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In this letter, a novel maximum Doppler spread estimation algorithm is presented for OFDM systems with the comb-type pilot pattern in doubly selective fading channels. First, the least-squared estimated channel frequency responses on pilot tones are used to generate two auto-correlation matrices with different lags. Then, according to these two matrices, a Doppler dependent parameter is measured. Based on a time-varying multipath channel model, the parameter is expanded and then transformed into a nonlinear high-order polynomial equation, from which the maximum Doppler spread is readily solved by using the Newton's method. The delay-subspace is utilized to reduce the noise that biases the estimator. Besides, the subspace tracking algorithm is adopted as well to automatically update the delay-subspace. Simulation results demonstrate that the proposed algorithm converges for a wide range of SNRs and Dopplers.