Robust LMMSE turbo equalization algorithm to imperfect channel estimations

To achieve reasonable bit error rate (BER) perfor- mance, accurate channel state information (CSI) is required for linear minimum mean squared error turbo equalizer(LMMSE- TE), which is hard to be obtained under the circumstance that long training sequence is not available or channel is time-varying. Soft and hard iterative channel estimation (HICE) algorithms were proposed as fine channel estimation schemes after coarse estimation. In this paper, a new iterative channel correction (ICC) algorithm that belongs to the HICE based on the least mean square (LMS) algorithm is proposed. A cost function using hard decision variables on the output of TE is formed. We show that the gradient descent (GD) algorithm is effective to iteratively minimize the cost function. Furthermore, the iterative step-size to guarantee the convergence for the ICC is analyzed, the mean squared error (MSE) lower bound of the estimated channels for the ICC is derived and validated by the simulations. Our simulations show that, given an imperfect CSI with MSE below the upper bound, the LMMSE-TE incorporated with the ICC yields small performance degradation compared to that with perfect CSI, while the traditional LMMSE-TE suffers from severe error floor even with more iterations, thus showing the robustness of our proposed algorithm to the imperfect channel estimations.