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We consider an iterative multiuser detector (MUD) design for bandwidth efficient bit-interleaved coded modulation (BICM) signals in code division multiple access (CDMA) systems operating over multipath fading channels. BICM, employing bit-wise interleaving at the encoder output and using an appropriate metric at the decoder, has been shown can achieve better performance than that of symbol-interleaved coded modulation in fading channels. The received BICM signals are demodulated and decoded based on the maximum a posteriori (MAP) decoding rules. The tentative decoder outputs are used not only to cancel both multiple access interference (MAI) and intersymbol interference (ISI) but also to demap the high order modulation symbols. Numerical results show the proposed design can achieve single user performance bound after only a few iterations. The effects of signal labeling methods on the performance of iterative MUD for BICM signals are also investigated.