Capacity calculations for rapidly fading communications channels

Communication over rapidly changing channels such as the underwater acoustic channel has been an active research area, as well as an engineering challenge, for more than three decades. 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.