In this article, the performance of cognitive radio system benefits from non-orthogonal multiple access (NOMA) scheme. We then examine system metrics to adjust its quality of signal processing. We focus on performance of the secondary network containing NOMA users which have some impacts from normal user and primary nodes. We refer to enhancement of the fairness and spectrum utilization by enabling spectrum sharing. In particular, the NOMA power allocation factors are assigned to provide different ergodic capacities for two NOMA users in the downlink of such cognitive radio-non-orthogonal multiple access (CR-NOMA) system. This article presents approximated ergodic capacity of secondary users, in which this system adopts the Rayleigh fading. The closed-form expressions are expected to match with Monte-Carklo simulation results and main system parameters can be determined to control performance of such CR-NOMA. Finally, this system is prominent once its performance outperforms than that of conventional orthogonal multiple access (OMA)-based system.
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