  In this paper, we investigate the reconfigurable intelligent surface (RIS)
assisted space shift keying (SSK) downlink communication systems under the
imperfect channel state information (CSI), where the channel between the base
station to RIS follows the Rayleigh fading, while the channel between the RIS
to user equipment obeys the Rician fading. Based on the maximum likelihood
detector, the conditional pairwise error probability of the composite channel
is derived. Then, the probability density function for a non-central chi-square
distribution with one degree of freedom is derived. Based on this, the
closed-form analytical expression of the RIS-SSK scheme with imperfect CSI is
derived. To gain more valuable insights, the asymptotic ABEP expression is also
given. Finally, we validate the derived closed-form and asymptotic expressions
by Monte Carlo simulations.
