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Joint estimation of the carrier frequency offset (CFO) and the channel is developed for a two-way relay network (TWRN) that comprises two source terminals and an amplify-and-forward (AF) relay. The terminals use orthogonal frequency division multiplexing (OFDM). New zero-padding (ZP) and cyclic-prefix (CP) transmission protocols, which maintain the carrier orthogonality and ensure low estimation and detection complexity, are proposed. Both protocols lead to the same estimation problem which can be solved by the nulling-based least square (LS) algorithm and perform identically when the block length is large. We present detailed performance analysis by proving the unbiasedness of the LS estimators at high signal-to-noise ratio (SNR) and by deriving the closed-form expression of the mean-square-error (MSE). Simulation results are provided to corroborate our findings.