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In this paper, we study power allocation for downlink multi-carrier non-orthogonal multiple access (MC-NOMA)systems and examine the effects of residual cancellation errors resulting from imperfect successive interference cancellation (SIC) on the system performance. In the presence of random SIC errors, we study outage probability of minimum reserved rate for individual user and formulate outage-constrained robust optimization to minimize the total transmit power. Since the problem is non-convex due to probabilistic constraints, complementary geometric programming (CGP) and arithmetic geometric mean approximation (AGMA) technique are employed to transform it into a convex form. An efficient iterative algorithm with low computational complexity is developed to solve the optimization problem. Simulation results demonstrate the performance of robust MC-NOMA with imperfect SIC and compare that to non …