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In millimeter-wave communication, digital beamsteering (DBS), only based on the user direction, is a promising angle-domain multi-antenna technique to mitigate the severe path loss and multiuser interference, with low-complexity and partial channel state information (CSI). In this paper, we design a power-domain non-orthogonal multiple access (NOMA) scheme that enhances the DBS performance trading-off complexity , energy-consumption and capacity performance. In particular, we propose a user-clustering algorithm to pair users, based on a geometric-interference metric, so that the inter-user interference is reduced. Afterward, based on a fixed inter-cluster power allocation, we derive analytically a sub-optimal intra-cluster power allocation optimization problem to maximize the network throughput. To address the issue of partial CSI, we rewrite the aforementioned optimization problem, by relying only on the user direction. Performance evaluation of the proposed schemes is developed in rural environment, based on the New York University millimeter-wave simulator. The obtained results demonstrate that the proposed low-complexity NOMA-DBS schemes with either full-or partial-CSI achieve significant performance improvement over the classical DBS, in terms of spectral-and energy-efficiencies (up to 26.8% bps/Hz rate gain for 45 users using the proposed scheme with partial CSI).