Terahertz (THz) wireless communication is envisioned as a promising technology, which is capable of providing ultra-high-rate transmission up to Terabit per second. However, some hardware imperfections, which are generally neglected in the existing literature concerning lower data rates and traditional operating frequencies, cannot be overlooked in the THz systems. Hardware imperfections usually consist of phase noise, in-phase/quadrature imbalance, and nonlinearity of power amplifier. Due to the timevariant characteristic of phase noise, frequent pilot insertion is required, leading to decreased spectral efficiency. In this paper, to address this issue, a novel pilot design strategy is proposed based on index modulation (IM), where the positions of pilots are flexibly changed in the data frame, and additional information bits can be conveyed by indices of pilots. Furthermore, a turbo receiving algorithm is developed, which jointly performs the detection of pilot indices and channel estimation in an iterative manner. It is shown that the proposed turbo receiver works well even under the situation where the prior knowledge of channel state information is outdated. Analytical and simulation results validate that the proposed schemes achieve significant enhancement of bit-error rate performance and channel estimation accuracy, whilst attaining higher spectral efficiency in comparison with its classical counterpart.