  This paper proposes a new design of non-orthogonal multiple access (NOMA)
under secrecy considerations. We focus on a NOMA system where a transmitter
sends confidential messages to multiple users in the presence of an external
eavesdropper. The optimal designs of decoding order, transmission rates, and
power allocated to each user are investigated. Considering the practical
passive eavesdropping scenario where the instantaneous channel state of the
eavesdropper is unknown, we adopt the secrecy outage probability as the secrecy
metric. We first consider the problem of minimizing the transmit power subject
to the secrecy outage and quality of service constraints, and derive the
closed-form solution to this problem. We then explore the problem of maximizing
the minimum confidential information rate among users subject to the secrecy
outage and transmit power constraints, and provide an iterative algorithm to
solve this problem. We find that the secrecy outage constraint in the studied
problems does not change the optimal decoding order for NOMA, and one should
increase the power allocated to the user whose channel is relatively bad when
the secrecy constraint becomes more stringent. Finally, we show the advantage
of NOMA over orthogonal multiple access in the studied problems both
analytically and numerically.
