Large deviation approach to the outage optical MIMO capacity

MIMO processing techniques in fiber optical communications have been proposed as a promising approach to meet increasing demand for information throughput. In this context, the multiple channels correspond to the multiple modes and/or multiple cores in the fiber. The lack of back-scattering necessitates the modeling of the transmission coefficients between modes as elements of a unitary matrix. Also, due to the scattering between modes the channel is modeled as a random Haar unitary matrix between N_t transmitting and N_r receiving modes. In this paper, we apply a large-deviations approach from random matrix theory to obtain the outage capacity for Haar matrices in the low outage limit, which is appropriate for fiber-optical communications. This methodology is based on the Coulomb gas method for the eigenvalues of a matrix developed in statistical physics. By comparing our analytic results to simulations, we see that, despite the fact that this method is nominally valid for large number of modes, our method is quite accurate even for small to modest number of channels.