On the capacity of multiple access and broadcast fading Channels with full channel state information at low power regime

We study the throughput capacity region of the Gaussian multi-access (MAC) fading channel with perfect channel state information (CSI) at the receiver and at the transmitters (CSI-TR), at low power regime. We show that it has a multidimensional rectangle structure and thus is simply characterized by single user capacity points. More specifically, we show that at low power regime, the boundary surface of the capacity region shrinks to a single point corresponding to the sum-rate maximizer and that the coordinates of this point coincide with single user capacity bounds. Using the duality of Gaussian MAC and broadcast channels (BC), we provide a simple characterization of the BC capacity region at low power regime.