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In this paper, channel estimation and training sequence design are considered for amplify-and-forward (AF)-based two-way relay networks (TWRNs) in a time-selective fading environment. A new complex-exponential basis expansion model (CE-BEM) is proposed to represent the mobile-to-mobile time-varying channels. To estimate such channels, a novel pilot symbol-aided transmission scheme is developed such that a low complex linear approach can estimate the BEM coefficients of the convoluted channels. More essentially, two algorithms are designed to extract the BEM coefficients of the individual channels. The optimal training parameters, including the number of the pilot symbols, the placement of the pilot symbols, and the power allocation to the pilot symbols, are derived by minimizing the channel mean-square error (MSE). The selections of the system parameters are thoroughly discussed in order to guide practical system design. Finally, extensive numerical results are provided to corroborate the proposed studies.