arXiv:1511.06074v1 [cs.IT] 19 Nov 2015 New Expressions for Ergodic Capacities of Optical Fibers and Wireless MIMO Channels Amor Nafkha, Nizar Demni, R´ emi Bonnefoi Abstract 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. I. I NTRODUCTION To accommodate the exponential growth of data traffic over the last few years, the space-division multiplexing (SDM) based on multi-core optical fiber (MCF) or multi-mode optical fiber (MMF) is expected to overcome the barrier from capacity limit of single-core fiber [1]–[3]. The main challenge in SDM occurs due to in-band crosstalk between multiple parallel transmission channels (cores/modes). This non-negligible crosstalk can be dealt with using multiple-input multiple-output (MIMO) signal processing techniques [2], [4]–[7]. Those techniques are widely used for wireless communication systems and they A. Nafkha and R. Bonnefoi are with SCEE/IETR of CentraleSup´ elec, Avenue de la Boulaie, 35576 Cesson S´ evign´ e, France. (e- mail: {amor.nafkha, Remi.Bonnefoi}@centralesupelec.fr). N. Demni works at Institut de Recherche Math´ ematique de Rennes (IRMAR), Universit´ e de Rennes 1, Campus de Beaulieu 35042 Rennes, France. (e-mail: nizar.demni@univ-rennes1.fr) January 23, 2021 DRAFT