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An integrated beamforming (spatial processing) and multiuser-detection (temporal processing) scheme is an effective approach to increase system capacity but is also impractical due to the high associated computational costs. To overcome this problem, researchers have developed reduced-rank approaches. Adding to this class of algorithms, this paper introduces a joint-domain adaptive algorithm, which processes spatial and temporal data within a localized region after transformation to a "beamspace." This new joint-domain-localized (JDL) adaptive algorithm is developed for single-cell uplink code-division multiple-access (CDMA) systems with a receive-antenna array. Given a rank constraint on the JDL transformation, this paper develops the optimal choice of transformation matrix and justifies a simpler suboptimal choice. The JDL algorithm is shown to have relatively low computation load. We also introduce the JDL-Z algorithm that combines JDL processing with zero forcing for multicell uplink CDMA systems. At the cost of higher computational complexity, this new scheme provides better performance and a faster convergence rate than the JDL algorithm. However, the key contribution is a framework wherein adaptive processing can be followed by yet another stage of adaptive processing. Simulations are used to illustrate the efficacy of the two algorithms.