Large system analysis of a randomly spread direct-sequence code-division multiple-access system in a frequency-selective channel is considered. The receiver uses iterative channel estimation and multiuser detection (MUD) with soft feedback from single-user decoders to refine both the decisions of the linear minimum mean square error (LMMSE) MUD, and the initial pilot-based estimates of the LMMSE channel estimator. Replica method, a tool from statistical physics, and density evolution with Gaussian approximation are used to obtain the asymptotic performance of the LMMSE MUD with soft parallel interference cancellation. The results indicate that as the channel coherence time grows, the performance of corresponding single-user system having perfect channel state information can be approached even in an overloaded multiuser system using channel estimation and vanishing pilot overhead. copyright by EURASIP.