Curtailed-Gaussian and Cosine Functions for Multihop Doppler Spectrum Modeling

Wireless channels are characterized among others by their Doppler spectrum. In the cooperative diversity, one of diversity branch may consist of several mobile relays forming multihop link which each hop introduced Doppler shift. With employing amplify-and-forward (AF) relays, the Doppler shift keeps accumulating to the end of the link. Doppler shift value affects the time varying channel rate, which is a challenge in broadband mobile communication system. Hence, the Doppler parameter is very important and must be considered in broadband mobile communication system design and analysis. Unfortunately, it is hard to derive the expressions of this Doppler spectrum in a closed form since a special function under integration such as complete elliptic integral exists. To solve this problem, curve-fitting method base on least-square is used. In this process, curtailed-Gaussian and cosine functions are proposed as an approximation function. Then, from Kullback-Leiber divergence test, it is showed that both proposed functions, i.e., curtailed-Gaussian and cosine functions have a good approximation as Doppler spectrum modeling of Multihop mobile channel with all gain relays assumed as 1 and all mobile terminals are assumed move with almost same velocity.