Uplink Non-Orthogonal Multiple Access with Statistical Delay Requirement: Effective Capacity, Power Allocation, and α Fairness

The proliferation of delay-sensitive Internet-of-Things (IoT) applications has ushered in a need for the statistical delay quality-of-service (QoS) guarantee for the applications. In this paper, we first derive an upper bound for the queuing delay violation probability (UB-QDVP) in uplink non-orthogonal multiple access (NOMA) by applying stochastic network calculus (SNC) to the Mellin transforms of service processes. A closed-form asymptotic approximation of the UB-QDVP is developed by proving the asymptotic convergence of the Mellin transform and its finite-length truncations. Given the closed-form asymptotic UB-QDVP, we propose two power allocation schemes. The first scheme minimizes the transmit power of a NOMA user pair while guaranteeing the statistical delay QoS of the pair. The second maximizes the \alpha -utility function of the effective capacity of the user pair, striking a balance between the energy efficiency and user fairness of uplink NOMA systems. Simulations validate the UB-QDVP and show the superiority of the proposed schemes to conventional power allocation schemes in terms of energy efficiency and fairness.