Proportional fairness-based energy-efficient power allocation in downlink MIMO-NOMA systems with statistical CSI

Proportional fairness (PF)-based energy-efficient power allocation is studied for multiple-input multiple-output (MIMO) non-orthogonal multiple access (NOMA) systems. In our schemes, statistical channel state information (CSI) is utilized for perfect CSI is impossible to achieve in practice. PF is used to balance the transmission efficiency and user fairness. Energy efficiency (EE) is formulated under basic data rate requirements and maximum transmitting power constraints. Due to the non-convex nature of EE, a two-step algorithm is proposed to obtain sub-optimal solution with a low complexity. Firstly, power allocation is determined by golden section search for fixed power. Secondly total transmitting power is determined by fractional programming method in the feasible regions. Compared to the performance of MIMO-NOMA without PF constraint, fairness is obtained at expense of decreasing of EE.