Binary Representation of Signal Constellations and its Use for Analyzing Modulated Signals

An analytical method is proposed for describing signal constellations in the form of a functional dependence on a multidimensional vector of binary variables. A transformation is given that allows one to move from the traditional tabular description of modulated signals to the proposed analytical description. The method makes it possible to more compactly describe signals modulated by digital information, especially with a high modulation order, and to identify some patterns in known modulation methods and extend them to higher order modulations. An analytical description of signal constellations makes it possible to synthesize new demodulation algorithms for various communication systems. Simple examples show the advantages of the proposed approach over traditional methods based on tabular representation of signals.