Stochastic ordering of fading channels

This paper introduces stochastic ordering of the instantaneous SNRs of fading channels as a tool to relate and compare the average performance of communication systems over different channels by harnessing the relation between completely monotone (c.m.) functions and the stochastic Laplace transform (LT) order. Toward this goal, instantaneous error rates of M-QAM and M-PSK modulations are shown to be c.m. functions of the instantaneous SNR, while the instantaneous capacity is seen to have a completely monotonic derivative (c.m.d.). Further, examples of commonly used parametric fading distributions which exhibit a monotonicity in the parameter with respect to the LT order are developed.