In this paper, we consider wireless powered communication networks (WPCNs) consisting of a power beacon (PB) with a single antenna, a base station (BS) with M antennas, and 2M energy harvesting users with N antennas, where N > M/2. A PB transfers energy to the users during downlink and the users transmit information using the harvested energy during uplink, where non-orthogonal multiple access (NOMA) is adopted. For NOMA, signal alignment is exploited to reduce the number of messages decoded by successive interference cancellation (SIC). The transmit/receive beamforming matrices can be further optimized in order to maximize the signal to noise ratios (SNRs) of the aligned signals. A sum-throughput maximization problem for the considered network is formulated, and is then transformed into an equivalent problem which is convex with respect to the time and energy resources. A novel algorithm to maximize the sum-throughput as well as to determine the beamforming matrices is presented.