Design of good constellations for single-subcarrier intensity-modulated optical systems

We address the problem of constellation design for single-subcarrier intensity-modulated direct-detected optical systems. We seek to design constellations that minimize the average electrical power, average optical power and peak optical power for a given minimum Euclidean distance between constellation points. The constellation design is formulated as a nonconvex optimization problem with a convex cost function, nonconvex quadratic constraints and second-order cone constraints. It is shown that this problem can be approximated by a second-order cone programming (SOCP) problem. We propose an iterative procedure in which the SOCP approximation is refined in each iteration. The new constellations are compared to the state-of-the-art constellations in terms of power efficiency. Our 32- and 64-point constellations outperform the corresponding QAM-based and face-centered cubic lattice constellations.