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Multimode/multicore fibers are expected to provide an attractive solution toovercome the capacity limit of the current optical communication system. In thepresence of high cross-talk between modes/cores, the squared singular values ofthe input/output transfer matrix follow the law of the Jacobi ensemble ofrandom matrices. Assuming that the channel state information is only availableat the receiver, we derive a new expression for the ergodic capacity of theMIMO Jacobi fading channel. This expression involves double integrals which canbe evaluated easily and efficiently. Moreover, the method used in deriving thisexpression does not appeal to the classical one-point correlation function ofthe random matrix model. Using a limiting transition between Jacobi andLaguerre polynomials, we derive a similar formula for the ergodic capacity ofthe MIMO Rayleigh fading channel. Moreover, we derive a new exact closed formexpressions for the achievable sum rate of MIMO Jacobi and Rayleigh fadingchannels employing linear minimum mean squared error (MMSE) receivers. Theanalytical results are compared to the results obtained by Monte Carlosimulations and the related results available in the literature, which showsperfect agreement.

Closed-Form Expressions of Ergodic Capacity and MMSE Achievable Sum Rate for MIMO Jacobi and Rayleigh Fading Channels