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Non-orthogonal multiple access (NOMA) and ambient backscatter communication are two promising techniques recommended for the fifth generation wireless network. This work combines these approaches to propose a backscatter NOMA system, which incorporates a backscatter device together with a downlink NOMA. Such NOMA employs the base station equipped with multiple antennas. To evaluate the performance of backscatter NOMA, the expressions of the outage probabilities are derived. Finally, the numerical results are provided to verify the theoretical analysis. [ABSTRACT FROM AUTHOR]