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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 subjectedto prescribed signal-to-interference-plus-noise ratio (SINR) requirements foreach user, and under the assumption that only imperfect channel stateinformation (CSI) is available at the transmitter. To this end, the fractionalprogramming (FP)-based quadratic transform is employed to reformulate thenon-convex SINR constraint of the original problem into a tractable quadraticform, which contains an estimate of the CSI error vector as a parameter. Takingadvantage of the fact that the zero duality gap holds for the non-convexquadratic problems, a closed-form expression for an estimate of the CSI errorvector is derived, completing the formulation. Finally, a novel iterativealgorithm based on both the herein derived CSI error vector and thesemidefinite relaxation (SDR) technique is contributed, which is shown tocapable of efficiently solving the constrained min-power problem. Simulationresults are given which illustrate the effectiveness of the proposed algorithm,which is found to sacrifice only small quantities of transmit power in returnfor a substantial increase in robustness against CSI imperfection.

Fractional Programming for Robust TX BF Design in Multi-User/Single-Carrier PD-NOMA