Systematic method for designing constellations for intensity-modulated optical systems

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16 Citations (Scopus)


We consider the design of compact multisub- carrier constellations for intensity-modulated direct- detected optical systems. The constellations are designed to minimize the average electrical, average optical, and peak optical power for a given minimum distance between constellation points. We formulate the constellation design as a nonconvex optimization problem with second-order cone constraints, (nonconvex) quadratic constraints, and a convex objective function. We show that this problem can be relaxed to a (convex) second-order cone program- ming (SOCP) problem. We introduce a simple iterative method in which the SOCP relaxation is improved in each iteration. Several numerical simulation examples are provided to illustrate the effectiveness of our method. For the single-subcarrier case, the new constellations are compared with the best known formats in terms of power and spectral efficiency. Our new constellations outper- form the corresponding face-centered cubic lattice and quadrature-amplitude-modulation-based constellations, with average electrical and optical power gains in the vicin- ity of 0.5 dB, for low symbol error rates. The corresponding peak optical power gains are also in the vicinity of 0.5 dB. By studying the mutual information inherent to the new constellations, we show that the potentials are still valid for coded systems. For the two-subcarrier case, we still out- perform two-subcarrier schemes based on conventional constellations and optimized single-subcarrier constella- tions with the same dimensions.
Original languageEnglish
Article number6822801
Pages (from-to)449-458
JournalIEEE/OSA Journal of Optical Communications and Networking
Issue number5
Publication statusPublished - May 2014


  • Direct detection
  • Intensity modulation
  • Lattice codes
  • Mutual information
  • Noncoherent communications
  • Nonconvex optimization
  • Second-order cone programming
  • Sphere packing
  • Wireless optical communications


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