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In this letter, we investigate a multi-cell uplink non-orthogonal multiple access (NOMA) system with imperfect successive interference cancellation (SIC). The objective of the formulated optimization problem is to minimize the total power consumption under users' quality-of-service constraints. The considered problem is first transformed into a linear programming problem, upon which centralized and distributed optimal solutions are proposed. Numerical results are presented to verify the performance of the proposed solutions and evaluate the impact of imperfect SIC on the system performance.

Power Minimization for Multi-Cell Uplink NOMA With Imperfect SIC