This paper investigates the application of non-orthogonal multiple access in millimeter-Wave communications (mmWave-NOMA). Particularly, we consider downlink transmission with a hybrid beamforming structure. A user grouping algorithm is first proposed according to the channel correlations of the users. Whereafter, a joint hybrid beamforming and power allocation problem is formulated to maximize the achievable sum rate, subject to a minimum rate constraint for each user. To solve this non-convex problem with high-dimensional variables, we first obtain the solution of power allocation under arbitrary fixed hybrid beamforming, which is divided into intra-group power allocation and inter-group power allocation. Then, given arbitrary fixed analog beamforming, we utilize the approximate zero-forcing method to design the digital beamforming to minimize the inter-group interference. Finally, the analog beamforming problem with the constant-modulus constraint is solved with a proposed boundary-compressed particle swarm optimization algorithm. Simulation results show that the proposed joint approach, including user grouping, hybrid beamforming and power allocation, outperforms the state-of-the-art schemes and the conventional mmWave orthogonal multiple access system in terms of achievable sum rate and energy efficiency.
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