In the study, we develop a fast forward-backward estimation (FFBE) method for multiple input multiple output (MIMO) space time block code (STBC) orthogonal frequency division multiplexing (OFDM) systems. We examined the matrix structure of the forward-backward (FB) correlation matrix and observed this matrix possessing permutation invariant (PI) property. We also investigated the eigen-property of a matrix with PI property and proved its eigenvectors possessing symmetric property, which can be calculated from two half dimensionality submatrices. Based on these analyses, we propose a fast eigen-decomposition algorithm to reduce the computations required in the eigendecomposition of FB correlation matrix. Then, the symmetric property of eigenvectors of the forward-backward correlation matrix is applied to develop the FFBE method to reduce the computation complexity in channel estimation. FFBE achieves the same performance as the existing forward-backward averaging (FBA) estimation method (Yu and Lin, 2009) and requires one-fourth computation complexity of FBA. Computer simulations demonstrate the effectiveness and accuracy of the proposed FFBE in channel estimation.

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