We consider the problem of simultaneous parameter estimation and data restoration in a synchronous CDMA system. Bayesian inference of all unknown quantities is made from the superimposed and noisy received signals. The Gibbs sampler, a Markov Chain Monte Carlo procedure, is employed to calculate the Bayesian estimates. The basic idea is to generate ergodic random samples from the joint posterior distribution of all unknowns, and then to average the appropriate samples to obtain the estimates of the unknown quantities. Being "soft-input soft-output" in nature, this technique is well suited for iterative processing in a coded system, which allows the adaptive Bayesian multiuser detector to refine its processing based on the information from the decoding stage, and vice versa-a receiver structure termed an adaptive turbo multiuser detector.