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Ambient backscatter communication (AmBC) is becoming increasingly popular for enabling green communication amidst the continual development of the Internet-of-things paradigm. Efforts have been put into backscatter signal detection as the detection performance is limited by the low signal-to-interference-plus-noise ratio (SINR) of the signal at the receiver. The low SINR can be improved by adopting a multi-antenna receiver. In this paper, the optimum multi-antenna receiver that does not impose any constraints on the types of binary modulation performed by the backscatter device and the waveform used by the ambient source system is studied. The proposed receiver owns a simple structure formed by two beamformers. Bit error rate (BER) performances of the optimum receiver are derived under constant-amplitude ambient signal and Gaussian-distributed ambient signal. Moreover, to facilitate the implementation of the optimum receiver, a simplified receiver is proposed and practical approximations to required beamformers are provided. The derived optimum receiver avoids the complex direct path interference cancellation and coherent reception, but exploits the fact that backscatter signal changes the composite channel impinging at the receiver and the directivity of receiver antenna array. Comparative simulation results show that the performance of the optimum receiver achieves the same performance as the coherent receiver even though it realizes non-coherent reception. The studied receivers provide high flexibility for implementing simple and low-cost receivers in different AmBC systems.