Ergodic capacity of block-fading Gaussian broadcast and multi-access channels for single-user-selection and constant-power

We consider the ergodic capacity region of block-fading Gaussian multiuser channels with channel-state information at both the transmitters and the receivers. We assume a single constraint on the total long-term average power used for both broadcast and multi-access channels. In addition to the optimal solution known from the literature, we provide analytic expressions - some of which are novel - to characterize the boundary surface of the capacity region under auxiliary constraints which include single-user-selection per block, constant total transmit-power per block and the combination of both. We also provide optimal resource allocation schemes to achieve the capacity limits for each case under consideration. Moreover, we provide numerical examples to compare the cases. As an illustrative example, we analyze the two-user case, although the results carry over to the M-user case.