This paper explores the performance of reconfigurable intelligent surface (RIS) assisted spatial modulation (SM) downlink communication systems, focusing on the average bit error probability (ABEP). Notably, in scenarios with a large number of reflecting units, the composite channel can be approximated by a Gaussian distribution using the central limit theorem. The receiver utilizes a maximum likelihood detector to recover information in both spatial and symbol domains. In the proposed RIS-SM system, we analytically derive a closed-form expression for the union tight upper bound of ABEP, employing the Gaussian-Chebyshev quadrature method. The validity of these results is rigorously confirmed through exhaustive Monte Carlo simulations.

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