The deterministic time-linearity of service provided by Rayleigh fading channels

In the paper, we study the channel service process of an independent and identically distributed (i.i.d.) Rayleigh channel. The channel service process S(t) is defined as the amount of service provided by the channel, i.e., integral of the instantaneous channel capacity over a time interval of length t. The channel side information (CSI) is assumed available at the receiver. Using the Moment Generation Function (MGF) approach and the infinitely divisible law, it is proved that the channel service process S(t) is a deterministic linear function of time t other than the generally recognized certain curve form, namely, S(t) = c* · t, where c* is a constant.