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In this paper, we analyze a linear multiuser receiver for code-division multiple-access systems that is based on a matrix polynomial expansion. We focus on the receiver where the polynomial coefficients are chosen to minimize the mean squared error at the output and observe that the resultant coefficients are also signal-to-interference ratio maximizing. We present a simple derivation for the (known) large system coefficients and signal-to-interference ratio of this optimal multistage receiver and make a significant step toward a direct derivation of Honig and Xiao's recursive expression for this large system signal-to-interference ratio. Finally, we extend these results to take into account arbitrary power distributions.