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The polynomial expansion (PE) multiuser detector (MUD) is a well known iterative approach to approximate the decorrelating or the minimum mean-squared error (MMSE) detectors. The computational complexity for the direct matrix inversion involved with the decorrelating and the MMSE detector is O(K3), where K is the number of users. Due to the iterative approximation, the computational complexity of the PE detector can be O(K2) instead. The text at hand presents a new method for a PE detector based on the estimation of the eigenvalues of the channel correlation matrix by the implicitly restarted Lanczos method (IRLM). The tight estimate of the eigenvalues results in faster convergence compared to the MMSE detector. Also, a better near-far resistance is achieved. As an application, the PE detectors presented here are tested in a UMTS terrestrial radio access (UTRA) frequency division duplex (FDD) uplink multiuser environment, where the multiple users are assumed to be asynchronous.