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In this paper, we investigate the benefits of exploiting the a priori information about the structure of the multipath channel on the performance of channel estimation for multiple-input multiple-output (MIMO)-orthogonal frequency-division multiplexing (OFDM) systems. We first approach this problem from the point of view of estimation theory by computing a lower bound on the estimation error and studying its properties. Then, based on the insight obtained from the analysis, efficient channel estimators are designed that perform close to the derived limit. The proposed channel estimators compute the long-term features of the multipath channel model through a subspace tracking algorithm by identifying the invariant (over multiple OFDM symbols) space/time modes of the channel (modal analysis). On the other hand, the fast-varying fading amplitudes are tracked by using least-squares techniques that exploit temporal correlation of the fading process (modal filtering). The analytic treatment is complemented by thorough numerical investigation in order to validate the performance of the proposed techniques. MIMO-OFDM with bit-interleaved coded modulation and MIMO-turbo equalization is selected as a benchmark for performance evaluation in terms of bit-error rate.