We consider uncoordinated random uplink non-orthogonal multiple access (NOMA) systems using a set of predetermined power levels. We propose to optimize the probabilities of selection of power levels in order to minimize performance metrics as block error probability (BLEP) or bit error probability (BEP). When the multiuser detection algorithm at the BS treats at most two colliding users' packets, our optimization problem is a quadratic programming problem. For more colliding users' packets, we solve the problem iteratively. Our solution is original because it applies to any multiuser detection algorithm and any set of power levels.

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