Sum of Fisher-Snedecor <italic>F</italic> Random Variables and Its Applications
The statistical characterization of a sum of random variables (RVs) is useful for investigating the performance of wireless communication systems. We derive exact closed-form expressions for the probability density function (PDF) and cumulative distribution function (CDF) of a sum of independent but...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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IEEE
2020-01-01
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| Series: | IEEE Open Journal of the Communications Society |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/9044870/ |
| _version_ | 1818331736465997824 |
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| author | Hongyang Du Jiayi Zhang Julian Cheng Bo Ai |
| author_facet | Hongyang Du Jiayi Zhang Julian Cheng Bo Ai |
| author_sort | Hongyang Du |
| collection | DOAJ |
| description | The statistical characterization of a sum of random variables (RVs) is useful for investigating the performance of wireless communication systems. We derive exact closed-form expressions for the probability density function (PDF) and cumulative distribution function (CDF) of a sum of independent but not identically distributed (i.n.i.d.) Fisher-Snedecor F RVs. Both PDF and CDF are expressed in terms of the multivariate Fox's H-function. Besides, a simple and accurate approximation to the sum of i.n.i.d. Fisher-Snedecor F variates is presented using the moment matching method. The obtained PDF and CDF are used to evaluate the performance of wireless communication applications including the outage probability, the effective capacity, and the channel capacities under four different adaptive transmission strategies. Moreover, the corresponding approximate expressions are obtained to provide useful insights for the design and deployment of wireless communication systems. In addition, we derive simple asymptotic expressions for the proposed mathematical analysis in the high signal-to-noise ratio regime. Finally, the numerical results demonstrate the accuracy of the derived expressions. |
| first_indexed | 2024-12-13T13:24:35Z |
| format | Article |
| id | doaj.art-d246d8c3efca4e5883000a04dbd17d7d |
| institution | Directory Open Access Journal |
| issn | 2644-125X |
| language | English |
| last_indexed | 2024-12-13T13:24:35Z |
| publishDate | 2020-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Open Journal of the Communications Society |
| spelling | doaj.art-d246d8c3efca4e5883000a04dbd17d7d2022-12-21T23:44:20ZengIEEEIEEE Open Journal of the Communications Society2644-125X2020-01-01134235610.1109/OJCOMS.2020.29827709044870Sum of Fisher-Snedecor <italic>F</italic> Random Variables and Its ApplicationsHongyang Du0https://orcid.org/0000-0002-8220-6525Jiayi Zhang1https://orcid.org/0000-0003-2434-4329Julian Cheng2https://orcid.org/0000-0001-6310-8236Bo Ai3https://orcid.org/0000-0001-6850-0595School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing, ChinaSchool of Electronic and Information Engineering, Beijing Jiaotong University, Beijing, ChinaSchool of Engineering, University of British Columbia, Kelowna, BC, CanadaState Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, ChinaThe statistical characterization of a sum of random variables (RVs) is useful for investigating the performance of wireless communication systems. We derive exact closed-form expressions for the probability density function (PDF) and cumulative distribution function (CDF) of a sum of independent but not identically distributed (i.n.i.d.) Fisher-Snedecor F RVs. Both PDF and CDF are expressed in terms of the multivariate Fox's H-function. Besides, a simple and accurate approximation to the sum of i.n.i.d. Fisher-Snedecor F variates is presented using the moment matching method. The obtained PDF and CDF are used to evaluate the performance of wireless communication applications including the outage probability, the effective capacity, and the channel capacities under four different adaptive transmission strategies. Moreover, the corresponding approximate expressions are obtained to provide useful insights for the design and deployment of wireless communication systems. In addition, we derive simple asymptotic expressions for the proposed mathematical analysis in the high signal-to-noise ratio regime. Finally, the numerical results demonstrate the accuracy of the derived expressions.https://ieeexplore.ieee.org/document/9044870/Channel capacityeffective capacityFisher-Snedecor <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">F</italic>-distributionsum of random variables |
| spellingShingle | Hongyang Du Jiayi Zhang Julian Cheng Bo Ai Sum of Fisher-Snedecor <italic>F</italic> Random Variables and Its Applications IEEE Open Journal of the Communications Society Channel capacity effective capacity Fisher-Snedecor <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">F</italic>-distribution sum of random variables |
| title | Sum of Fisher-Snedecor <italic>F</italic> Random Variables and Its Applications |
| title_full | Sum of Fisher-Snedecor <italic>F</italic> Random Variables and Its Applications |
| title_fullStr | Sum of Fisher-Snedecor <italic>F</italic> Random Variables and Its Applications |
| title_full_unstemmed | Sum of Fisher-Snedecor <italic>F</italic> Random Variables and Its Applications |
| title_short | Sum of Fisher-Snedecor <italic>F</italic> Random Variables and Its Applications |
| title_sort | sum of fisher snedecor italic f italic random variables and its applications |
| topic | Channel capacity effective capacity Fisher-Snedecor <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">F</italic>-distribution sum of random variables |
| url | https://ieeexplore.ieee.org/document/9044870/ |
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