Golden Angle Modulation: Geometric- and Probabilistic-shaping

TL;DR

This paper introduces Golden Angle Modulation (GAM), a novel circular symmetric modulation scheme inspired by plant spiral arrangements, designed to reduce the shaping-loss of traditional QAM and improve communication efficiency.

Contribution

The paper presents geometric, probabilistic, and joint shaping schemes for GAM that nearly eliminate the 1.53 dB shaping-loss of QAM, with the joint scheme achieving the highest mutual information performance.

Findings

Joint geometric and probabilistic GAM outperforms other schemes in mutual information.

GAM schemes significantly reduce the traditional shaping-loss of QAM.

Potential applications include resource-limited communication links like satellites and space probes.

Abstract

Quadrature amplitude modulation (QAM), deployed in billions of communication devises, exhibits a shaping-loss of $\pi \mathrm{e}/6$ ($\approx 1.53$ dB) compared to the Shannon-Hartley theorem. With inspiration gained from special (leaf, flower petal, and seed) packing arrangements (so called spiral phyllotaxis) found among plants, we have designed a shape-versatile, circular symmetric, modulation scheme, \textit{the Golden angle modulation (GAM)}. Geometric- and probabilistic-shaping-based GAM schemes are designed that practically overcome the shaping-loss of 1.53 dB. Specifically, we consider mutual information (MI)-optimized geometric-, probabilistic-, and joint geometric-and-probabilistic-GAM, under SNR-equality, and PAPR-inequality, constraints. Out of those, the joint scheme yields the highest MI-performance, and then comes the probabilistic schemes. This study finds that GAM could be an interesting candidate for future communication systems. Transmitter resource limited links, such as space probe-to-earth, satellite, and mobile-to-basestation, are scenarios where capacity achieving GAM could be of particular value.