  Non-orthogonal multiple access (NOMA) is a promising solution for secure
transmission under massive access. However, in addition to the uncertain
channel state information (CSI) of the eavesdroppers due to their passive
nature, the CSI of the legitimate users may also be imperfect at the base
station due to the limited feedback. Under both channel uncertainties, the
optimal power allocation and transmission rate design for a secure NOMA scheme
is currently not known due to the difficulty of handling the probabilistic
constraints. This paper fills this gap by proposing novel transformation of the
probabilistic constraints and variable decoupling so that the security
guaranteed sum-rate maximization problem can be solved by alternatively
executing branch-and-bound method and difference of convex programming. To
scale the solution to a truly massive access scenario, a first-order algorithm
with very low complexity is further proposed. Simulation results show that the
proposed first-order algorithm achieves identical performance to the
conventional method but saves at least two orders of magnitude in computation
time. Moreover, the resultant transmission scheme significantly improves the
security guaranteed sum-rate compared to the orthogonal multiple access
transmission and NOMA ignoring CSI uncertainty.
