Channel estimation and optimal training with the LMMSE criterion for OFDM-based two-way relay networks

In this paper, we consider the linear minimum mean square error (LMMSE) estimation of channel for the two-way relay network employing analog network coding and orthogonal frequency division multiplexing. The channel responses required for self-interference cancelation and coherent detection are estimated in the time domain with the preamble. We derive the optimal training condition for minimizing the mean square error (MSE) of the LMMSE estimator and obtain the corresponding MSE. It is observed that the LMMSE estimator has the optimal training condition equivalent to that of the least square estimator and that the former is less sensitive to the training sequences than the latter. We also propose new training sequences not only satisfying the optimal training condition but also providing the minimum peak-to-average power ratio.