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This paper deals with the uplink of a wireless multiple-input multiple-output (MIMO) communication system based on multicarrier (MC) code division multiple access (CDMA). We focus on time-varying channels for users moving at vehicular speeds. The optimal maximum a posteriori (MAP) receiver for such a system is prohibitively complex and can be approximated using iterative linear minimum mean-square error (LMMSE) multiuser detection and parallel interference cancellation (PIC). For time-varying channels, two LMMSE filters for channel estimation and multiuser detection need to be computed at every time instant, making implementation in a real-time system difficult. We develop a novel low-complexity receiver that exploits the multiple antenna structure of the system and performs joint iterative multiuser detection and channel estimation. Our receiver algorithms are based on the Krylov subspace method, which solves a linear system with low complexity, trading accuracy for efficiency. The computational complexity of the channel estimator can be reduced by one order of magnitude. For multiuser detection, a PIC scheme in the user space, i.e., after the matched filter, allows simultaneous detection of all users as well as drastic computational complexity reduction by more than one order of magnitude.