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We consider transmission power adaptations in multicarrier code-division multiple-access communications, where the transmission power is adapted in frequency and/or time domain in response to channel variations. With frequency-domain power adaptation, we propose to allocate the transmission power over N' (1 les N' les N) strongest subcarriers (which have the highest channel gains) rather than over all possible N subcarriers. We examine the effect of choosing N' on the performance of the frequency-domain power adaptation scheme and find that there exists an optimal N' that minimizes the average bit error rate (BER). In the time domain, we consider adapting the transmission power so that the desired signal strength at the receiver output remains at a fixed level. We analyze the BER performances of frequency-, time-, and combined frequency-time-domain power adaptations with an average transmission power constraint. Our results show that the frequency-and time-domain power adaptation schemes outperform the nonadaptive (i.e., constant uniform power over all subcarriers) scheme, particularly for the noise-and interference-limited regions, respectively. The combined frequency-time-domain power adaptation is shown to have a significant performance gain over the power adaptation in only the frequency or time domain, as well as over the nonadaptive scheme. We also present numerical results to investigate the effect of channel estimation error on the performance of the proposed power adaptation schemes.