The Wigner Distribution of Sum-of-Cissoids and Sum-of-Chirps Processes for the Modelling of Stationary and Non-Stationary Mobile Channels

This paper concerns the time-frequency analysis of stationary and non-stationary multipath flat fading channels. For the modelling of stationary multipath fading channels, we use a sum-of-cisoids (SOC
_i
) process, while the non-stationary channel is modelled by a sum-of-chirps (SOC
_h
) process that captures the time-variant Doppler effect caused by speed variations of the mobile station. For the time-frequency analysis, we apply the concept of the Wigner distribution. Closed-form solutions are provided for the Wigner distribution of SOCi and SOCh processes. It is shown that the obtained Wigner distributions can be expressed by the sum of an auto-term representing the true Doppler power spectral density (PSD) and an interfering cross-term that does physically not exist. A simple method is proposed to eliminate the interfering cross-term. The proposed method allows tracing the instantaneous Doppler frequencies of multipath fading channels in non-stationary propagation environments, which is an important topic in mobile radio channel modelling.