Non-orthogonal multiple access (NOMA) is consid-ered as one of the predominant multiple access techniques for next-generation cellular networks. We consider a 2-user pair downlink NOMA system with imperfect successive interference cancellation (SIC). We consider bounds on the power allocation factors and then formulate the power allocation as an optimization problem to achieve α-Fairness among the paired users. We show that α-Fairness based power allocation factor coincides with lower bound on power allocation factor in case of perfect SIC and alpha > 2. Further, as long as the proposed criterion is satisfied, it converges to the upper bound with increasing imperfection in SIC. Similarly, we show that for 0 < alpha < 1, the optimal power allocation factor coincides with the derived lower bound on power allocation. Based on these observations, we then propose a low complexity sub-optimal algorithm. Through extensive simulations, we analyze the performance of the proposed algorithm and compare it against the state-of-the-art algorithms. We show that the proposed optimal and sub-optimal algorithms ensure that each user achieves a rate at least equivalent to its orthogonal multiple access counterparts. Further, we also show significant improvements in terms of fairness with the proposed algorithm as compared to the state-of-the-art algorithms. © 2022 IEEE.