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.

中文翻译：

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Hermitian Jacobi 过程：矩量的简化公式及其在光纤 MIMO 信道中的应用

摘要

使用对称函数代数中基的变化，我们计算 Hermitian Jacobi 过程的矩。在对术语进行仔细安排和对“几乎上三角”矩阵的行列式进行评估之后，我们最终得到了一个矩公式，它比 [8] 中推导出的公式要简单得多。作为一个应用，我们提出 Hermitian Jacobi 过程作为光纤 MIMO 信道的动态模型，并在低功率发射机的情况下计算其香农容量。此外，当 Hermitian Jacobi 过程的大小大于矩阶时，我们的矩公式可以写成平衡终止\({}_4F_3\) -系列的线性组合，以单元参数计算。