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In this paper, we study the resource allocation problem, including the joint consideration of user grouping and power allocation, of an, underlay cognitive radio (CR) network employing non-orthogonal multiple access (NOMA), which is referred to as the NOMA-CR network. Based on the non-transferable utility coalition formation game theory, the so-called distributed sequential coalition formation (DSCF) algorithm is leveraged to solve the user grouping problem, where multiple cognitive users within a group can access the primary user's spectrum band while satisfying a minimum rate requirement of the primary user. The simulation results show that a near-optimal performance can be achieved by implementing the proposed DSCF as well as the optimal power allocation algorithms. Furthermore, the results validate that NOMA-CR can significantly outperform the traditional orthogonal multiple access CR, in terms of throughput. Finally, it is shown that by applying a novel adaptive trellis turbo coded modulation technique to the underlay NOMA-CR network, a significant throughput gain can be achieved.