Coherent Detection for Short-Packet Physical-Layer Network Coding with FSK Modulation

TL;DR

This paper proposes a belief propagation-based coherent detection method for short-packet physical-layer network coding with FSK modulation, eliminating the need for channel preambles and prior channel knowledge, thus improving efficiency in two-way relay channels.

Contribution

It introduces a practical joint channel estimation and detection algorithm for short packets without preambles, using belief propagation with Gaussian mixtures, and demonstrates comparable performance without prior channel knowledge.

Findings

Achieves near-optimal detection performance without channel priors.

Reduces overhead by eliminating preambles in short-packet transmissions.

Demonstrates effectiveness through numerical simulations.

Abstract

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.