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This letter generalizes the application of signal space diversity (SSD) over multiplicative fading channels, where fading is represented by the product of K statistically independent Nakagami-m random variables. The pairwise error probability (PEP) for the systems is first obtained in a closed-form using generalized hypergeometric functions. Based on the obtained PEP expression, it is shown that the error performance over multiplicative fading channels can be significantly improved by using high diversity constellations. Furthermore, by employing SSD with a sufficiently large dimension, it is observed that the adverse effects of multiplicative fading can be practically eliminated without any power nor bandwidth expansion. Simulation results for both uncoded and coded systems are provided to show the agreement with the analysis.