On the Efficient Simulation of the Distribution of the Sum of Gamma-Gamma Variates with Application to the Outage Probability Evaluation Over Fading Channels

dc.contributor.authorBen Issaid, Chaouki
dc.contributor.authorRached, Nadhir B.
dc.contributor.authorKammoun, Abla
dc.contributor.authorAlouini, Mohamed-Slim
dc.contributor.authorTempone, Raul
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentElectrical Engineering Program
dc.contributor.departmentStatistics Program
dc.date.accessioned2017-05-01T12:02:40Z
dc.date.available2017-05-01T12:02:40Z
dc.date.issued2017-01-26
dc.date.published-online2017-01-26
dc.date.published-print2017-04
dc.description.abstractThe Gamma-Gamma distribution has recently emerged in a number of applications ranging from modeling scattering and reverberation in sonar and radar systems to modeling atmospheric turbulence in wireless optical channels. In this respect, assessing the outage probability achieved by some diversity techniques over this kind of channels is of major practical importance. In many circumstances, this is related to the difficult question of analyzing the statistics of a sum of Gamma- Gamma random variables. Answering this question is not a simple matter. This is essentially because outage probabilities encountered in practice are often very small, and hence the use of classical Monte Carlo methods is not a reasonable choice. This lies behind the main motivation of the present work. In particular, this paper proposes a new approach to estimate the left tail of the sum of Gamma-Gamma variates. More specifically, we propose robust importance sampling schemes that efficiently evaluates the outage probability of diversity receivers over Gamma-Gamma fading channels. The proposed estimators satisfy the well-known bounded relative error criterion for both maximum ratio combining and equal gain combining cases. We show the accuracy and the efficiency of our approach compared to naive Monte Carlo via some selected numerical simulations.
dc.description.sponsorshipThis work is in part supported by the Qatar National Research Fund (a member of Qatar Foundation) under NPRP Grant NPRP9-077-2-036 and in part by the KAUST-KFUPM initiative.
dc.eprint.versionPost-print
dc.identifier.citationBen Issaid C, Ben Rached N, Kammoun A, Alouini M-S, Tempone R (2017) On the Efficient Simulation of the Distribution of the Sum of Gamma–Gamma Variates With Application to the Outage Probability Evaluation Over Fading Channels. IEEE Transactions on Communications 65: 1839–1848. Available: http://dx.doi.org/10.1109/TCOMM.2017.2658575.
dc.identifier.doi10.1109/TCOMM.2017.2658575
dc.identifier.issn0090-6778
dc.identifier.journalIEEE Transactions on Communications
dc.identifier.urihttp://hdl.handle.net/10754/623306
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)
dc.relation.urlhttp://ieeexplore.ieee.org/document/7835220/
dc.rights(c) 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.
dc.subjectmaximum ratio combining
dc.subjectGamma-Gamma
dc.subjectgeneralized-K
dc.subjectimportance sampling
dc.subjectMonte Carlo
dc.subjectbounded relative error
dc.subjectoutage probability
dc.titleOn the Efficient Simulation of the Distribution of the Sum of Gamma-Gamma Variates with Application to the Outage Probability Evaluation Over Fading Channels
dc.typeArticle
display.details.left<span><h5>Type</h5>Article<br><br><h5>Authors</h5><a href="https://repository.kaust.edu.sa/search?query=orcid.id:0000-0002-4481-8168&spc.sf=dc.date.issued&spc.sd=DESC">Ben Issaid, Chaouki</a> <a href="https://orcid.org/0000-0002-4481-8168" target="_blank"><img src="https://repository.kaust.edu.sa/server/api/core/bitstreams/82a625b4-ed4b-40c8-865a-d6a5225a26a4/content" width="16" height="16"/></a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Rached, Nadhir B.,equals">Rached, Nadhir B.