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In this paper, we investigate the optimum energy allocation of dual-hop communication systems with AF protocol where we consider both coherent and differential transmission schemes. First, we demonstrate the performance of dual-hop communication systems in terms of symbol error rate (SER). Then, we carry out the optimum energy allocation which minimizes the error rate. Based on the optimized energy allocation, its effects on system performance are analyzed, and these results are compared with DF-based systems. We also compare the performance of AF-based systems depending on the transmission scheme.