TY - JOUR
T1 - The Hermitian Jacobi Process
T2 - A Simplified Formula for the Moments and Application to Optical Fiber MIMO Channels
AU - Demni, N.
AU - Hamdi, T.
AU - Souissi, A.
N1 - Publisher Copyright:
© 2020, Pleiades Publishing, Ltd.
PY - 2020/10
Y1 - 2020/10
N2 - Abstract: 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 [8]. 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.
AB - Abstract: 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 [8]. 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.
KW - Jacobi unitary ensemble
KW - MIMO channels
KW - orthogonal projection
KW - Schur polynomials
KW - Shannon capacity
KW - symmetric Jacobi polynomials
KW - unitary Brownian motion
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U2 - 10.1134/S0016266320040036
DO - 10.1134/S0016266320040036
M3 - Article
AN - SCOPUS:85107352295
SN - 0016-2663
VL - 54
SP - 257
EP - 271
JO - Functional Analysis and Its Applications
JF - Functional Analysis and Its Applications
IS - 4
ER -