The broad goal of this research is to exploit the nature of both the future communications traffic and the communications channel in the construction of high performance receivers for multi-user Code-Division Multiple-Access (CDMA) signals. Issues include bandwidth efficiency, receiver/transmitter complexity, and quality of service (QoS). Two main research areas within CDMA receiver design will be investigated: multi rate communications and channel equalization. In order to accommodate a variety of potentially disparate sources (voice, data and video signals), multi-rate communication schemes must be developed. Possible sources such as voice, video, and data communications have inherently different QoS requirements. QoS parameters include: bit-rate, allowable delay, performance, and source priority. The constant bit-rate paradigm of the current wireless network will not serve such multi-rate services of the future. The focus of this research is to: (a) develop optimal detectors for the various multi-rate access methods and compared, (b) create performance measures which capture QoS needs will be constructed and (c) construct multi-user receivers to explicitly exploit the redundancy in the mixture of narrowband and wideband user signals. A major consideration is the distortion induced by the propagation effects of the radio channel. Receivers to combat the effects of multipath and fading will be developed and analyzed. While equalization in the context of wireless systems is a well-explored problem, the novelty of this research lies in the consideration of (a) parameter estimation methods necessary for the accommodation of new users, (b) the specialization of existing blind equalization techniques for CDMA signals which are achieved with moderate complexity, and (c) the development of partially blind methods to fully exploit any information present about the CDMA signals and the communication channel.