The aim of this paper is to study how to enlarge the performance gap between non-orthogonal multiple access (NOMA) and conventional orthogonal multiple access (MA) by applying user pairing. Particularly two user pairing schemes achieving different quality of service (QoS) requirements, namely NOMA with fixed power allocation (F-NOMA) and cognitive radio inspired NOMA (CR-NOMA), are proposed. For F-NOMA, both analytical and numerical results are provided to demonstrate that F-NOMA can offer a larger sum rate than orthogonal MA, and the performance gain of F-NOMA over conventional MA can be further enlarged by selecting users whose channel conditions are more distinctive. For CR-NOMA, the QoS requirements for users with poorer channel conditions can be guaranteed since the transmit power allocated to other users is constrained following the concept of cognitive radio networks. Because of this constraint, CR-NOMA has different behavior compared to F-NOMA, as demonstrated by the developed analytical results.