  Reconfigurable intelligent surface (RIS)-assisted index modulation system
schemes are considered a promising technology for sixth-generation (6G)
wireless communication systems, which can enhance various system capabilities
such as coverage and reliability. However, obtaining perfect channel state
information (CSI) is challenging due to the lack of a radio frequency chain in
RIS. In this paper, we investigate the RIS-assisted full-duplex (FD) two-way
space shift keying (SSK) system under imperfect CSI, where the signal emissions
are augmented by deploying RISs in the vicinity of two FD users. The maximum
likelihood detector is utilized to recover the transmit antenna index. With
this in mind, we derive closed-form average bit error probability (ABEP)
expression based on the Gaussian-Chebyshev quadrature (GCQ) method and provide
the upper bound and asymptotic ABEP expressions in the presence of channel
estimation errors. To gain more insights, we also derive the outage probability
and provide the throughput of the proposed scheme with imperfect CSI. The
correctness of the analytical derivation results is confirmed via Monte Carlo
simulations. It is demonstrated that increasing the number of elements of RIS
can significantly improve the ABEP performance of the FD system over the
half-duplex (HD) system. Furthermore, in the high SNR region, the ABEP
performance of the FD system is better than that of the HD system.
