Code-division multiple-access (CDMA) systems have multiple users that simultaneously share a common channel using pre-assigned signature waveforms. The conventional receiver suffers from the near-far problem when the received signal power of the desired user is weaker than those of the other users. Optimum and suboptimum multi-user detectors outperform the conventional receiver at the expense of a significant increase in complexity and need for side-information about interfering users. Complexity of these detectors may not be acceptable for many practical applications and communication security may restrict the distribution of all users' signature waveforms to all the receivers;For a single-user receiver, the multi-user detection problem is viewed as an interference suppression problem. This dissertation presents a cost-constraint strategy to implement adaptive single-user receivers that suppress the multiple-access interference without using training sequences. A constrained LMS algorithm that converges to a near-optimum solution by using the received signal and some known properties of the desired signal is developed. The constrained LMS receiver is useful for static CDMA detection where the channel accessed by the desired user is time-invariant. The dissertation also develops an adaptive space-alternating generalized EM (SAGE) algorithm. This algorithm jointly updates estimates of filter weights and adaptive reference signal in a sequential manner. The SAGE receiver out-performs the existing: blind receiver that employ the constrained output-power-minimizing algorithm while using the same amount of information. The SAGE receiver is applicable to dynamic CDMA detection where the channel accessed by the desired user is time-varying. The dissertation further generalizes the adaptive SAGE algorithm to an adaptive space-alternating generalized projection (SAGP) algorithm that uses the same amount of information as in the conventional receiver;Proposed receivers are tested by simulations and compared with the existing receivers that use the same amount of information. Throughout the analytical analysis and simulations of the proposed receivers, the dissertation shows that, for realistic CDMA communications, achieving both the near-far resistance and the near-optimum performance is possible with the same or similar information required by the conventional receiver.