Throughput analysis of cellular downlink with different types of channel state information

Scaling laws for multiuser systems have recently attained much attention. These scaling laws are usually derived under the assumption of identical user distributions and for high SNR values. In the current work, we study the broadcast channel (BC) with perfect channel state information (CSI) at the mobiles and different types of CSI at the base station, i.e. without CSI, with long-term CSI and with perfect CSI. We analyse the impact of the fading distributions on the achievable average sum capacity. We show for the case in which the base station has no CSI, that the maximum average sum rate is obtained for fading channels which have their second order moments equally distributed, i.e. the sum rate is Schur-concave with respect to the fading variances. For the case in which the base station has information about the long-term statistics of the fading channels in terms of the fading variances, we derive the optimum transmit strategy. In this case the sum capacity is maximised if one user has largest second order moment, i.e. the sum capacity is Schurconvex. Finally, in the case in which the base has perfect CSI, only the best user is supported. For this type of CSI, the average sum capacity is maximal if one user has large fading variance and all other users have very low fading variances, i.e. in this case the average sum rate is Schur-convex, too. Finally, we derive the loss or gain due to the fading statistics and illustrate the results by simulations.