  A new stochastic order between two fading distributions is introduced. A
fading channel dominates another in the ergodic capacity ordering sense, if the
Shannon transform of the first is greater than that of the second at all values
of average signal to noise ratio. It is shown that some parametric fading
models such as the Nakagami-m, Rician, and Hoyt are distributions that are
monotonic in their line of sight parameters with respect to the ergodic
capacity order. Some operations under which the ergodic capacity order is
preserved are also discussed. Through these properties of the ergodic capacity
order, it is possible to compare under two different fading scenarios, the
ergodic capacity of a composite system involving multiple fading links with
coding/decoding capabilities only at the transmitter/receiver. 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. Applications to
multiple access channels, and extensions to multiple-input multiple-output
(MIMO) systems are also discussed.
