This paper presents an iterative scheme for joint timing acquisition, multi-channel parameter estimation, and multiuser soft-data decoding. As an example, an asynchronous convolutionally coded direct-sequence code-division multiple-access system is considered. The proposed receiver is derived within the space-alternating generalized expectation-maximization framework, implying that convergence in likelihood is guaranteed under appropriate conditions in contrast to many other iterative receiver architectures. The proposed receiver iterates between joint posterior data estimation, interference cancellation, and single-user channel estimation and timing acquisition. A Markov Chain Monte Carlo technique, namely Gibbs sampling, is employed to compute the a posteriori probabilities of data symbols in a computationally efficient way. Computer simulations in flat Rayleigh fading show that the proposed algorithm is able to handle high system loads unlike many other iterative receivers.