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

TL;DR

This paper derives new closed-form and integral expressions for the ergodic capacity and MMSE achievable sum rate of MIMO Jacobi and Rayleigh fading channels, providing efficient computation methods and insights into optical fiber communication systems.

Contribution

It introduces novel closed-form and integral formulas for ergodic capacity and sum rate in MIMO Jacobi and Rayleigh channels, avoiding classical correlation function methods.

Findings

Derived efficient integral expressions for ergodic capacity.

Established closed-form formulas for MMSE achievable sum rate.

Validated results with Monte Carlo simulations and existing literature.

Abstract

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.