We consider channel modeling issues in the context where communicating objects are evolving in impulsive environments. It was shown recently that α-stable random processes are attractive solution for representing the ultra wide band communication channel in relatively large spatial areas. In this paper, we consider the α-stable channel modeling in an evolutionary context where the model features depend on spatial locations. We introduce a methodological approach consisting of two parametric and non parametric components: the latter can be seen as black box model to describe the spatial evolution and it can be learned from historical observations of the transfer function. The other component concerns the frequency dependence and has an auto-regressive structure.