  This paper studies a multiple-input single-output non-orthogonal multiple
access cognitive radio network relying on simultaneous wireless information and
power transfer. A realistic non-linear energy harvesting model is applied and a
power splitting architecture is adopted at each secondary user (SU). Since it
is difficult to obtain perfect channel state information (CSI) in practice,
instead either a bounded or gaussian CSI error model is considered. Our robust
beamforming and power splitting ratio are jointly designed for two problems
with different objectives, namely that of minimizing the transmission power of
the cognitive base station and that of maximizing the total harvested energy of
the SUs, respectively. The optimization problems are challenging to solve,
mainly because of the non-linear structure of the energy harvesting and CSI
errors models. We converted them into convex forms by using semi-definite
relaxation. For the minimum transmission power problem, we obtain the rank-2
solution under the bounded CSI error model, while for the maximum energy
harvesting problem, a two-loop procedure using a one-dimensional search is
proposed. Our simulation results show that the proposed scheme significantly
outperforms its traditional orthogonal multiple access counterpart.
Furthermore, the performance using the gaussian CSI error model is generally
better than that using the bounded CSI error model.
