Max-Min Fair Precoder Design and Power Allocation for MU-MIMO NOMA

In this paper, a downlink multiple input multiple output (MIMO) non-orthogonal multiple access (NOMA) wireless communication system is considered. In NOMA systems, the base station has unicast data for all users, and multiple users in a group share the same resources. The objective is to design transmit precoders and power allocation coefficients jointly that provide max-min fairness (MMF) among the strongest users in each group, while maintaining minimum target rates for all the other users. The problem is solved via two main iterative approaches. The first method is based on semi-definite relaxation (SDR) and successive convex approximation (SCA), and the second method is based on the equivalency between achievable rate and minimum mean square error (MMSE) expressions. For the latter approach, Karush-Kuhn-Tucker (KKT) optimality conditions are derived and the expressions satisfied by the optimal receivers, MMSE weights and the optimal precoders are obtained. Proposed algorithms are compared with rate-splitting (RS), orthogonal multiple access (OMA) and multi-user linear precoding (MULP) schemes in terms of MMF rates, energy efficiency and complexity. It is shown that while RS has the best MMF rates and energy efficiency, the MMSE approach based on KKT optimality conditions has the least complexity. Moreover, the SDR/SCA approach offers an excellent tradeoff. It offers high MMF rates, low complexity and superior energy efficiency.