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This paper presents and analyzes a novel low-complexity reduced-rank linear interference suppression technique for direct-sequence code-division multiple access (DS-CDMA) systems based on the set-membership joint iterative optimization of receive parameters. Set-membership filtering is applied to the design and adaptation of the dimensionality-reducing projection matrix and the reduced-rank interference suppression filter. The specification of error bounds on the projection matrix and reduced-rank filter lead to the formation of two constraint sets from which estimates of the adaptive structures are selected at each time instant. The result is a low-complexity sparsely updating reduced-rank technique that does not require eigendecomposition or subspace tracking procedures. We develop least squares and stochastic gradient-type algorithms and a low-complexity rank-selection algorithm and also devise a time-varying adaptive error bound implementation. We present a stability and mean-square-error convergence analysis of the proposed algorithms along with a study of their complexity. The proposed schemes are applied to interference suppression in the uplink of a multiuser spread-spectrum DS-CDMA system, and the results confirm the validity of the analysis and the effective operation of the schemes. Performance comparisons are given against existing reduced-rank and full-rank algorithms, which act to highlight the improvements obtained by the proposed technique and algorithms.