In this research, a DS-CDMA system with QPSK modulation and multiuser interference is analyzed and simulated. We investigate the BER performance for disparate data and chip rates on the I- and Q- channels for synchronous and asynchronous transmission using both orthogonal and random codes. Comparisons are made concerning the performance of the system in AWGN and Rayleigh fading channels. Power spectra for various cases are analyzed and the results show that we obtain moderate spectrum shaping and reduction in side lobes for some parameter sets. This thesis shows through using theoretical analysis and computer simulations that synchronous and asynchronous transmissions with random codes have similar performance. Our results also show that the BER is a function of the number of interfering users and processing gain, and that our disparate chip and data rate scheme presents another effective option for multi-rate transmission.