  Vendor interoperability is one of the desired future characteristics of
optical networks. This means that the transmission system needs to support a
variety of hardware with different components, leading to system uncertainties
throughout the network. For example, uncertainties in signal-to-noise ratio and
laser linewidth can negatively affect the quality of transmission within an
optical network due to e.g. mis-parametrization of the transceiver signal
processing algorithms. In this paper, we propose to geometrically optimize a
constellation shape that is robust to uncertainties in the channel conditions
by utilizing end-to-end learning. In the optimization step, the channel model
includes additive noise and residual phase noise. In the testing step, the
channel model consists of laser phase noise, additive noise and blind phase
search as the carrier phase recovery algorithm. Two noise models are considered
for the additive noise: white Gaussian noise and nonlinear interference noise
model for fiber nonlinearities. The latter models the behavior of an optical
fiber channel more accurately because it considers the nonlinear effects of the
optical fiber. For this model, the uncertainty in the signal-to-noise ratio can
be divided between amplifier noise figures and launch power variations. For
both noise models, our results indicate that the learned constellations are
more robust to uncertainties in channel conditions compared to a standard
constellation scheme such as quadrature amplitude modulation and standard
geometric constellation shaping techniques.
