Analysis of QAM Constellations with Binary Signal Representation

In this paper we propose to use a new method of digital modulated signal representation for the analysis of quadrature amplitude modulation (QAM) constellations based on an analytical description in the form of function of binary symbols (bits). It is shown that this method of signal representation makes it possible to observe the interaction between bits. It can be used to discover some patterns for further generation of constellations and also to generate new higher order constellations with the same properties.Analysis of well-known constellations for communication systems with coded modulation with bits interleaving BICM (Bit-Interleaved Coded Modulation) using proposed method illustrates the possibilities of the described approach.Here it is shown that for the case of rectangular QAM constellations the description of the signal as a function of binary symbols provides to represent the process of constellation generation in the form of a combination of block non-redundant (primitive) coding with Gray constellation mapping and DAC (digital-to-analog conversion). The described signal representation allows us to solve the task of QAM constellation optimization, finding the optimal block non-redundant code for independent multidimensional binary channel.The simulation shows that even the proposed combination of a simple primitive block code with Gray’s constellation mapping allows to obtain an energy gain about 1–1.5 dB compared to the usual square QAM constellation with Gray’s code and about 0.5–1.25 dB in comparison with known constellations optimized for use in systems with BICM.