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One of the critical missions for next-generation wireless communication systems is to fulfill the high demand for massive Machine-Type Communications (mMTC). In mMTC systems, a sporadic transmission is performed between machine users and base station (BS). Lack of coordination between the users and BS in time destroys orthogonality between the subcarriers, and causes inter-carrier interference (ICI). Therefore, providing services to asynchronous massive machine users is a major challenge for Orthogonal Frequency Division Multiplexing (OFDM). In this study, OFDM with index modulation (OFDM-IM) is proposed as an eligible solution to alleviate ICI caused by asynchronous transmission in uncoordinated mMTC networks. In OFDM-IM, data transmission is performed not only by modulated subcarriers but also by the indices of active subcarriers. Unlike classical OFDM, fractional subcarrier activation leads to less ICI in OFDM-IM technology. A novel subcarrier mapping scheme (SMS) named as Inner Subcarrier Activation is proposed to further alleviate adjacent user interference in asynchronous OFDM-IM-based systems. ISA reduces inter-user interference since it gives more activation priority to inner subcarriers compared with the existing SMS-s. The superiority of the proposed SMS is shown through both theoretical analysis and computer-based simulations in comparison to existing mapping schemes for asynchronous systems.