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In this paper coded multicarrier systems, like the MC-CDMA, the time-frequency-localized (TFL) (or variable-spreading factor CDMA) and the OFDMA system in the downlink are discussed with different modulation cardinalities and different detection techniques. The effect of the multiple-access interference (MAI) is addressed by using different detection schemes like a carrier-based MMSE and a soft parallel interference cancellation (PIC) scheme. The multiple access interference is a major drawback that reduces the performance for MC-CDMA considerably and for TFL-CDMA slightly. It was shown in recent papers that this could be tackled by using a soft PIC for MC-CDMA. For 4-QAM modulation the loss due to MAI can be reduced through a soft PIC and allows us to exploit the available diversity. However, our investigations show that it is no longer a dominant advantage for systems with a 64-QAM alphabet. Therefore, considering the lower complexity, simple OFDMA is a reasonable choice for 64-QAM and higher. In addition we propose to keep the length of the spreading sequence flexible depending on the system load. The flexible approach of spread spectrum for one user combining with OFDMA offers the use of the simple MRC detector. Therefore we name that scheme SS-MRC-OFDMA. The CDMA based systems need more complex detectors to decrease the effect of MAI. The SS-MRC-OFDMA outperforms the MC-CDMA scheme even with a channel code rate of 3/4 and the complex soft PIC for the 64-QAM modulation scheme in a half loaded system by more than half a dB.