Modulation with hexagonal decision regions for wireless communication systems

Quadrature Amplitude Modulation (QAM) is commonly employed with rectangular constellation arrangement and square decision regions. However, it is well known that hexagons regions provide the most compact regular tiling of the space. A compact tiling means a dense packing of constellation points and thus more energy efficient transmission of information. This modulation with hexagonal decision regions can be difficult to implement because it does not fit well with the usual power-of-two symbol sizes for binary data. In this paper, we introduce this modulation to provide a system which is compatible with binary data. It is shown to provide improved energy efficiency and spectrum utilization and to maximize the minimum distance between symbols and thus minimize the symbol error probability for a given signal energy, as well as the peak-to-average-power ratio for OFDM systems.