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Physical-layer network coding is a protocol capable of increasing throughput over conventional relaying in the two-way relay channel, but is sensitive to phase and frequency offsets among transmitted signals. Modulation techniques which require no phase synchronization such as non-coherent FSK can compensate for phase offset, however, the relay receiver must still compensate for frequency offset. In this work, a soft-output non-coherent detector for the relay is derived, under the assumption that the source oscillators generating FSK tones lack frequency synchronization. The derived detector is shown through simulation to improve error rate performance over a conventional detector which does not model offset, for offset values on the order of a few hundredths of a fraction of FSK tone spacing.
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