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.

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