This paper proposes an iterative receiver derived from recent advances in narrowband turbo equalization for the multicode transmission scheme of the downlink of DS-CDMA systems with long scrambling sequences. The proposed scheme is based on a chip-rate linear equalizer exchanging soft information on the composite multiuser signal with the channel decoder in an iterative process. When all spreading codes are known from the receiver, the equalizer may evolve from a linear minimum mean square error (MMSE) equalizer to an inter-chip interference (ICI) canceller, according to the reliability of the estimation of the chip-rate multiuser signal previously performed. When only partial knowledge about the codes is available, the equalizer becomes a hybrid structure between the linear MMSE equalizer and the ICI canceller. Numerical simulations demonstrate the efficiency of the proposed scheme compared to linear equalizers and multistage interference cancellers. In particular, it is shown that this receiver can still achive high performance in the présence of unknown codes, which makes it particularly attractive for future downlink high speed packet transmission systems.