In two-way OFDM relay, carrier frequency offsets (CFOs) between relay and terminal nodes introduce severe intercarrier interference (ICI) which degrades the performance of traditional physical-layer network coding (PLNC). Moreover, traditional algorithm to compute the posteriori probability in the presence of ICI would incur prohibitive computational complexity at the relay node. In this paper, we proposed a two-step asynchronous PLNC scheme at the relay to mitigate the effect of CFOs. In the first step, we intend to reconstruct the ICI component, in which space-alternating generalized expectation-maximization (SAGE) algorithm is used to jointly estimate the needed parameters. In the second step, a channel-decoding and network-coding scheme is proposed to transform the received signal into the XOR of two terminals' transmitted information using the reconstructed ICI. It is shown that the proposed scheme greatly mitigates the impact of CFOs with a relatively lower computational complexity in two-way OFDM relay.
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