  Regular perturbation is applied to space-division multiplexing (SDM) on
optical fibers and motivates a correlated rotation-and-additive noise (CRAN)
model. For S spatial modes, or 2S complex-alphabet channels, the model has
4S(S+1) hidden independent real Gauss-Markov processes, of which 2S model phase
noise, 2S(2S-1) model spatial mode rotation, and 4S model additive noise.
Achievable information rates of multi-carrier communication are computed by
using particle filters. For S=2 spatial modes with strong coupling and a 1000
km link, joint processing of the spatial modes gains 0.5 bits/s/Hz/channel in
rate and 1.4 dB in power with respect to separate processing of 2S
complex-alphabet channels without considering CRAN.
