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This paper proposes a low-complexity multicarrier-code-division-multiple-access (MC-CDMA) space-time receiver with full-interference-suppression capabilities. First, we derive a complete model of the interference which takes into account multiple-access, intersymbol, and intercarrier interferences. Based on this model, we introduce a new multicarrier-interference-subspace-rejection (MC-ISR) receiver and analyze its performance in an unknown time-varying Rayleigh channel with multipath, carrier offset, and cross correlation between subcarrier channels. We also propose a realistic implementation of this receiver, which includes an efficient strategy for carrier-offset recovery in a multicarrier- and multiuser-detection scheme. In addition, based on the Gaussian assumption, we derive a link-/system-level performance analysis of the MC-ISR over the two MC-CDMA air-interface configurations, which are the multitone CDMA and the multicarrier direct-sequence CDMA, and validate it by simulations. The gains in the throughput, which are attainable by the MC-ISR, are significant and evaluated in this paper as functions of the air-interface configuration, the number of subcarriers, and the modulation order.