In this paper, we investigate power allocation algorithms in a downlink millimeter wave non-orthogonal multiple access (mmWave-NOMA) system, which consists of one base station (BS) and a group of two-user clusters. Specifically, two optimization problems are formulated to maximize the achievable sum rate (ASR) and energy efficiency (EE), respectively, while satisfying the individual quality of service (QoS) constraints. To ensure the stability of successive interference cancellation (SICstability), we specially add the power order constraints, which are often neglected in existing works. By dividing each formulated problem into more tractable inter-cluster and intra-cluster sub-problems, and deriving the corresponding solutions, we propose the ASR maximization based power allocation (ASRMax-PA) and EE maximization based power allocation (EEMax-PA) algorithms. Numerical results show that the proposed ASRMax-PA (EEMax-PA) algorithm is much better than the state-of-the-art schemes in term of ASR (EE), while yields quite good EE (ASR) performance simultaneously. Moreover, both the two proposed algorithms can ensure SIC-stability, which is shown to have a significant impact on the NOMA system performance.
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