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This article considers non‐orthogonal multiple access (NOMA) enabled full‐duplex (FD) underlay cognitive relay networks (ie, NOMA‐FDCRNs) with partial relay selection scheme. The secondary network, where NOMA is used, consists of a secondary base station (SBS) sending messages to two secondary users (SUs), that is, a near SU (SU1) and a far SU (SU2), by utilizing a dedicated relay selected from a set of FD decode‐and‐forward nodes. We obtain analytical expressions for the outage probabilities (OPs) of the SUs and then deduce the asymptotic OP expressions as well. Further, expressions are obtained for the optimal power allocation (OPA) coefficients at the SBS and at the relay that separately maximizes the throughput of the secondary network in NOMA‐FDCRN. Furthermore, the jointly optimal power allocation (JOPA) coefficients that maximize the throughput are also determined. The analyses …