Spiral Constellations for Phase Noise Channels

In this paper, we consider the design of spiral constellations for channels affected by phase noise. The strength of the proposed constellations resides both on the performance and on the extreme simplicity of the design. The symbols can in fact be expressed in analytical form, and are uniquely defined through a single parameter that accounts for the phase and thermal noise variances. The structure of the proposed constellations allows to easily determine the points that are closest to any point in the complex plane, therefore we also propose a low complexity detector that is suitable for phase noise channels in medium-high signal-to-noise ratio conditions. The performance of the proposed constellations are assessed in terms of information rate and error rate. Despite their simplicity, the new spiral constellations have excellent performance, especially when the constellation size grows large.