MIMO channels are often assumed to be constant over a block or packet. This assumption of block stationarity is valid for many fixed wireless scenarios. However, for communications in a mobile environment, the stationarity assumption will result in considerable performance degradation. In this paper, we focus on a new channel estimation technique for Turbo coded MIMO systems using OFDM. In the proposed MIMO–OFDM system, pilots are placed on selected subcarriers and used by a pair of Kalman filter (KF) channel estimators at the receiver. The KF channel estimates are then utilized by a MIMO–OFDM soft data detector based on the computationally efficient QRD-M algorithm. The soft detector output is fed back to the Kalman filters to iteratively improve the channel estimates. The extrinsic information generated by the Turbo decoder is also used as a priori information for the soft data detector. The overall receiver thus combines MIMO data detection, KF-based channel estimation, and Turbo decoding in a joint iterative structure yielding computational efficiency and improved bit-error rate (BER) performance.
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Computation of Composite Noise Covariance
Computation of Composite Noise Covariance
Recall that
Hence
Note that only in the special case \({E\left\{{\mathbf f}^{p,q}(n) {\mathbf f}^{p,q}(n)^{H}\right\} = \sigma_f^2 {\mathbf I}}\) , the matrix \({E\left\{ {\mathbf C}^T{\mathbf f}^{p,q}(n) {\mathbf f}^{p,q}(n)^H {\mathbf C}^{\ast} \right\}}\) becomes Toeplitz. Now using the following relationship
we have
The data error correlation matrix is
In the computation of (A.6), we assume uncorrelated symbol errors across the carriers thus
Denoting by
the l-th channel expectation in (A.4), we have
Now substituting (A.6) into (A.2) yields (13), which completes the derivation.
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Kim, K.J., Iltis, R.A. Iterative Soft-Kalman Filter-based Data Detection and Channel Estimation for Turbo Coded MIMO–OFDM Systems. Int J Wireless Inf Networks 14, 175–189 (2007). https://doi.org/10.1007/s10776-007-0059-0
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DOI: https://doi.org/10.1007/s10776-007-0059-0