Linear channel estimation and training for frequency-selective fading channels in two-way relay networks

The linear minimum mean square error (LMMSE) estimation of frequency selective fading channels is addressed in two-way relay networks. We estimate the channel responses required for self-interference cancelation and coherent detection in the time domain. The optimal training condition for the minimization of the mean square error (MSE) of the LMMSE estimator is derived and, taking into account the peak-to-average power ratio, new training sequences satisfying the optimal training condition are proposed. It is shown that the LMMSE estimator significantly outperforms the least square (LS) estimator in the low SNR regime and that the LMMSE estimator is less sensitive to the training sequences than the LS estimator.