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In wireless OFDM systems, the time-varying channel is often estimated by a Wiener filter-type MMSE estimator based on pilot symbols. Such an estimator, however, requires statistical prior knowledge that is not easily obtained. Here, we propose adaptive Wiener filters for channel estimation that do not require statistical prior knowledge. We also calculate the performance limits of finite-length and infinite-length MMSE estimation. Simulation results demonstrate the good performance of our adaptive estimators.