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Orthogonal frequency-division multiplexing (OFDM) is a promising scheme for multicarrier (MC) transmission. The combination of OFDM and code-division multiple access (CDMA) which is referred to as OFDM-CDMA, has recently attracted much research interest in wireless communications. In this paper, we evaluate the downlink performance for two forms of adaptive OFDM-CDMA receivers in multipath fading channels: 1) MC-CDMA and 2) MC-direct sequence (DS)-CDMA. We propose theoretical minimum mean square errors (MMSEs) for MC-CDMA and MC-DS-CDMA to compare the performances in different situations. Moreover, one drawback of OFDM schemes is the rate reduction due to the cyclic prefix (CP) overhead, which significantly affects the channel utilization in MC-DS-CDMA systems. We propose adaptive receiver structures with both subcarrier- and code-interval equalizations to improve the performance of MC-DS-CDMA systems with shorter or no CP. Simulation results demonstrate the effectiveness of the proposed receivers and the correctness of the theoretical derivations.