Ergodic capacity ordering of fading channels

In this paper, a new stochastic order between two fading distributions is introduced. A fading channel dominates another in the capacity ordering sense, if the ergodic capacity of the first is greater than that of the second at all values of average signal to noise ratio. We show that many parametric fading models such as the Nakagami-m, Rician and Hoyt fading satisfy the capacity order, in the sense that the distribution with a larger line of sight parameter is larger in the ergodic capacity sense. Further, we obtain closure properties of the capacity order for the first time, because such a stochastic order has not been considered in either stochastic ordering literature, or information theory literature. Through these properties, we develop sufficient conditions for comparing the ergodic capacity of a composite system involving multiple capacity ordered fading links with coding/decoding capabilities only at the transmitter/receiver, when operated in two different fading scenarios. Such comparisons can be made even in cases when a closed form expression for the ergodic capacity of the composite system is not analytically tractable. We also show that capacity ordering of point-to-point links has applications to multiple access channels.