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In this paper, we present a pilot assisted two-way relay network (TWRN) single-carrier frequency domain equalization (SCFDE) system with no cyclic prefix (CP), where two source terminals exchange their information through a relay terminal using the amplify-and-forward relaying scheme. During Phase I of the proposed system, two source terminals transmit the orthogonal pilot sequence and the single-carrier data blocks alternately. During Phase II, the relay terminal amplifies and forwards the combined data from the two source terminals, and both source terminals utilize a certain interference cancellation based algorithm of joint time domain circularly correlated channel estimation and data detection proposed for the non-CP single-carrier data structure. Simulation results show that, compared with TWRN SCFDE based on iterative reconstruction RR channel estimation, the proposed system based on non-CP TWRN SCFDE improves the performance of detection and achieves good channel estimation and tracking at the same time.