We study the performance of uplink transmission in a large-scale (massive) MIMO system, where all the transmitters have single antennas and the base station has a large number of antennas. Specifically, we first derive the rates that are possible through minimum mean-squared error (MMSE) channel estimation and three linear receivers: maximum ratio combining (MRC), zero-forcing (ZF), and MMSE. Based on the derived rates, we quantify the amount of energy savings that are possible through increased number of base-station antennas or increased coherence interval. We also analyze achievable total degrees of freedom (DoF) of such a system without assuming channel state information at the receiver, which is shown to be the same as that of a point-to-point MIMO channel. Linear receiver is sufficient to achieve total DoF when the number of users is less than the number of antennas. When the number of users is equal to or larger than the number of antennas, nonlinear processing is necessary to achieve the full degrees of freedom. Finally, the training period and optimal training energy allocation under the average and peak power constraints are optimized jointly to maximize the achievable sum rate when either MRC or ZF receiver is adopted at the receiver.