This paper considers a downlink non-orthogonal multiple access (NOMA) system where the source intends to transmit independent information to the users at targeted data rates under statistical channel state information at the transmitter. The problem of outage balancing among the users is studied with the issues of power allocation, decoding order selection, and user grouping being taken into account. Specifically, with regard to the max-min fairness criterion, we derive the optimal power allocation in closed-form and prove the corresponding optimal decoding order for the elementary downlink NOMA system. By assigning a weighting factor for each user, the analytical results can be used to evaluate the outage performance of the downlink NOMA system under various fairness constraints. Further, we investigate the case with user grouping, in which each user group can be treated as an elementary downlink NOMA system. The associated problems of power and resource allocation among different user groups are solved. The implementation complexity issue of NOMA is also considered with focus on that caused by successive interference cancellation and user grouping. The complexity and performance tradeoff is analyzed by simulations, which provides fruitful insights for the practical application of NOMA. The simulation results substantiate our analysis and show considerable performance gain of NOMA when compared with orthogonal multiple access.