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In this paper, we study the performance of complete complementary code-based spread-time code-division multiple access (CC-ST-CDMA) in frequency-nonselective and frequency-selective fading channels. The theoretical bit-error-rate (BER) expressions conditioned on the number of users and the sequence length (and the number of resolvable paths for multipath frequency-selective fading) are obtained. The theoretical approximation of the BER for the system using long-sequence-length complete complementary codes is investigated as well. The simulations are conducted over flat-fading and two-path frequency-selective fading channels and have been used to verify the theoretical analysis. The results show that the proposed CC-ST-CDMA system has a comparable BER performance with complete complementary code-based multicarrier direct-sequence code-division multiple access (CC-MC-DSCDMA) for a flat-fading channel. However, for a frequency-selective fading channel, the CC-ST-CDMA is found to be more resistant, resulting in about 2-3 dB better performance than the CC-MC-DSCDMA.