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The linear successive interference canceler (LSIC) is a multiuser detector that separates code-division multiple-access (CDMA) signals in a multistage manner. In each stage, a user is detected, and its contribution is regenerated and canceled from the input of that stage. A user's spreading sequence is employed for despreading and respreading, and the magnitude of the despreader output is used as the amplitude estimate to reconstruct that user's signal. This paper describes a generalized version of the LSIC (GLSIC) that employs various types of linear filters for the despreading and respreading operations. We analyze the bit error rate (BER), asymptotic multiuser efficiency (AME), and the mean and variance of the amplitude estimates of the GLSIC. It is shown that for certain choices of linear filters, complete cancellation of a user can be achieved, irrespective of the reliability of the symbol estimates. We also demonstrate that, from a BER and AME viewpoint, it is not beneficial to use a linear canceler with a decorrelator or a minimum mean-square-error (MMSE) receiver.