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This paper presents indirectly estimated adaptive (IDEA) detectors for signals in CDMA channels. Multiuser CDMA detection is formulated as an inverse problem in the presence of noise and the estimation of the detector parameters is accomplished using elements of regularization theory. The development of IDEA detectors relies on computational procedures designed to reduce the effect of noise and interfering users on their performance. The detector parameters can be computed by an adaptive algorithm that requires no matrix inversion.