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We consider an OFDM system employing bit-interleaved coded-modulation (BICM) and investigate the problem of reliable data detection in the presence of narrowband interference (NBI). Such a scenario may arise in many practical contexts, including cellular applications and wireless transmissions over unlicensed frequency bands. It is known that conventional BICM decoding strategies suffer from significant performance degradation when the received signal is plagued by NBI. To overcome this difficulty, in the present work we model the interference power on each subcarrier as a nuisance parameter which is averaged out from the likelihood function. This approach results into a novel bit-metric that makes use of a suitable estimate of the NBI power obtained from previous data decisions. Numerical simulations indicate that the error rate performance of the proposed scheme is close to that of a maximum likelihood (ML) Viterbi decoder having perfect knowledge of the NBI power across the signal spectrum.