Abstract
Coherent optical transmission systems have a four-dimensional
(4–D) signal space (two quadratures in two polarizations). These
four dimensions can be used to create modulation formats that have a better
power efficiency (higher sensitivity) than the conventional binary phase
shift keying/quadrature phase shift keying (BPSK/QPSK) signals. Several
examples are given, with some emphasis on a 24-level format and an 8-level
format, including descriptions of how they can be realized and expressions
for their symbol and bit error probabilities. These formats are,
respectively, an extension and a subset of the commonly used 16-level
dual-polarization QPSK format. Sphere packing simulations in 2, 3, and 4
dimensions, up to 32 levels, are used to verify their optimality. The
numerical results, as the number of levels increases, are shown to agree
with lattice-theoretical results. Finally, we point out that the use of
these constellations will lead to improved fundamental sensitivity limits
for optical communication systems, and they may also be relevant as a way of
reducing power demands and/or nonlinear influence.
© 2009 IEEE
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