The Deterministic Time-Linearity of Service Provided by Fading Channels

In the paper, we study the service process S(t) of an independent and identically distributed (i.i.d.) Nakagami-m fading channel, which is defined as the amount of service provided, i.e., the integral of the instantaneous channel capacity over time t. By using the Moment Generation Function (MGF) approach and the infinitely divisible law, it is proved that, other than certain generally recognized curve form or a stochastic process, the channel service process S(t) is a deterministic linear function of time t, namely, S(t)=c_m* · t where c_m* is a constant determined by the fading parameter m. Furthermore, we extend it to general i.i.d. fading channels and present an explicit form of the constant service rate c_p*. The obtained work provides such a new insight on the system design of joint source/channel coding that there exists a coding scheme such that a receiver can decode with zero error probability and zero high layer queuing delay, if the transmitter maintains a constant data rate no more than c_p*. Finally, we verify our analysis through Monte Carlo simulations.