Hexagonal signal constellation's symbol error rate performance and its numerical analysis

The symbol error rate performance of arbitrary points hexagonal constellation signal was deduced and a numerical analysis method for SER performance was presented. A unified mathematical formula was derived for arbitrary points hexagonal constellation, based on which the analytical formula of available points under a certain unified peak energy constraint was put forward. With the aid of such analytical formula, SER performance of arbitrary points hexagonal constellation signal was deduced and a Gauss-Legendre based method was presented for SER performance numerical analysis. Simulations show the consistency of the results between the available point formula and actual constellations, as well as between the numerical analysis method and Monte-Carlo simulations. Therefore, the numerical analysis method can replace the Monte Carlo simulation, SER performance analysis of arbitrary points hexagonal constellation signal can be achieved with lower computational complexity.