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This paper focuses on a two-way denoise-and-forward relaying system using non-coherent Differential Binary Phase-Shift Keying (DBPSK) modulation. The relay denoising function and source decoders are designed using Maximum Likelihood (ML) principles. As the ML denoising function is hard to manipulate, it is approximated as a multi-user detector followed by a physical layer network coding encoder, based on which the closed-form relay decoding error is obtained. It is further shown that the ML source decoder is actually equivalent to the typical DBPSK decoder to the relay-source channel, and the exact end-to-end Bit Error Rate (BER) is derived then. A power allocation problem is also formulated to minimize the average BER at high Signal-to-Noise Ratio (SNR).
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