The significance of Terahertz (THz) communication for the upcoming sixth generation (6G) communications, which offers abundant bandwidth for high-speed data transmission. However, THz frequencies face challenges such as propagation attenuation and molecular absorption that limit their coverage range. To address this issue, the use of reconfigurable intelligent surfaces (RIS) and index modulation (IM) has been proposed to extend coverage and reduce bit error rates (BER) at low transmitted power. This paper introduces a novel RIS-assisted IM system for THz communication, employing semi-definite relaxation (SDR) optimization techniques for passive beam forming at the detector. The proposed system, named PRIS-IM, demonstrates superior performance compared to conventional RIS-IM (CRIS-IM) and conventional IM (CIM) without RIS in THz frequencies. Simulation results illustrate a lower BER at a higher signal to-noise ratio (SNR) achieved by increasing the number of passive elements. Furthermore, the mutual information (MI) of the PRIS-IM system is derived and validated with simulation, and the achievable rate of the PRIS-IM system is improved by increasing the number of transmitting antennas and reflecting elements. Moreover, the PRIS-IM system is analyzed in different channel scenarios and distances. Overall, the proposed system exhibits the potential to significantly enhance the BER and MI performance of THz communication, indicating promising prospects for future wireless networks.
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