New Expressions for Ergodic Capacities of Optical Fibers and Wireless MIMO Channels

Multimode/multicore fibers are expected to provide an attractive solution to overcome the capacity limit of current optical communication system. In presence of high crosstalk 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 in this paper a new expression for the ergodic capacity of the Jacobi MIMO 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 Gaussian MIMO channel. The analytical results are compared with Monte Carlo simulations and related results available in the literature. A perfect agreement is obtained. Index Terms Jacobi MIMO channel, Gaussian MIMO channel, Jacobi polynomials, Laguerre polynomials, Ergodic capacity.