The Hermitian Jacobi Process: A Simplified Formula for the Moments and Application to Optical Fiber MIMO Channels

Using a change of basis in the algebra of symmetric functions, we compute the moments of the Hermitian Jacobi process. After a careful arrangement of terms and the evaluation of the determinant of an “almost upper-triangular” matrix, we end up with a moment formula which is considerably simpler than the one derived in [L. Deleaval, N. Demni, J. Theoret. Probab., 31:3 (2018), 1759–1778]. As an application, we propose the Hermitian Jacobi process as a dynamical model for an optical fiber MIMO channel and compute its Shannon capacity in the case of a low-power transmitter. Moreover, when the size of the Hermitian Jacobi process is larger than the moment order, our moment formula can be written as a linear combination of balanced terminating ${}_4F_3$-series evaluated at unit argument.