In this study, user selection‐based downlink power domain‐non‐orthogonal multiple access (NOMA) system is investigated over generalized fading channels, that is, η‐μ and κ‐μ fading channels. In particular, this system considers multiple users and out of which two users are selected to serve with NOMA principle in perfect channel state information scenario. The outage probability expressions of the system are derived with respect to the fixed target rate and the orthogonal multiple access (OMA) rate. In addition, the average sum‐rate and rate of paired users of the system are derived and compared with that of OMA. Further, the optimum power allocation coefficients are derived for the system to ensure fixed and dynamic rate requirements. The impact of imperfect successive interference cancelation on the system performance is discussed. The paper also investigates the effect of various parameters on the performance of the system. The extensive simulations show the accuracy of the derived expressions.