| Wireless cellular networks provide means to communicate and retrieve data with increased flexibility. As services and content become available, consumer demand increases and pushes for higher transmission data rates. However, transmission rates are limited because limited resources are shared between the users. The maximum transmission rate that can be achieved, while keeping the communication reliable, is known as capacity.; This thesis documents some of the possibilities to approach the capacity of wireless cellular networks when transmitting data from several users to a common access point (uplink) and vice versa (downlink). We use the medium access control layer model for the uplink and the physical layer model for the downlink.; In the first case, the capacity can be viewed as the condition for stability of the users' queues. We have rigorously proven necessary and sufficient stability conditions and provided steady-state and delay analyses for asymmetric (multi-rate) systems of a class of network-assisted diversity multiple access (xNDMA) protocols.; In the second case, the capacity is considered in the information-theoretic sense, that is, the maximum transmission rate subject to the limited bandwidth and power. We have considered a class of greedy multi-user downlink transmission algorithms based on zero-forcing beamforming assuming that the channel can be accurately acquired under certain conditions. We have shown that these algorithms yield throughput---sum of data rates of individual links from the base station to users---close to capacity for scenarios encountered in practice. In addition, we have shown that the computational complexity of this class of algorithms is significantly smaller than the complexity of optimal algorithms and it is acceptable for real-time implementation. |