  Multimode/multicore fibers are expected to provide an attractive solution to
overcome the capacity limit of the current optical communication system. In the
presence of high cross-talk between modes/cores, the squared singular values of
the input/output transfer matrix follow the law of the Jacobi ensemble of
random matrices. Assuming that the channel state information is only available
at the receiver, we derive a new expression for the ergodic capacity of the
MIMO Jacobi fading channel. This expression involves double integrals which can
be evaluated easily and efficiently. Moreover, the method used in deriving this
expression does not appeal to the classical one-point correlation function of
the random matrix model. Using a limiting transition between Jacobi and
Laguerre polynomials, we derive a similar formula for the ergodic capacity of
the MIMO Rayleigh fading channel. Moreover, we derive a new exact closed form
expressions for the achievable sum rate of MIMO Jacobi and Rayleigh fading
channels employing linear minimum mean squared error (MMSE) receivers. The
analytical results are compared to the results obtained by Monte Carlo
simulations and the related results available in the literature, which shows
perfect agreement.
