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

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Functional Analysis and Its Applications Aims and scope

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.

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Notes

  1. As in the case of fixed \(t > 0\), we omit the dependence of the stationary moments on \((r,s,m)\) from the notation.

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Funding

The authors gratefully acknowledge the financial support of Qassim University represented by the Deanship of Scientific Research under grant no. cba-2019-2-2-I-5394 during the academic year 1440AH/2019AD.

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Authors and Affiliations

  1. Institut de Mathématiques de Marseille (I2M, UMR 7373), Aix-Marseille Université, Centre National de la Recherche Scientifique, Marseille, France

    N. Demni

  2. Department of Management Information Systems, College of Business Management, Qassim University, Ar Rass, Saudi Arabia

    T. Hamdi

  3. Laboratoire d’Analyse Mathématiques et Applications LR11ES11, Université de Tunis El-Manar, Tunis, Tunisie

    T. Hamdi

  4. Department of Accounting, College of Business Management, Qassim University, Ar Rass, Saudi Arabia

    A. Souissi

  5. Preparatory Institute for scientific and Technical Studies, Carthage University, Tunis, Tunisie

    A. Souissi

Authors
  1. N. Demni
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  2. T. Hamdi
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  3. A. Souissi
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Corresponding authors

Correspondence to N. Demni, T. Hamdi or A. Souissi.

Additional information

Translated from Funktsional'nyi Analiz i ego Prilozheniya, 2020, Vol. 54, pp. 37-55 https://doi.org/10.4213/faa3774.

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Demni, N., Hamdi, T. & Souissi, A. The Hermitian Jacobi Process: A Simplified Formula for the Moments and Application to Optical Fiber MIMO Channels. Funct Anal Its Appl 54, 257–271 (2020). https://doi.org/10.1134/S0016266320040036

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  • DOI: https://doi.org/10.1134/S0016266320040036

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