  Spectrally-efficient secure non-orthogonal multiple access (NOMA) has
recently attained a substantial research interest for fifth generation
development. This work explores crucial security issue in NOMA which is stemmed
from utilizing the decoding concept of successive interference cancellation.
Considering untrusted users, we design a novel secure NOMA transmission
protocol to maximize secrecy fairness among users. A new decoding order for two
users' NOMA is proposed that provides positive secrecy rate to both users.
Observing the objective of maximizing secrecy fairness between users under
given power budget constraint, the problem is formulated as minimizing the
maximum secrecy outage probability (SOP) between users. In particular,
closed-form expressions of SOP for both users are derived to analyze secrecy
performance. SOP minimization problems are solved using pseudoconvexity
concept, and optimized power allocation (PA) for each user is obtained.
Asymptotic expressions of SOPs, and optimal PAs minimizing these approximations
are obtained to get deeper insights. Further, globally-optimized power control
solution from secrecy fairness perspective is obtained at a low computational
complexity and, asymptotic approximation is obtained to gain analytical
insights. Numerical results validate the correctness of analysis, and present
insights on optimal solutions. Finally, we present insights on global-optimal
PA by which fairness is ensured and gains of about 55.12%, 69.30%, and 19.11%,
respectively are achieved, compared to fixed PA and individual users' optimal
PAs.
