On the basis of analyzing the principle of multicarrier 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- m fading channel. Without any cyclic preflx (CP), the proposed system can avoid the decrease of spectrum e-ciency and data rate of conventional multicarrier DS-CDMA with CP. Meanwhile, the space diversity combining (SDC) technique based on multi-antenna receiver is employed to improve the system performance further. By the mathematical derivation, the BER analysis of the system with or without SDC is given in detail. Theoretical analysis and simulation results show that the proposed multicarrier system outperforms the conventional multicarrier DS-CDMA system and real wavelet packet based multicarrier DS-CDMA system due to the superior properties of the optimized multiband complex wavelet. Especially, the application of SDC technique can efiectively improve the system ability against spatial fading and interferences, and thus the superior performance is obtained.