  As the research on beyond 5G heats up, we survey and explore power and
bandwidth efficient modulation schemes in details. In the existing publications
and in various communication standards, initially square quadrature amplitude
modulation (SQAM) constellations (even power of 2) were considered. However,
only the square constellations are not efficient for varying channel conditions
and rate requirements, and hence, odd power of 2 constellations were
introduced. For odd power of 2 constellations, rectangular QAM (RQAM) is
commonly used. However, RQAM is not a good choice due to its lower power
efficiency, and a modified cross QAM (XQAM) constellation is preferred as it
provides improved power efficiency over RQAM due to its energy efficient two
dimensional (2D) structure. The increasing demand for high data-rates has
further encouraged the research towards more compact 2D constellations which
lead to hexagonal lattice structure based constellations, referred to as
hexagonal QAM (HQAM). In this work, various QAM constellations are discussed
and detailed study of star QAM, XQAM, and HQAM constellations is presented.
Generation, peak and average energies, peak-to-average-power ratio,
symbol-error-rate, decision boundaries, bit mapping, Gray code penalty, and
bit-error-rate of star QAM, XQAM, and HQAM constellations with different
constellation orders are presented. Finally, a comparative study of various QAM
constellations is presented which justifies the supremacy of HQAM over other
QAM constellations. With this, it can be claimed that the use of the HQAM in
various wireless communication systems and standards can further improve the
performance targeted for beyond 5G wireless communication systems.
