Non-orthogonal multiple access (NOMA) has attracted great attention due to its potential of providing high spectral efficiency and massive connectivity. Combining it with multipleinput multiple-output (MIMO) technology can further improve the spectrum efficiency. In this paper, the power allocation problem in downlink multi-cluster MIMO-NOMA systems is investigated for maximizing the fairness utility function. First, a long-term fairness function is considered and the optimization problem is formulated as a weighted sum-rate maximization problem. The problem is transformed into a convex form by introducing two sets of auxiliary variables, and propose an iterative algorithm to update the weight factors and the auxiliary variables. Then, an instantaneous fairness is considered and the optimization problem is formulated as a minimum data-rate maximization problem. It is transfiormed into a one-dimensional optimization problem based on an iterative algorithm and a closed-form power allocation expression is deduced. Simulation results illustrate that the proposed two fairness power allocation schemes have better performance of edge-user rate than the comparable schemes.
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