  The effects of transmitter-side multidimensional signal rotations on the
performance of multichannel optical transmission are studied in the presence of
laser phase noise. In particular, the laser phase noise is assumed to be
uncorrelated between channels. To carry out this study, a simple multichannel
laser-phase-noise model that has been experimentally validated for
weakly-coupled multicore-fiber transmission is considered. As the considered
rotation scheme is intended to work in conjunction with receiver-side carrier
phase estimation (CPE), the model is modified to further assume that imperfect
CPE has taken place, leaving residual phase noise in the processed signal.
Based on this model, two receiver structures are derived and used to
numerically optimize transmitter-side signal rotations through Monte Carlo
simulations. For reasonable amounts of residual phase noise, rotations based on
Hadamard matrices are found to be near-optimal for transmission of
four-dimensional signals. Furthermore, Hadamard rotations can be performed for
any dimension that is a power of two. By exploiting this property, an increase
of up to 0.25 bit per complex symbol in an achievable information rate is
observed for transmission of higher-order constellations.
