  We present a new Beamforming-based (BB) Multiple-Input Single-Output
(MISO)-Non-orthogonal Multiple Access (NOMA) scheme for Power Domain NOMA
(PD-NOMA), in which the total transmit power consumption is minimized subjected
to prescribed signal-to-interference-plus-noise ratio (SINR) requirements for
each user, and under the assumption that only imperfect channel state
information (CSI) is available at the transmitter. To this end, the fractional
programming (FP)-based quadratic transform is employed to reformulate the
non-convex SINR constraint of the original problem into a tractable quadratic
form, which contains an estimate of the CSI error vector as a parameter. Taking
advantage of the fact that the zero duality gap holds for the non-convex
quadratic problems, a closed-form expression for an estimate of the CSI error
vector is derived, completing the formulation. Finally, a novel iterative
algorithm based on both the herein derived CSI error vector and the
semidefinite relaxation (SDR) technique is contributed, which is shown to
capable of efficiently solving the constrained min-power problem. Simulation
results are given which illustrate the effectiveness of the proposed algorithm,
which is found to sacrifice only small quantities of transmit power in return
for a substantial increase in robustness against CSI imperfection.
