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We study the throughput capacity region of the Gaussian multi-access (MAC)fading channel with perfect channel state information (CSI) at the receiver andat the transmitters, at low power regime. We show that it has amultidimensional rectangle structure and thus is simply characterized by singleuser capacity points. More specifically, we show that at low power regime, theboundary surface of the capacity region shrinks to a single point correspondingto the sum rate maximizer and that the coordinates of this point coincide withsingle user capacity bounds. Inspired by this result, we propose an on-offscheme, compute its achievable rate, and show that this scheme achieves singleuser capacity bounds of the MAC channel for a wide class of fading channels atasymptotically low power regime. We argue that this class of fading encompassesall known wireless channels for which the capacity region of the MAC channelhas even a simpler expression in terms of users' average power constraintsonly. Using the duality of Gaussian MAC and broadcast channels (BC), we deducea simple characterization of the BC capacity region at low power regime andshow that for a class of fading channels (including Rayleigh fading),time-sharing is asymptotically optimal.

On the Capacity of Multiple Access and Broadcast Fading Channels with Full Channel State Information at Low SNR