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The linear successive interference canceler (LSIC) is a multiuser detector that employs the magnitude of the matched filter (MF) output as the received amplitude estimate of the detected user for use in signal reconstruction. This paper investigates the performance of the LSIC when random spreading sequences are employed. Specifically, the conditional mean and the signal-to-interference-plus-noise ratio (SINR) of the decision variable in each stage are derived to quantify the effects due to imperfect symbol and amplitude estimates. In addition, under the constraint that each user must achieve a certain SINR requirement, we examine the received powers needed for each of a specified number of users and the maximum number of users that a system can support when the LSIC is used in a base station. Computer simulations are presented to compare these results with those of several linear multiuser detectors.