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

摘要

Multimode/multicore fibers are expected to provide an attractive solution toovercome the capacity limit of current optical communication system. Inpresence of high crosstalk 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 in this paper a new expression for the ergodiccapacity of the Jacobi MIMO channel. This expression involves double integralswhich can be evaluated easily and efficiently. Moreover, the method used inderiving this expression does not appeal to the classical one-point correlationfunction of the random matrix model. Using a limiting transition between Jacobiand Laguerre polynomials, we derive a similar formula for the ergodic capacityof the Gaussian MIMO channel. The analytical results are compared with MonteCarlo simulations and related results available in the literature. A perfectagreement is obtained.