On the Capacity of Nakagami-m Fading Channels with Full Channel State Information at Low SNR

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The capacity of flat Rayleigh fading channels with full channel state information (CSI) at the transmitter and at the receiver at asymptotically low SNR has been recently shown to scale essentially as SNR log(1/SNR). In this paper, we investigate the Nakagami-m fading channel capacity with full CSI, and show that the capacity of this channel scales essentially as Ω/m SNR log (1/SNR), where m is the Nakagami-m fading parameter and where Ω is the channel mean-square. We also show that one-bit CSI at the transmitter is enough to achieve this asymptotic capacity using an On-Off power control scheme. Our framework may be seen as a generalization of previous works as it captures the Rayleigh fading channel as a special case by taking m = 1.