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In this work, we consider the two-way relay network (TWRN) where two terminals exchange their information through a relay node in a bi-directional manner and study the training-based channel estimation under the amplify-and-forward (AF) relay scheme. We propose a two-phase training protocol for channel estimation: in the first phase, the two terminals send their training signals concurrently to the relay; and in the second phase, the relay amplifies the received signal and broadcasts it to both terminals. Each terminal then estimates the channel parameters required for data detection. First, we assume the channel parameters to be deterministic and derive the maximum-likelihood (ML) -based estimator. It is seen that the newly derived ML estimator is nonlinear and differs from the conventional least-square (LS) estimator. Due to the difficulty in obtaining a closed-form expression of the mean square error (MSE) for …