This paper investigates noncoherent detection in a two-way relay channel operated with physical layer network coding (PNC), assuming FSK modulation and short-packet transmissions. For noncoherent detection, the detector has access to the magnitude but not the phase of the received signal. For conventional communication in which a receiver receives the signal from a transmitter only, the phase does not affect the magnitude, hence the performance of the noncoherent detector is independent of the phase. PNC, however, is a multiuser system in which a receiver receives signals from multiple transmitters simultaneously. The relative phase of the signals from different transmitters affects the received signal magnitude through constructive-destructive interference. In particular, for good performance, the noncoherent detector in PNC must take into account the influence of the relative phase on the signal magnitude. Building on this observation, this paper delves into the fundamentals of PNC noncoherent detector design. To avoid excessive overhead, we do away from preambles. We show how the relative phase can be deduced directly from the magnitudes of the received data symbols. Numerical results show that our detector performs nearly as well as a "fictitious" optimal detector that has perfect knowledge of the channel gains and relative phase.
The authors of @cite_2 put forth a noncoherent detector for power-balanced channels, assuming the detector has perfect knowledge of channel gains. The detector in @cite_2 detects symbols by marginalizing the relative phase between @math in each symbol duration, assuming uniform relative phase distribution (i.e., assuming zero knowledge of the relative phase). By contrast, we will show in our paper here that we can in fact derive the relative phase from the signal magnitudes and that this knowledge can be used to improve the detection performance. In addition, our noncoherent detector can be applied in the more general scenarios with power-imbalanced channels.
@cite_2
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In this work we extend the existing concept of De- Noise and Forward (DNF) for bidirectional relaying to utilise non-coherent modulation schemes. This is done in order to avoid the requirement of phase tracking in coherent detection. As an example BFSK is considered, and through analysis the decision regions for the denoise operation in DNF are identified. The throughput performance of BFSK in DNF is compared to BPSK.