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This paper investigates the application of a cooperative non-orthogonal multiple access (NOMA) network with two down-link users in Nakagami-m fading scenario. The near user acts as a decode-and-forward full-duplex relay for the far user. An eavesdropper is also present in the network, which tries to access messages intended for legitimate users. In full-duplex mode, the near user will send jamming signals and receive desired signals during the first phase. During the second phase, the base station sends jamming signals. Analytical expressions for the secrecy outage probabilities and the overall system secrecy outage probability (SOP) are derived. Also, the optimal power allocation coefficient that minimizes the overall SOP is determined using the simulated annealing (SA) algorithm. We establish that using optimal power allocation coefficients can reduce the overall outage probability significantly as compared …