Convexity of Weighted Sum Rate Maximization in NOMA Systems

This letter investigates the optimal power allocation for weighted sum rate maximization (WSRM) in nonorthogonal multiple access (NOMA) systems with power order and quality-of-service (QoS) constraints. We show that the NOMA WSRM problem is a convex problem under some condition of the user weights. The optimal solution to the WSRM problem without QoS constraints is analytically characterized in two cases. Then, we investigate the feasibility of the WSRM problem with QoS constraints. We further show that the power order constraint can be omitted without loss of any optimality under some mild condition of the QoS thresholds, which enables us to derive an analytical expression of the optimal power allocation.