Optimum and suboptimum scheduling schemes are proposed in the uplink of array antenna systems. We assume that once a user is permitted to transmit the data, the user transmits the data using the maximum power, and adjusts the transmission bit rate so that the energy-per-bit-to-interference-plus-noise-density ratio should be equal or higher than a threshold. In this system model, we consider an optimization problem: How many and which users should be selected to transmit their data at a time in order to maximize the throughput? Based on the analysis on the complexity of the optimum scheme, we propose another optimum scheme having reduced complexity. To reduce the complexity further, we also propose three suboptimum scheduling schemes by limiting the number of users simultaneously transmitting, by choosing the users with higher channel gains, and by partitioning a cell into multiple parts. In circular and linear arrays, the performance results of all the proposed schemes are presented and compared.