Uniquely Factorable Hexagonal Constellation Designs for Noncoherent SIMO Systems

In this paper, we propose the design of a uniquely factorable hexagonal constellation for a noncoherent wireless communication system with a single transmitter antenna and multiple receiver antennas [single-input multiple-output (SIMO)]. The hexagonal constellation has a densely packed 2-D “honeycomb” structure and is more energy efficient than the commonly used cross quadrature amplitude modulation (QAM) constellations. By using the hexagonal lattice formed from the Eisenstein integers and the recently developed concept of the uniquely factorable constellation (UFC) for the QAM constellation, an algorithm is developed to effectively and efficiently construct constant norm hexagonal UFCs of various sizes. In addition, an optimal energy scale is found to maximize the coding gain for the constant norm training hexagonal UFC schemes subject to a transmission bit rate constraint. Computer simulations show that the hexagonal unitary UFC proposed in this paper has the best error performance in comparison to the current literature results for the noncoherent SIMO system.