A multilevel coded modulation approach for hexagonal signal constellation

We propose a new coded modulation called hexagonal shell modulation (HSM). The HSM has a signal constellation composed of shell-like tiling of hexagons and thus has a lower peak-to-average power ratio (PAR) than a standard square quadrature amplitude modulation (QAM) with comparable bandwidth efficiency and minimum Euclidean distance. The main challenge is that HSM has a non-power-of-two number of constellation points, and thus assignment of binary information to HSM is not straightforward. We resolve this by applying a multilevel coded modulation (MLC) scheme where a ternary set partitioning combined with binary-input ternary-output (BITO) turbo codes is employed to fully exploit the property of the nonpower- of-two constellation points. Throughout this letter, we focus on an 18-ary HSM with the information rate of 3 bit/symbol as a specific example. It is shown that this system outperforms the standard square 16-QAM with the same rate when PAR is constrained.