This paper investigates coherent detection for physical-layer network coding (PNC) with short packet transmissions in a two-way relay channel (TWRC). PNC turns superimposed EM waves into network-coded messages to improve throughput in a relay system. To achieve this, accurate channel information at the relay is a necessity. Much prior work applies preambles to estimate the channel. For long packets, the preamble overhead is low because of the large data payload. For short packets, that is not the case. To avoid excessive overhead, we consider a set-up in which short packets do not have preambles. A key challenge is how the relay can estimate the channel and detect the network-coded messages jointly based on the received signals from the two end users. We design a coherent detector that makes use of a belief propagation (BP) algorithm to do so. For concreteness, we focus on frequency-shift-keying (FSK) modulation. We show how the BP algorithm can be simplified and made practical with Gaussian-mixture passing. In addition, we demonstrate that prior knowledge on the channel distribution is not needed with our framework. Benchmarked against the detector with prior knowledge of the channel distribution, numerical results show that our detector can have nearly the same performance without such prior knowledge.
@cite_20: Physical-layer network coding (PNC) is an attractive technique because it can significantly enhance the throughput of a wireless network with a relatively simple implementation, as compared with conventional network coding (NC) schemes. In this paper, the authors first investigate PNC with frequency shift keying (FSK) through the derivation of its bit-error rate (BER) and capacity, as well as the impact of imperfect synchronization to the overall performance. Based on the discussions on PNC with 2FSK, the authors then further expand the analysis to PNC with M -ary FSK (MFSK). Theoretical results indicate that the BER performance of PNC with 2FSK is a bit worse than that of PNC with 2PSK. As the constellation dimension M increases, the BER performance of PNC with M -ary FSK improves at the expense of bandwidth efficiency degradation.
The authors of @cite_20 put forth a coherent FSK-PNC detector for power-balanced channels, assuming that the channels are perfectly known at the relay. That is, the detector does not need to do channel estimation and only has to do detection. Although channel estimation can be performed using a preamble in the packet, a preamble would have occupied a large portion of a short packet, causing large overhead. To avoid the overhead, we consider short packets without preambles. In addition, we do not assume power-balanced channel and our detector can work with arbitrary channel distributions.