On the Subtleties of q-PAM Linear Physical-Layer Network Coding

TL;DR

This paper analyzes the performance of q-PAM physical-layer network coding in two-way relay channels, revealing its sensitivity to power imbalance and proposing an asynchronous approach with belief propagation decoding to enhance robustness.

Contribution

It provides a systematic analysis of the relationship between constellation minimum distance and channel gain ratio for all q, and introduces an asynchronous PNC scheme with BP decoding to mitigate power imbalance issues.

Findings

Performance is highly sensitive to slight power imbalances, especially for higher q.

Minimum distance varies piecewise linearly with channel-gain ratio.

Asynchronous PNC with BP decoding improves robustness against power imbalance.

Abstract

This paper investigates various subtleties of applying linear physical-layer network coding (PNC) with q-level pulse amplitude modulation (q-PAM) in two-way relay channels (TWRC). A critical issue is how the PNC system performs when the received powers from the two users at the relay are imbalanced. In particular, how would the PNC system perform under slight power imbalance that is inevitable in practice, even when power control is applied? To answer these questions, this paper presents a comprehensive analysis of q-PAM PNC. Our contributions are as follows: 1) We give a systematic way to obtain the analytical relationship between the minimum distance of the signal constellation induced by the superimposed signals of the two users (a key performance determining factor) and the channel-gain ratio of the two users, for all q. In particular, we show how the minimum distance changes in a piecewise linear fashion as the channel-gain ratio varies. 2) We show that the performance of q-PAM PNC is highly sensitive to imbalanced received powers from the two users at the relay, even when the power imbalance is slight (e.g., the residual power imbalance in a power-controlled system). This sensitivity problem is exacerbated as q increases, calling into question the robustness of high-order modulated PNC. 3) We propose an asynchronized PNC system in which the symbol arrival times of the two users at the relay are deliberately made to be asynchronous. We show that such asynchronized PNC, when operated with a belief propagation (BP) decoder, can remove the sensitivity problem, allowing a robust high-order modulated PNC system to be built.