Capacity calculations for rapidly fading communications channels

This paper derives an upper bound for the Shannon channel capacity-cost function for a class of randomly time-varying channels under an average power constraint. The channels considered can be characterized by a series of uncorrelated parallel diversity channels with Gaussian-distributed random gain and additive white Gaussian noise parameters. The resulting expression for the single-channel case clearly shows that such channels have finite capacity even when the source power is unconstrained. Extensions are made to the multiple-diversity-channel case with a modified ''water-filling'' problem resulting.