Base vectors linear combination modulation approach for hexagonal signal constellation

A unified mathematical formula is derived for Hexagonal Signal Constellation (HSC) of arbitrary rank, which leads to several interesting theoretical and practical implications. First, we prove that given a certain normalized peak amplitude A_K, the amount of available constellation points B_K is previously underestimated. Second, we re-evaluate the uncoded Symbol Error Rate (SER) of HSC of arbitrary rank. Contrary to conventional beliefs, it is shown the gap in power efficiency between HSC and Quadrature Amplitude Modulation (QAM) is narrowed as the modulation rank increases. Third, by using the proposed formula, we have also conceived a novel modulation and demodulation approach for HSC, named Base Vectors Combination (BVC) and Base Vectors Projection (BVP), which compares favorably against traditional Quadrature (I/Q) mod and demodulators in terms of computational complexity. Simulation results are provided to validate our findings.