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 multicarrier 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.