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Non-orthogonal multiple access (NOMA) is considered as one of the predominantmultiple access technique for the next-generation cellular networks. Weconsider a 2-user pair downlink NOMA system with imperfect successiveinterference cancellation (SIC). We consider bounds on the power allocationfactors and then formulate the power allocation as an optimization problem toachieve {$\alpha$-Fairness} among the paired users. We show that{$\alpha$-Fairness} based power allocation factor coincides with lower bound onpower allocation factor in case of perfect SIC and $\alpha > 2$. Further, aslong as the proposed criterion is satisfied, it converges to the upper boundwith increasing imperfection in SIC. Similarly, we show that, for $0<\alpha<1$,the optimal power allocation factor coincides with the derived lower bound onpower allocation. Based on these observations, we then propose a low complexitysub-optimal algorithm. Through extensive simulations, we analyse theperformance of the proposed algorithm and compare the performance against thestate-of-the-art algorithms. We show that even though Near-Far based pairingachieves better fairness than the proposed algorithms, it fails to achieverates equivalent to its orthogonal multiple access counterparts with increasingimperfections in SIC. Further, we show that the proposed optimal andsub-optimal algorithms achieve significant improvements in terms of fairness ascompared to the state-of-the-art algorithms.

$\alpha$-Fairness User Pairing for Downlink NOMA Systems with Imperfect Successive Interference Cancellation