  This paper investigates the application of simultaneous wireless information
and power transfer (SWIPT) to cooperative non-orthogonal multiple access
(NOMA). A new cooperative multiple-input single-output (MISO) SWIPT NOMA
protocol is proposed, where a user with a strong channel condition acts as an
energy-harvesting (EH) relay to help a user with a poor channel condition. The
power splitting (PS) scheme is adopted at the EH relay. By jointly optimizing
the PS ratio and the beamforming vectors, the design objective is to maximize
the data rate of the "strong user" while satisfying the QoS requirement of the
"weak user". It boils down to a challenging nonconvex problem. To resolve this
issue, the semidefinite relaxation (SDR) technique is applied to relax the
quadratic terms related with the beamformers, and then it is solved to its
global optimality by two-dimensional exhaustive search. We prove the rank-one
optimality, which establishes the equivalence between the relaxed problem and
the original one. To further reduce the high complexity due to the exhaustive
search, an iterative algorithm based on successive convex approximation (SCA)
is proposed, which can at least attain its stationary point efficiently. In
view of the potential application scenarios, e.g., IoT, the single-input
single-output (SISO) case of the cooperative SWIPT NOMA system is also studied.
The formulated problem is proved to be strictly unimodal with respect to the PS
ratio. Hence, a golden section search (GSS) based algorithm with closed-form
solution at each step is proposed to find the unique global optimal solution.
It is worth pointing out that the SCA method can also converge to the optimal
solution in SISO cases. In the numerical simulation, the proposed algorithm is
numerically shown to converge within a few iterations, and the SWIPT-aided NOMA
protocol outperforms the existing transmission protocols.
