On the Consistency of Non-Stationary Multipath Fading Channels with Respect to the Average Doppler Shift and the Doppler Spread

This paper is concerned with the consistency of non-stationary multipath fading channels. We introduce conditions under which a channel model is consistent w.r.t. the average Doppler shift and the Doppler spread. The conditions are applied to two classes of non-stationary channel models. The first class, which is termed Class A, is characterized by channel models based on an integral relationship between the path phases and the associated time-variant Doppler frequencies. The second class of models, called the Class B models, emerges from standard sum-of-cisoids (SOC) models by replacing the time-independent Doppler frequencies by time-dependent Doppler frequencies. It is shown that the Class A models fulfil the consistency conditions, while the Class B models are inconsistent. The majority of existing non- stationary channel models with time-dependent Doppler frequencies fall in the Class B category, meaning that these models suffer from a lack of physical soundness. The importance of the paper comes from the fact that it provides guidelines for the design of consistent and physically reasonable non-stationary channel models.