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Inspired by multiuser detection theory, we propose a linear minimum mean-square error (LMMSE) multiuser detector (MUD) to suppress cochannel interference (CCI) with unknown signal format for coded OFDM systems over single input/single output frequency-selective slowly fading channels by considering each sub-carrier as an individual user. To eliminate the residual interference contributed by other sub-carriers at the output of the LMMSE MUD, we propose a multistage interference cancellation (MIC) algorithm which makes use of the reliable tentative decisions of other sub-carriers generated from the decoder outputs of the first LMMSE MUD stage. To improve the performance further, we propose an enhanced multistage interference cancellation (EMIC) algorithm which is the LMMSE estimate of the information bit, provided that the signal components of other sub-carriers are precisely removed from the received signal. From computer simulations, the MIC and the EMIC algorithms effectively improve the performance of the LMMSE MUD. Furthermore, the performance of the EMIC is very close to the optimal when the desired OFDM signal employs quadrature phase-shift keying (QPSK) or 16-ary quadrature amplitude modulation (16-QAM).