Low SNR Characterization of the Channel Capacity of Generalized Fading Channels

This paper aims to characterize the low signal-to-noise ratio (SNR) capacity of generalized fading channels. The work was performed during my graduation internship at King Abdullah University and Science and Technology. The multiple-input multiple-output (MIMO) Rayleigh fading channel and the single-input single-output (SISO) Log-normal shadowing channel are successively considered. General expressions of the ergodic capacities under different assumptions on channel state information (CSI) availability at the transmitter are presented. Then asymptotic analysis are made to derive low and high SNR asymptotic expressions of the capacities. The capacity of those channels has been shown to be affected by CSI availability at the transmitter only at low SNR. The tremendous capacity gain with multiple antennas was also retrieved and shown to decrease with the SNR. Simple on-off transmission schemes were then constructed and shown to be asymptotically capacity-achieving. Those schemes require only one bit feedback from the receiver to the transmitter so that the transmitter does not need to perfectly track the channel, showing that the proposed transmission schemes are really interesting from a practical point of view.