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MIMO Channel Capacity with Full CSI at Low SNR

In this paper, we characterize the ergodic capacity of Multiple Input Multiple Output (MIMO) Rayleigh fading channels with full channel state information (CSI) at both the transmitter (CSI-T) and the receiver (CSI-R) at asymptotically low signal-to-noise ratio (SNR). A simple analytical expression of the capacity is derived for any number of transmit and receive antennas. This characterization clearly shows the substantial gain in terms of capacity over the no CSI-T case and gives a good insight on the effect of the number of antennas used. In addition, an On-Off transmission scheme is proposed and is shown to be asymptotically capacity-achieving.