In this paper, we consider effective performance transmission under generalized α − κ − µ the fading distribution. The source-user links are assumed to be non-orthogonal multiple access (NOMA) channels through a downlink power do-main. Two users are selected to service in a situation with perfect channel state information (CSI) in accordance with the NOMA protocol. The closed-form ex-pressions of outage probability (OP) and bit error rate (BER) are derived with the effect of power allocation coefficient, target rate, and channel fading param-eters. In addition, we calculate numerical results to demonstrate the asymptotic expansion in the high signal-to-noise ratio (SNR) analysis. Finally, Monte Carlo simulations are provided to validate and assess the accuracy of the analytical framework proposed.