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In this paper, we consider a radio-frequency identification (RFID) backscatter system with two scenarios: single input multiple output (SIMO) and multiple input single output (MISO). We investigate the impact of channel correlation between the forward and backscatter links on the symbol error rate (SER), and we compare the performance of SIMO and MISO RFID systems with maximum ratio combining reception over arbitrarily correlated Nakagami-m fading channels. In order to gain an insight for the system design, closed-form expressions for the asymptotic SER and an upper bound are derived for M-ary phase-shift keying and quadrature amplitude modulation. The diversity order in the fully correlated cases, revealed from these expressions, is half of that in the partially correlated and uncorrelated cases. Finally, simulations are performed to validate the theoretical analysis.