This paper finds the capacity of single-user discrete-time channels subject to both frequency-selective and time-selective fading, where the channel output is observed in additive Gaussian noise. A coherent model is assumed where the fading coefficients are known at the receiver. Capacity depends on the first-order distributions of the fading processes in frequency and in time, which are assumed to be independent of each other, and a simple formula is given when one of the processes is

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... nt identically distributed (i.i.d.) and the other one is sufficiently mixing. When the frequency-selective fading coefficients are known also to the transmitter, we show that the optimum normalized power spectral density is the waterfilling power allocation for a reduced signal-to-noise ratio (SNR), where the gap to the actual SNR depends on the fading distributions. Asymptotic expressions for high/low SNR and easily computable bounds on capacity are also provided. Index Terms-Additive Gaussian noise, channel capacity, coherent communications, frequency-flat fading, frequency-selective fading, orthogonal frequency-division multiplexing (OFDM), random matrices, waterfilling.