Ben Rached, N, Botev, Z, Kammoun, A et al. (2 more authors) (2018) On the Sum of Order Statistics and Applications to Wireless Communication Systems Performances. IEEE Transactions on Wireless Communications, 17 (11). pp. 7801-7813. ISSN 1536-1276
Abstract
We consider the problem of evaluating the cumulative distribution function (CDF) of the sum of order statistics, which serves to compute outage probability (OP) values at the output of generalized selection combining receivers. Generally, closed-form expressions of the CDF of the sum of order statistics are unavailable for many practical distributions. Moreover, the naive Monte Carlo (MC) method requires a substantial computational effort when the probability of interest is sufficiently small. In the region of small OP values, we instead propose two effective variance reduction techniques that yield a reliable estimate of the CDF with small computing cost. The first estimator, which can be viewed as an importance sampling estimator, has bounded relative error under a certain assumption that is shown to hold for most of the challenging distributions. A possible improvement of this estimator is then proposed for the Pareto and the Weibull cases. The second is a conditional MC estimator that achieves the bounded relative error property for the generalized Gamma case and the logarithmic efficiency for the Log-normal case. Finally, the efficiency of these estimators is compared via various numerical simulations.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Keywords: | Order statistics, outage probability, generalized selection combining, Monte Carlo, variance reduction techniques, importance sampling, conditional MC |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 25 Oct 2023 15:05 |
Last Modified: | 25 Oct 2023 15:05 |
Published Version: | https://ieeexplore.ieee.org/document/8472928 |
Status: | Published |
Publisher: | IEEE |
Identification Number: | 10.1109/twc.2018.2871201 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:195466 |