This paper extends our previously proposed non-orthogonal multiple access (NOMA) scheme to the base station (BS) cooperative multiple-input multiple-output (MIMO) cellular downlink for future radio access. The proposed NOMA scheme employs intra-beam superposition coding of a multiuser signal at the transmitter and the spatial filtering of inter-beam interference followed by the intra-beam successive interference canceller (SIC) at the user terminal receiver. The intra-beam SIC cancels out the inter-user interference within a beam. This configuration achieves reduced overhead for the downlink reference signaling for channel estimation at the user terminal in the case of non-orthogonal user multiplexing and enables the use of the SIC receiver in the MIMO downlink. The transmitter beamforming (precoding) matrix is controlled based on open loop-type random beamforming using a block-diagonalized beamforming matrix, which is very efficient in terms of the amount of feedback information from the user terminal. Simulation results show that the proposed NOMA scheme with block-diagonalized random beamforming in BS cooperative multiuser MIMO and the intra-beam SIC achieves better system-level throughput than orthogonal multiple access (OMA), which is assumed in LTE-Advanced. We also show that BS cooperative operation along with the proposed NOMA further enhances the cell-edge user throughput gain which implies better user fairness and universal connectivity.