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On the Effective Throughput of Shadowed Beaulieu-Xie Fading Channel

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Abstract

With the demanding need for next-generation wireless networks and the emergence of real-time applications in wireless communication, data rate performance over these systems is being researched for different fading channels. This study looked into the effective throughput analysis of the shadowed Beaulieu-Xie composite fading channel. The probability density function based approach is used to derive the expressions of the effective capacity (EC) for the aforementioned system. To get the simplified relationship between the performance parameter and channel parameters, the low signal-to-noise-ratio (SNR) and the high-SNR approximations of the effective rate are also provided. The derived expressions are evaluated for different values of fading and shadowing parameters to study its effect on the EC. Also, the impact of the delay parameter on the EC is investigated. The accuracy of the inferred theoretical expressions is confirmed by the results of the Monte-Carlo simulation.

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Funding

No funding was received for this work.

Author information

Authors and Affiliations

  1. Department of CSE, Delhi Technological University, Delhi, India

    Manpreet Kaur

  2. Department of ECE, Pranveer Singh Institute of Technology, Kanpur, India

    Puspraj Singh Chauhan

  3. Central Research Laboratory, BEL, Ghaziabad, India

    Sandeep Kumar

  4. Department of ECE, Mahatma Gandhi Mission’s College of Engineering and Technology, Noida, India

    Poonam Yadav

Authors
  1. Manpreet Kaur
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  2. Puspraj Singh Chauhan
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  3. Sandeep Kumar
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  4. Poonam Yadav
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All the authors have equally contributed in this manuscript.

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Correspondence to Sandeep Kumar.

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Appendix

Appendix

The error in (9) by truncation the series by D number of terms can be given by

$$E_{D} = \sum\limits_{d = D}^{\infty } {\frac{{\Gamma \left( {m_{Y} + d} \right)z^{d} }}{d!}} U\left( {m_{X} + d;m_{X} + d + 1 - A;\frac{{m_{X} C}}{{\overline{\gamma } \Omega_{X} }}} \right).$$
(21)

Substituting g = d-D in the above equation and rearranging the terms, we get

$$E_{D} = \sum\limits_{g = 0}^{\infty } {z^{D} \frac{{\Gamma \left( {m_{Y} + D + g} \right)}}{{\left( {D + g} \right)!}}} z^{d} U\left( {m_{X} + D + g;m_{X} + D + g + 1 - A;\frac{{m_{X} C}}{{\overline{\gamma } \Omega_{X} }}} \right).$$
(22)

Since \(U\left( {m_{X} + D + g;m_{X} + D + g + 1 - A;\frac{{m_{X} C}}{{\overline{\gamma } \Omega_{X} }}} \right)\) is a monotonically decreasing function with respect to g,\(E_{D}\) can be upper bounded as

$$E_{D} \le \frac{{z^{D} \Gamma \left( {m_{Y} + D} \right)}}{D!}U\left( {m_{X} + D;m_{X} + D + 1 - A;\frac{{m_{X} C}}{{\overline{\gamma } \Omega_{X} }}} \right)\sum\limits_{g = 0}^{\infty } {\frac{{\left( 1 \right)_{g} \left( {m_{Y} + D} \right)_{g} }}{{g!\left( {D + 1} \right)_{g} }}} z^{g} .$$
(23)

Using the infinite series expansion of \({}_{2}F_{1} \left( {.,.;.;.} \right)\) in the above equation, the closed-form expression of the upper bound of the truncation error can be obtained as (10).

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Kaur, M., Chauhan, P.S., Kumar, S. et al. On the Effective Throughput of Shadowed Beaulieu-Xie Fading Channel. Wireless Pers Commun 136, 165–180 (2024). https://doi.org/10.1007/s11277-024-11248-3

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