Golden Angle Modulation: Geometric- and Probabilistic-shaping

Quadrature amplitude modulation (QAM), deployed in billions of communication devises, exhibits a shaping-loss of πe/6 (≈ 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, the Golden angle modulation (GAM). Geometricand 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-probabilisticGAM, 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 probeto-earth, satellite, and mobile-to-basestation, are scenarios where capacity achieving GAM could be of particular value.