Comparison of fading channel capacity under different CSI assumptions

This paper explores the relationship between the ergodic fading channel capacity with transmitter and receiver channel state information (CSI), the ergodic fading channel capacity with receiver CSI only, and the zero outage capacity. In particular, we obtain general order relations for these different capacity definitions and also compare them to the capacity of an additive white Gaussian noise channel (AWGN) channel with the same average signal-to-noise ratio (SNR). We determine conditions under which transmitter CSI significantly increases ergodic capacity, and we show that the ergodic capacity of a fading channel can exceed the capacity of an AWGN channel with the same average SNR. We also discuss the relative difference between the capacity of fading channels with transmitter and receiver CSI versus the capacity with receiver CSI only. We show that while this difference is negligible on a Nakagami fading channel it might be relatively significant on a two-state Nakagami fading channel. We also discuss the implications of this work for practical coding schemes.