A detailed document explaining a newly proposed modulation scheme called orthogonal frequency division multiplexing with subcarrier gap modulation (OFDM-SGM). The proposed scheme embeds extra information bits by exploiting the gap between the active subcarriers in each subblock. The proposed scheme differs from the OFDM-index modulation (OFDM-IM), in which information bits are transmitted using the index of active subcarriers. This OFDM-SGM technique provides superior spectral and energy efficiencies compared to the OFDM-IM, particularly when using binary phase-shift keying (BPSK)-like low constellation schemes, that suit the Internet of Things (IoT) applications that have low complexity. The theoretical error performance of the proposed scheme is presented, and the consistency between the theoretically derived error performance and the simulated one is also provided.