Upgrading SIM–OFDM Using a Threshold for Correct Operation with Analytical Proofs

A new upgrade to the SIM–OFDM is suggested to solve a critical problem that crashes the system even over noiseless channel. This problem is the interference of the zeros at the IFFT output with the BOOK's zeros that confuses the receiver during demodulation which leads to BER accumulation. The suggested solution is to use a threshold to differentiate the data carried by the BOOK from the IFFT's symbols. The new system is called Threshold SIM–OFDM (TSIM–OFDM). The mathematical analysis of TSIM–OFDM proves it operates normally and meets the theoretical bounds. The TSIM–OFDM preserves the probability of 1 equal to 1/2. This preservation comes from the direct connection of the ON/OFF switching bits to the subcarrier which overrides the majority condition. This new switching technique simplifies the system operation resulting in higher transmission speed and increased spectral and power efficiency. A simple approach to derive the BER for the SIM–OFDM is presented which proves that the SIM–OFDM will never reach zero BER level unlike the TSIM–OFDM. The simulation results show that the TSIM–OFDM BER reaches zero level and the output power is almost half of the OFDM. Adding the threshold will increase the transmitted power slightly and tends to decrease with the increase of IFFT length.