On the Max-Min Fairness of Beamspace MIMO-NOMA

Non-orthogonal multiple access (NOMA) based beamspace multiple-input multiple-output (MIMO) is a MIMO-NOMA scheme for millimeter-wave (mmWave) communications to improve the number of connections with increased sum rate. However, most of existing works only aim at maximizing the sum rate, which may cause an unbearable rate loss to weak users. To guarantee the rate performance for all served users, we maximize the minimal rate of the system from the max-min fairness perspective, where the NOMA users in the same beam share the same digital precoding vector, i.e., the beam-specific digital precoding, is adopted. The challenge is that, both the inter-beam and intra-beam interferences exist in the system, which makes the minimal rate maximization problem non-convex and thus hard to solve. To cope with this challenge, we propose an alternating optimization method to optimize the power allocation for each user and the digital precoding vector for each beam. Moreover, we break the commonly adopted beam-specific digital precoding scheme by using the user-specific digital precoding, i.e., each user is assigned with a unique digital precoding vector, to further improve the max-min rate. This can be achieved by the proposed two-stage optimization method, where the user-specific digital precoding vectors are firstly designed, and then the power allocation for all users is finetuned. Simulation results verify the proposed two methods. Moreover, the two-stage optimization method for the user-specific digital precoding outperforms the alternating optimization method for the beam-specific digital precoding, since the former can provide more degrees of freedom for designing the digital precoding vectors.