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Radio frequency identification (RFID) backscatter communication systems play an important part in the future Internet of Things (IoT) applications. In this paper, we consider a multiple input single output (MISO) backscatter system, where the reader is equipped with multiple antennas and the tag is equipped with single antenna. The impact of the channel correlation between the forward and backscatter links on the symbol error rate (SER) is investigated. Then, we derive expressions for asymptotic SER and an upper bound, assuming M-ary phase-shift keying (M-PSK) and quadrature amplitude modulation (M-QAM) with maximum ratio combining (MRC) reception, over arbitrarily correlated Nakagami-m fading channels. From these expressions, we can directly obtain the diversity order. Finally, numerical results and simulations are provided to demonstrate the accuracy of the theoretical expressions.