To improve the utilization of spectrum and system capacity, non-orthogonal multiple access (NOMA) is considered as a promising multiple access method for emerging communication technologies. Its advantageous benefits are implemented in two-way wireless networks. Power allocation factors assigned to multiple users play a key role in the successful deployment of fairness balance in NOMA. This paper considers fixed power allocation, and performance degradation is predicted in worse situation in which non-optimal power scheme and the imperfect channel state information (CSI) happen. More challenging issue happens in this system, and this paper addresses the situation of NOMA supporting multi-pair of users, in which group of users can communicate to other users to achieve acceptable throughout in two kinds of mode, i.e. delay-limited mode and delay-tolerant mode. Two performance metrics have been considered, namely, ergodic rate and outage probability. For both metrics, we derived closed-form analytical expressions as well as asymptotic performance. Numerical results show that the proposed system presents benefits to cellular networks by extending ability to serve more users who have different demands on data communication. Monte Carlo simulations are provided throughout to validate the accuracy of the derived analytical expressions.