACF). The closed-form solutions disclose several unwanted effects that come with the limited sample space. One phenomenon is that the spectrogram changes with time, even if the underlying SOC process is ergodic. Another phenomenon is that the bandwidth of the spectrogram is not limited to the physical range determined by the maximum Doppler shift. These two phenomena can lead to misinterpretations of the spectrogram. Measures are discussed to reduce these effects. The results of this paper are important for the performance assessment of channel simulators as well as for the evaluation of measurement data collected in all kinds of mobile radio channels.