This thesis is concerned with interference suppression in multi-rate Code-division multiple-access (CDMA) communication systems. Specifically, the following problems within the area of CDMA communication systems have been addressed: interference suppression through chip waveform design, interference reduction through new diversity techniques for users having low mobility by exploiting inherent channel diversity and joint spatial-temporal interference suppression; all with the ultimate goal to increase the system capacity. First, we examine interference issues in the multi-rate CDMA communication systems. We minimize the interference by designing different chip waveforms for different data rate users. A general chip waveform design framework is formulated. It is shown that it is better to separate different data rate users in spectrum if their quality of service requirements are quite different. Next, we propose a new receiver structure targeting those users having low mobility but whose channels have small dispersion in frequency. We show that even a very small delay spread can be exploited to achieve significant gain in terms of the signal-to-noise ratio. Then we consider joint spatial and temporal interference suppression through an adaptive antenna array. We show that adaptive spatial and temporal correlation control between different users can give us higher system capacity. Sub-optimal algorithms with low complexity are proposed and analyzed. We show that the proposed algorithms reduce the transmit power significantly, therefore, greatly increase the system capacity. Finally, we examine the role of the adaptive antenna array in the multi-rate CDMA communication systems. We show that if we perform beamforming for different data rate users, most of the achieved gain is due to the high data rate users if the total power of the high data rate users is much higher than that of the low rate users. Thus, significant computational savings can be achieved but with near optimum transmit power.