With the rise in smartphone usage, the system models have rapidly evolved to meet ever-growing needs for capacity in wireless networks. Indeed, there have been large advances in technology, from single-user single-antenna point-to-point communications to multi-cell multi-antenna cellular networks. In fact, multiple-input multiple-output (MIMO) technology for wireless communications is now incorporated into wireless broadband standards since 3G. Adding multiple antennas at both the transmitter and the receiver sides enables spatial multiplexing (i.e. sending multiple data streams simultaneously), which allows to increase data rates, and spatial diversity exploitation, which allows to greatly improve link quality. The multi-user MIMO downlink (so-called Broadcast Channel (BC)) has been a well investigated subject in wireless communications because of the high potential it offers in improving the system throughput. Therefore, different design criteria for multi-user MIMO communication have been investigated in the literature. Most of the downlink designs consider optimization problems w.r.t. the sum-capacity of all users. On the other hand, the major bottleneck of modern wireless communication is the interference (intracell and intercell) due to frequency reuse. Thus, in a multi-user MIMO scenario, when optimizing the overall efficiency, the power allocation is focused on the good channels, i.e., users that are subject to strong interference (e.g. cell-edge users) are neglected. The result is an unfair distribution of rate among users. In order to avoid this effect, different fairness notions have been introduced, like max-min fairness, weighted fairness, or proportional fairness.
In this thesis, we focus on the weighted max-min fairness. In particular, we study the (weighted) user rate balancing problem in a multi-cell multi-user MIMO system. We address this problem by joint beamforming and power allocation optimization, aiming to satisfy the fairness requirements. In the first part, we consider perfect knowledge of the channel to solve the problem. Therein, we maximize the minimum (weighted) rate via i) weighted user Mean Square Error (MSE) uplink/downlink duality and ii) Lagrangian duality. In the second part, we consider partial knowledge of the channel. We optimize the ergodic rate balancing problem via i) weighted expected MSE by exploiting the rate – MSE relation, and ii) two approximations of the expected rate as the Expected Signal and Interference Power (ESIP) rate at the stream level and the received signal level. Furthermore, we study the transmit power minimization problem with fixed user-rate targets and provide a strategy exploiting the proposed rate balancing approaches.