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Current wireless multicarrier systems commonly adopt pilot-aided channel estimation, for which a simplest and least restrictive technique is polynomial interpolation in the frequency domain. For channels with large delay spreads, however, the performance of low-order polynomial interpolation suffers from modeling error. The problem may be remedied by adding a linear phase shift to the interpolator, or equivalently, a "window shift" in the time domain. We derive a method to estimate the optimal window shift, in the minimum mean-square error (MMSE) sense, for polynomial-interpolative channel estimation of arbitrary order. As a practical application, we show how to apply the resultant technique to Mobile WiMAX downlink channel estimation. In addition, we propose a method to automatically select the interpolation order based on some estimated MSE.