Effective Rate Evaluation of RIS-Assisted Communications Using the Sums of Cascaded α-μ Random Variates
This paper begins with the characterization of the sum of M versions of cascaded α-μ (equivalently, N <sub>*</sub> (α-μ)) distributed random variates (RVs), and later on, explores the feasibility and applicability of the obtained results in the...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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IEEE
2021-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/9312154/ |
| _version_ | 1818448925336535040 |
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| author | Long Kong Yun Ai Symeon Chatzinotas Bjorn Ottersten |
| author_facet | Long Kong Yun Ai Symeon Chatzinotas Bjorn Ottersten |
| author_sort | Long Kong |
| collection | DOAJ |
| description | This paper begins with the characterization of the sum of M versions of cascaded α-μ (equivalently, N <sub>*</sub> (α-μ)) distributed random variates (RVs), and later on, explores the feasibility and applicability of the obtained results in the recent proposed reconfigurable intelligent surface (RIS)-assisted communications. More specifically, the sum of cascaded α-μ distributed RVs is exactly characterized by the probability density function (PDF) expressed in terms of the programmable multivariate Fox's H-function, and approximated with the mixture of Gaussian (MoG) distribution. The approximation accuracy is further validated by the Kolmogorov-Smirnov (KS) goodness of fit test. Based on the obtained statistical results, a promising application, i.e., RIS-assisted communication, is considered and evaluated from the effective rate perspective. The exact, asymptotic, and approximated effective rate are derived with closed-form expressions. Finally, our analytical results are further validated using the Monte-Carlo simulation, their accuracy is confirmed with the analytical error indicator. One can conclude that (i) the exact effective rate expression is complex in the manner of mathematical representation; (ii) the MoG-based effective rate expression is simple and provides a highly tight approximation to the exact expression, besides it indeed acts as a highly tight upper bound for the exact effective rate expression; and (iii) the MoG-based solution outperforms the multivariate Fox's H-function based approach with reducing complexity. |
| first_indexed | 2024-12-14T20:27:15Z |
| format | Article |
| id | doaj.art-7f113f890d144fb0bf84970ecda70c8c |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-14T20:27:15Z |
| publishDate | 2021-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-7f113f890d144fb0bf84970ecda70c8c2022-12-21T22:48:36ZengIEEEIEEE Access2169-35362021-01-0195832584410.1109/ACCESS.2020.30488829312154Effective Rate Evaluation of RIS-Assisted Communications Using the Sums of Cascaded α-μ Random VariatesLong Kong0https://orcid.org/0000-0001-6963-7489Yun Ai1https://orcid.org/0000-0002-3409-8152Symeon Chatzinotas2https://orcid.org/0000-0001-5122-0001Bjorn Ottersten3https://orcid.org/0000-0003-2298-6774Interdisciplinary Center for Security, Reliability and Trust (SnT), University of Luxembourg, Luxembourg City, LuxembourgFaculty of Engineering, Norwegian University of Science and Technology, Gjøvik, NorwayInterdisciplinary Center for Security, Reliability and Trust (SnT), University of Luxembourg, Luxembourg City, LuxembourgInterdisciplinary Center for Security, Reliability and Trust (SnT), University of Luxembourg, Luxembourg City, LuxembourgThis paper begins with the characterization of the sum of M versions of cascaded α-μ (equivalently, N <sub>*</sub> (α-μ)) distributed random variates (RVs), and later on, explores the feasibility and applicability of the obtained results in the recent proposed reconfigurable intelligent surface (RIS)-assisted communications. More specifically, the sum of cascaded α-μ distributed RVs is exactly characterized by the probability density function (PDF) expressed in terms of the programmable multivariate Fox's H-function, and approximated with the mixture of Gaussian (MoG) distribution. The approximation accuracy is further validated by the Kolmogorov-Smirnov (KS) goodness of fit test. Based on the obtained statistical results, a promising application, i.e., RIS-assisted communication, is considered and evaluated from the effective rate perspective. The exact, asymptotic, and approximated effective rate are derived with closed-form expressions. Finally, our analytical results are further validated using the Monte-Carlo simulation, their accuracy is confirmed with the analytical error indicator. One can conclude that (i) the exact effective rate expression is complex in the manner of mathematical representation; (ii) the MoG-based effective rate expression is simple and provides a highly tight approximation to the exact expression, besides it indeed acts as a highly tight upper bound for the exact effective rate expression; and (iii) the MoG-based solution outperforms the multivariate Fox's H-function based approach with reducing complexity.https://ieeexplore.ieee.org/document/9312154/Effective ratequality-of-service (QoS)cascaded α-μreconfigurable intelligent surfaces (RIS)Kolmogorov-Smirnov (KS) goodness of fit testFox’s <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">H</italic>-function |
| spellingShingle | Long Kong Yun Ai Symeon Chatzinotas Bjorn Ottersten Effective Rate Evaluation of RIS-Assisted Communications Using the Sums of Cascaded α-μ Random Variates IEEE Access Effective rate quality-of-service (QoS) cascaded α-μ reconfigurable intelligent surfaces (RIS) Kolmogorov-Smirnov (KS) goodness of fit test Fox’s <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">H</italic>-function |
| title | Effective Rate Evaluation of RIS-Assisted Communications Using the Sums of Cascaded α-μ Random Variates |
| title_full | Effective Rate Evaluation of RIS-Assisted Communications Using the Sums of Cascaded α-μ Random Variates |
| title_fullStr | Effective Rate Evaluation of RIS-Assisted Communications Using the Sums of Cascaded α-μ Random Variates |
| title_full_unstemmed | Effective Rate Evaluation of RIS-Assisted Communications Using the Sums of Cascaded α-μ Random Variates |
| title_short | Effective Rate Evaluation of RIS-Assisted Communications Using the Sums of Cascaded α-μ Random Variates |
| title_sort | effective rate evaluation of ris assisted communications using the sums of cascaded x03b1 x03bc random variates |
| topic | Effective rate quality-of-service (QoS) cascaded α-μ reconfigurable intelligent surfaces (RIS) Kolmogorov-Smirnov (KS) goodness of fit test Fox’s <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">H</italic>-function |
| url | https://ieeexplore.ieee.org/document/9312154/ |
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