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We analyze the performance of a second-order linear multistage multiuser code-division multiple-access receiver. The receiver's filtered output is designed to converge to that of the linear minimum mean-squared error solution as the number of stages increase. Our analysis is based on a related second-order stationary iterative solution method. We derive the large system output signal to interference-plus-noise ratio for each stage. We use this result to perform a numerical optimization with respect to the two second-order parameters of our receiver. Within this iterative framework, we can achieve performance extremely close to the optimal linear multistage multiuser receiver.