| Summary: | This paper addresses the carrier frequency offset (CFO) problem in OFDM modulated physical-layer network coding (PNC) operated in a two-way relay channel (TWRC). CFO, caused by node-motion induced Doppler shifts and/or asynchronous oscillators, induces inter-carrier interference (ICI) between OFDM subcarriers and hence, degrades PNC performance. To mitigate the CFO/ICI effect in PNC, this paper considers channel-coded PNC and focuses on the receiver design at the relay. CFO compensation, signal detection, and channel decoding are the three basic signal processing blocks at the relay node. For the latter two, we consider both a joint and a separate design. For the joint design, we construct a factor graph to integrate channel coding with ICI, and then, propose a scheme based on belief propagation. For the separate design, two low-complexity schemes differing in channel decoding are proposed. Our simulation results, using repeat-accumulate channel codes, reveal that (1) a CFO compensation approach that amounts to positioning the relay's oscillator frequency at the middle of the received frequencies from the two end nodes is bit error rate (BER)-optimal for all the three schemes; (2) the joint design is superior at low SNR and/or high CFO levels; and (3) more importantly, with the joint design, for low-to-medium CFO levels, the BER of the channel-coded PNC is comparable with that of traditional point-to-point communications without CFO, thus manifesting itself as a promising technique in OFDM modulated TWRC with practical CFO constraints.
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