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On the basis of analyzing the principle of multicarrier DS-CDMA (MC-DS-CDMA), we propose a novel multiband complex wavelet based multicarrier DS-CDMA system in this paper by using the optimized multiband complex wavelet as multicarrier basis function. The system bit error rate (BER) performance is investigated over Nakagami fading channel. Without any cyclic prefix (CP), the proposed system can avoid the decrease of spectrum efficiency and data rate of conventional MC-DS-CDMA with CP. Consider the uplink, the space diversity combining (SDC) technique based multi-antenna receiver is employed to improve the system performance further. Theoretical analysis and simulation results show that the proposed multicarrier system outperforms the conventional MC-DS-CDMA system and real wavelet packet based MC-DS-CDMA system. Especially, the application of SDC technique can effectively improve the system ability against spatial fading and various interferences, and thus lower BER is obtained.