Modelling of a Wireless Channel with Time Dependent Parameters

It is convenient to analyse wireless channels and links by exploiting their input-output description. This approach relies on treating the system as a black box, whose behaviour can be fully described by the relationship between the input and output signals. In this paper, we study a relationship of the above type for linear wireless channels having time-dependent parameters, which also takes a multipath propagation environment into account. A starting point for the derivations presented here is a relationship derived in the literature for this type of model with the application of a single sinusoidal input signal. The subject of this paper is the generalization of that relationship for periodic input signals and then of non-periodic signals. To the best of our knowledge, the literature lacks a suitably convincing generalization. The derivations of this paper exploit a principle of superposition valid for linear systems as well as the relations existing between Fourier series and the Fourier integrals. The discussion is illustrated by the results of simulations performed with the help of the MATLAB program.