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In this paper, we consider the average transmit power minimization problem in a non-orthogonal multiple access (NOMA) system under the strict outage constraints of users. In particular, we assume the base station (BS) only knows the statistical channel state information (CSI) of the users and the users have heterogeneous quality of service requirements. Without loss of generality, we assume user 1 is a delay-aware user with low target rate requirement and user 2 is a delay-tolerant user with high target rate requirement. Due to the high target rate requirement of user 2, it may fail to decode its own information. Thus we proposed a partial hybrid automatic repeat request (HARQ) scheme to guarantee the communication reliability of user 2. By deriving the outage probability of users as closed-form expressions, the average transmit power minimization problem boils down to a nonconvex optimization problem and …