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This paper investigates outage and throughput performance of non-orthogonal multiple access (NOMA) based underlay cognitive radio (i.e., CR-NOMA) network under partial relay selection (PRS) scheme. Here NOMA is used in the secondary network, where K half duplex, decode-and-forward (DF) relays are available for assisting the secondary base station (SBS) to deliver information to the secondary users (SUs). We derive analytical expressions for the outage probabilities experienced by the SUs under imperfect successive interference cancellation (i-SIC) conditions. The interference threshold constraint of the primary receiver and the maximum transmit power constraint of the secondary nodes are considered for the analysis. To provide more insights on the outage performance, we obtain expressions for the asymptotic outage probabilities of the SUs in the high transmit power region. Next, we derive analytical …