Performance Analysis of Two-Way Relaying with Non-Coherent Differential Modulation

This work focuses on a two-way denoise-and-forward relaying system using non-coherent Differential Binary Phase-Shift Keying (DBPSK) modulation, which has the well-defined relay denoising function when channel state information is unknown. We first design the relay denoising function and source decoders using Maximum Likelihood (ML) principles for the general case with K parallel relays. As the ML denoising function is hard to manipulate, we approximate it as a multi-user detector followed by a physical layer network coding encoder and obtain the closed-form relay decoding error. For the single-relay case, we show that the ML source decoder is actually equivalent to the typical DBPSK decoder for the relay-source channel and thus derive the exact end-to-end Bit Error Rate (BER). To minimize the average BER, we also investigate the power allocation problem by use of asymptotic analysis at high Signal-to-Noise Ratio (SNR). We show that the optimal source power is inversely proportional to the square root of the channel gain of the source-relay channel, and the optimal relay power decreases with SNR. For the multi-relay case, though the exact analysis is intractable, we develop upper bound and lower bound on BER and show that the diversity order is exactly inverted right perpendicular k/2 inverted right perpendicular.