Distributed antenna system (DAS) has been deployed for over a decade. DAS has advantages in capacity especially for the cell edge users, in both single-cell and multi-cell environments. In this paper, non-orthogonal multiple access (NOMA) is suggested in single-cell DAS to maximize user fairness and sumrate. Two transmission strategies are considered: NOMA with single selection transmission and NOMA with blanket transmission. In a two-user scenario, the center base station (BS) uses NOMA to serve both users and the remote radio units (RRUs) serve only the weak user based on the transmission scheme. The signals sent from the RRUs are not considered as interference at both user sides. At one side, the signals from the RRUs are used to detect the required data and at the other side, the signals are used to perform successive interference cancellation (SIC). The max-min performance is studied when instantaneous channel gain information (CGI) or channel distribution information (CDI) is known at the transmitter. A closed-form expression of the upper bound is derived for the data rate of each user with only CDI. In addition, the sum-rate is studied with a minimum rate constraint when instantaneous CGI known at the transmitter. The results show that NOMA with blanket transmission gives the best performance compared to other schemes; conventional-NOMA, conventional single selection scheme and joint-transmission (JT) NOMA. It is also shown that with less transmit power, NOMA with single selection transmission gives better performance than conventional-NOMA.