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This paper considers the secrecy outage performance of a multiple-relayassisted non-orthogonal multiple access (NOMA) network over Nakagami-$m$ fadingchannels. Two slots are utilized to transmit signals from the base station todestination. At the first slot, the base station broadcasts the superpositionsignal of the two users to all decode-and-forward relays by message mappingstrategy. Then the selected relay transmits superposition signal to the twousers via power-domain NOMA technology. Three relay selection (RS) schemes,i.e., optimal single relay selection (OSRS) scheme, two-step single relayselection (TSRS) scheme, and optimal dual relay selection (ODRS) scheme, areproposed and the secrecy outage performance are analyzed. As a benchmark, wealso examine the secrecy outage performance of the NOMA systems withtraditional multiple relays combining (TMRC) scheme in which all the relay thatsuccessfully decode signals from the source forward signals to the NOMA userswith equal power. Considering the correlation between the secrecy capacity oftwo users and different secrecy requirement for two NOMA users, the closed-formexpressions for the security outage probability (SOP) of the proposed OSRS,TSRS, and ODRS schemes along with the TMRC scheme are derived and validated viasimulations. To get more insights, we also derive the closed-form expressionsfor the asymptotic SOP for all the schemes with fixed and dynamic powerallocations. Furthermore, the secrecy diversity order (SDO) of cooperative NOMAsystems is obtained. The results demonstrate that our proposed schemes cansignificantly enhance the secrecy performance compared to the TMRC scheme andthat all the RS schemes with fixed power allocation obtain zero SDO and theOSRS scheme with dynamic power allocation obtains the same SDO as TMRC.

Secrecy Outage Analysis for Cooperative NOMA Systems with Relay Selection Scheme