  This paper studies the impact of probabilistic shaping on effective
signal-to-noise ratios (SNRs) and achievable information rates (AIRs) in a
back-to-back configuration and in unrepeated nonlinear fiber transmissions. For
back-to-back, various shaped quadrature amplitude modulation (QAM)
distributions are found to have the same implementation penalty as uniform
input. By demonstrating in transmission experiments that shaped QAM input leads
to lower effective SNR than uniform input at a fixed average launch power, we
experimentally confirm that shaping enhances the fiber nonlinearities. However,
shaping is ultimately found to increase the AIR, which is the most relevant
figure of merit as it is directly related to spectral efficiency. In a detailed
study of these shaping gains for the nonlinear fiber channel, four strategies
for optimizing QAM input distributions are evaluated and experimentally
compared in wavelength division multiplexing (WDM) systems. The first shaping
scheme generates a Maxwell-Boltzmann (MB) distribution based on a linear
additive white Gaussian noise channel. The second strategy uses the
Blahut-Arimoto algorithm to optimize an unconstrained QAM distribution for a
split-step Fourier method based channel model. In the third and fourth
approach, MB-shaped QAM and unconstrained QAM are optimized via the enhanced
Gaussian noise (EGN) model. Although the absolute shaping gains are found to be
relatively small, the relative improvements by EGN-optimized unconstrained
distributions over linear AWGN optimized MB distributions are up to 59%. This
general behavior is observed in 9-channel and fully loaded WDM experiments.
