Ambient Backscatter Communication (AmBC) is an emerging communication technology enabling green Internet-of-Things deployments. The widespread acceptance of this paradigm is limited by the low Signal-to-Interference-Plus-Noise Ratio (SINR) of the signal impinging on the receiver antenna due to the strong direct path interference and unknown ambient signal. The adverse impact of these two factors can be mitigated by using non-coherent multi-antenna receivers, which are known to require a higher SINR to reach the Bit-Error-Rate (BER) performance of coherent receivers. However, considering the unknown ambient signal, unknown location of AmBC tags, and varying channel conditions, coherent receivers for AmBC systems are rarely studied in literature. In this paper, a coherent multi-antenna receiver, which requires no prior information of the ambient signal for decoding the Binary-Phase-shift-Keying (BPSK) modulated signal, is presented. The performance of the proposed receiver is compared with an ideal coherent receiver that has perfect phase information, and also with the performance of a non-coherent receiver, which assumes distributions for ambient signal and phase offset caused by the excess length of the backscatter path. Comparative simulation results show the designed receiver can achieve the same BER performance of the ideal coherent receiver with 1-dB more SINR, which corresponds to 5-dB or more gain with respect to non-coherent reception of On-Off-Keying modulated signals. Variation in the detection performance with the tag location shows that the coverage area is in the close vicinity of the transmitter and a larger region around the receiver, which is consistent with the theoretical results.