  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.
