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Wavelet packets have good properties such as orthogonality and multirate flexibility, and have resulted in a number of works for its applications to code-division multiple-access (CDMA) communications. In this paper we investigate the use of a special set of the wavelet packets, i.e., the waveforms formed from a full binary wavelet packet tree, in multicarrier CDMA systems. In the conventional multicarrier CDMA systems, a simple frequency-domain combining receiver is commonly used to achieve frequency diversity. To combat multipath channel effects, guard intervals are inserted between consecutive symbols. On the other hand, wavelet packets have the property of localization in both time and frequency domains. A novel receiver design utilizing this property to achieve both frequency and time diversity is proposed and evaluated in this paper. This receiver eliminates the need for guard intervals. Simulations are given to support the system and receiver design. This analysis can be extended to the more general wavelet packet basis waveform sets.