Multiple antenna multiple user channels: optimisation in low SNR

We study the sum capacity of multiple antenna multi-user wireless channels. We assume that base station and mobiles have perfect channel state information (CSI). The optimal transmission strategy for the single-antenna multiple-access channel is to allocate power only for the best user (R. Knopp et al., 1995). If multiple antennas are used at the base station and further on at the mobiles, it turns out that more than one user is allowed to transmit in the same time slot. In addition to this, the number of active users depends on the SNR. The higher the SNR the more users are active. It can be shown that for SNR values below some threshold only one user is active. We analyse the low SNR behaviour and give necessary and sufficient conditions for this threshold value. Finally, our development of the results is accompanied by many examples and illustrations and numerical simulations.