Modern long-haul fiber-optic transmission systems use polarization multiplexing with advanced modulation formats to transport large amounts of data with higher spectral efficiency, and coherent reception with digital signal processing (DSP) to recover the transmitted information. This article discusses modeling of probabilistically shaped (PS) coherent systems in OptSim, a topic that has attracted a lot of attention lately in order to achieve the data transmission capacity close to the Shannon limit.
Basics of Probabilistic Shaping
Probabilistic Constellation Shaping (PCS) is a DSP technique that transmits a quadrature amplitude modulated (QAM) signal, where each constellation point is transmitted with a different probability . In general, this technique provides two advantages over standard QAM transmission:
- High data rate flexibility (changing the probability to be transmitted of a constellation reduces, in general, its data rate).
- Small sensitivity gain, due to a better “match” between constellation and channel.
For these two reasons, PCS has been widely adopted in optical communications.
In general, the probability distribution of constellation points can be arbitrarily chosen. In practice, the optical channel is very well approximated by an additive white Gaussian noise (AWGN) channel, i.e., a channel that adds a random white Gaussian noise. For this channel, it has been shown that the optimal distribution is the Maxwell-Boltzmann distribution: