This work investigates the application of non-orthogonal multiple access (NOMA) scheme for the uplink of wireless powered communication networks (WPCN). We maximize the sum rate by jointly designing of the time allocation, the downlink energy beamforming and receiver beamforming. To solve this nonconvex problem, a method of two stages optimization is proposed. In the first stage, we apply the series approximations to obtain the optimal energy beamforming and receive beamforming with fixed time allocation. In the second stage, one-dimensional search is considered to obtain the optimal time allocation. For the approximation part, successive convex approximation (SCA) method is used to convert a mixed integer non-linear program into its convex approximation problem. The numerical results illustrate that the proposed algorithm converges to the local optimum solution and the proposed scheme outperforms the fixed time allocation scheme and orthogonal multiple access (OMA).
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