| Summary: | Based on the high-direction characteristic of millimeter wave (mmWave) transmission, randomly directional beamforming (RDB) can be used for the mmWave massive multiple-input single-output (MISO) non-orthogonal multiple access (NOMA) system to reduce the number of radio frequency (RF) chains. However, the impact of RDB on the signal-to-interference-plus-noise ratio (SINR) of each user is related to the corresponding beamforming gain and interference from other users. Thus, in this paper, we investigate the max-min SINR among all users to evaluate user fairness. In particular, we focus on the single-cell downlink mmWave MISO-NOMA system with RDB, where single-antenna users are divided into multiple NOMA clusters according to their azimuth angles. We formulate the minimum achievable SINR maximization problem associated with power allocation and propose the sum of power allocation coefficients based iterative algorithm (SPACIA) to find the max-min SINR. We also prove that the max-min SINR monotonically decreases as the number of paired users in an NOMA cluster increases as well as the number of beams in the cell with large-scale base station (BS) antenna array increases. Moreover, we derive the upper bound of the max-min SINR. Simulation results verify our theoretical analyses and demonstrate that the proposed algorithm guarantees user fairness, thus outperforming existing schemes.
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