</a><br><a href="https://repository.kaust.edu.sa/search?query=orcid.id:0000-0002-0195-3159&spc.sf=dc.date.issued&spc.sd=DESC">Kammoun, Abla</a> <a href="https://orcid.org/0000-0002-0195-3159" target="_blank"><img src="https://repository.kaust.edu.sa/server/api/core/bitstreams/82a625b4-ed4b-40c8-865a-d6a5225a26a4/content" width="16" height="16"/></a><br><a href="https://repository.kaust.edu.sa/search?query=orcid.id:0000-0003-4827-1793&spc.sf=dc.date.issued&spc.sd=DESC">Alouini, Mohamed-Slim</a> <a href="https://orcid.org/0000-0003-4827-1793" target="_blank"><img src="https://repository.kaust.edu.sa/server/api/core/bitstreams/82a625b4-ed4b-40c8-865a-d6a5225a26a4/content" width="16" height="16"/></a><br><a href="https://repository.kaust.edu.sa/search?query=orcid.id:0000-0003-1967-4446&spc.sf=dc.date.issued&spc.sd=DESC">Tempone, Raul</a> <a href="https://orcid.org/0000-0003-1967-4446" target="_blank"><img src="https://repository.kaust.edu.sa/server/api/core/bitstreams/82a625b4-ed4b-40c8-865a-d6a5225a26a4/content" width="16" height="16"/></a><br><br><h5>KAUST Department</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.department=Applied Mathematics and Computational Science Program,equals">Applied Mathematics and Computational Science Program</a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.department=Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division,equals">Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division</a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.department=Electrical Engineering Program,equals">Electrical Engineering Program</a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.department=Statistics Program,equals">Statistics Program</a><br><br><h5>Online Publication Date</h5>2017-01-26<br><br><h5>Print Publication Date</h5>2017-04<br><br><h5>Date</h5>2017-01-26</span>
display.details.right<span><h5>Abstract</h5>The Gamma-Gamma distribution has recently emerged in a number of applications ranging from modeling scattering and reverberation in sonar and radar systems to modeling atmospheric turbulence in wireless optical channels. In this respect, assessing the outage probability achieved by some diversity techniques over this kind of channels is of major practical importance. In many circumstances, this is related to the difficult question of analyzing the statistics of a sum of Gamma- Gamma random variables. Answering this question is not a simple matter. This is essentially because outage probabilities encountered in practice are often very small, and hence the use of classical Monte Carlo methods is not a reasonable choice. This lies behind the main motivation of the present work. In particular, this paper proposes a new approach to estimate the left tail of the sum of Gamma-Gamma variates. More specifically, we propose robust importance sampling schemes that efficiently evaluates the outage probability of diversity receivers over Gamma-Gamma fading channels. The proposed estimators satisfy the well-known bounded relative error criterion for both maximum ratio combining and equal gain combining cases. We show the accuracy and the efficiency of our approach compared to naive Monte Carlo via some selected numerical simulations.<br><br><h5>Citation</h5>Ben Issaid C, Ben Rached N, Kammoun A, Alouini M-S, Tempone R (2017) On the Efficient Simulation of the Distribution of the Sum of Gamma–Gamma Variates With Application to the Outage Probability Evaluation Over Fading Channels. IEEE Transactions on Communications 65: 1839–1848. Available: http://dx.doi.org/10.1109/TCOMM.2017.2658575.<br><br><h5>Acknowledgements</h5>This work is in part supported by the Qatar National Research Fund (a member of Qatar Foundation) under NPRP Grant NPRP9-077-2-036 and in part by the KAUST-KFUPM initiative.<br><br><h5>Publisher</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.publisher=Institute of Electrical and Electronics Engineers (IEEE),equals">Institute of Electrical and Electronics Engineers (IEEE)</a><br><br><h5>Journal</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.journal=IEEE Transactions on Communications,equals">IEEE Transactions on Communications</a><br><br><h5>DOI</h5><a href="https://doi.org/10.1109/TCOMM.2017.2658575">10.1109/TCOMM.2017.2658575</a><br><br><h5>Additional Links</h5>http://ieeexplore.ieee.org/document/7835220/</span>
kaust.personBen Issaid, Chaouki
kaust.personRached, Nadhir B.
kaust.personKammoun, Abla
kaust.personAlouini, Mohamed-Slim
kaust.personTempone, Raul
orcid.authorBen Issaid, Chaouki::0000-0002-4481-8168
orcid.authorRached, Nadhir B.
orcid.authorKammoun, Abla::0000-0002-0195-3159
orcid.authorAlouini, Mohamed-Slim::0000-0003-4827-1793
orcid.authorTempone, Raul::0000-0003-1967-4446
orcid.id0000-0003-1967-4446
orcid.id0000-0003-4827-1793
orcid.id0000-0002-0195-3159
orcid.id0000-0002-4481-8168
refterms.dateFOA2018-06-14T04:36:50Z
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