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In this paper, we propose a novel low-complexity reduced-rank scheme and consider its application to linear interference suppression in direct-sequence ultrawideband systems (DS-UWB). First, we investigate a generic reduced-rank scheme that jointly optimizes a projection vector and a reduced-rank filter by using the minimum mean square error (MMSE) criterion. Then, a low-complexity scheme, which are denoted the switched approximation of adaptive basis functions (SAABFs), is proposed. The SAABF scheme is an extension of the generic scheme, in which the complexity reduction is achieved by using a multibranch framework to simplify the structure of the projection vector. Adaptive implementations for the SAABF scheme are developed by using least mean squares (LMS) and recursive least squares (RLS) algorithms. We also develop algorithms for selecting the branch number and the model order of the SAABF scheme. Simulations show that, in the scenarios with severe intersymbol interference (ISI) and multiple-access interference (MAI), the proposed SAABF scheme has fast convergence and remarkable interference suppression performance with low complexity.