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An accurate estimate of the channel frequency response (CFR) needed for OFDM equalisation can be obtained using the linear minimum mean square error (MMSE) algorithm. However, for an optimal operation such an estimator requires real-time inversion of the CFR correlation matrix that is found to be impractical due to considerable increase of the receiver's complexity. In this article, we develop the ways of design of the MMSE channel estimator yielding near-optimum performance and being computationally efficient at the same time. The proposed technique is based on the transform-domain processing and tracking of the correlation of the channel impulse response (CIR) observation. The former feature allows reducing the size of the correlation matrix, whereas the latter one leads to a design form with no matrix inversions. Simulations show that the developed algorithm achieves performance close to the optimal MMSE estimator and is particularly beneficial for both the sample-spaced and the non-sample-spaced sparse multipath channels.