A Simple Bound on the Outage Probability With Lognormally Distributed Interferers

Berggren, Fredrik; Slimane, S.B.

doi:10.1109/lcomm.2004.827448

Cited by 51 publications

(37 citation statements)

References 5 publications

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“…The corresponding slope is 1 s on lognormal paper, which proves (10). In order to prove the lower tail slope, we first need a couple of approximations.…”

Section: Discussionmentioning

confidence: 79%

“…The MPLN method introduced here seems to perform no worse, and often better, than the existing closed-form methods [9], [10], [16], while being of comparable complexity. Its performance is particularly good for cases where the σ APPENDIX A…”

Section: Discussionmentioning

confidence: 80%

“…We do not show the method in [10], which performs very poorly for values of σ i of more than 4 dB, and is designed to analyse intra-cell interference in CDMA systems. We make the following observations: 1) In the case of identically distributed terms (Figure 1), the MPLN method is nearly identical to the bound method (which is equivalent to Farley's method in this case).…”

Section: Simulations and Comparisonsmentioning

confidence: 96%

“…We can also categorise the methods based on their complexity: most methods require extensive numerical integration, and many are iterative. Only [9], [10], [16] are closed-form, and [18] is mostly closed-form, similarly to our method.…”

Section: Introductionmentioning

confidence: 99%

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Fitting the Modified-Power-Lognormal to the Sum of Independent Lognormals Distribution

Szyszkowicz

Yanıkömeroğlu

2009

GLOBECOM 2009 - 2009 IEEE Global Telecommunications Conference

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Abstract-We propose a new method for calculating a tight approximation to the distribution of the sum of independent lognormal random variables. We make use of a three-parameter modified-power-lognormal distribution function as the approximating distribution. We use theoretical results from our previous work on the tails of the distribution of the sum of lognormals to match the slope of the modified-power-lognormal function at both tails. This would not have been possible with many of the recently-proposed distribution functions, which do not behave properly in the tails. We then also use moment-matching to find the best curve match. Our method is mostly closed-form, requiring only one simple numerical integral.We compare our method with those in literature in terms of complexity and accuracy. We conclude that our method is more accurate than the simple (closed-form) methods, and much simpler to understand and implement than the more accurate methods which rely heavily on numerical integration.Index Terms-sum of lognormals, interference analysis

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“…The corresponding slope is 1 s on lognormal paper, which proves (10). In order to prove the lower tail slope, we first need a couple of approximations.…”

Section: Discussionmentioning

confidence: 79%

Section: Discussionmentioning

confidence: 80%

Section: Simulations and Comparisonsmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Fitting the Modified-Power-Lognormal to the Sum of Independent Lognormals Distribution

Szyszkowicz

Yanıkömeroğlu

2009

GLOBECOM 2009 - 2009 IEEE Global Telecommunications Conference

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show abstract

“…In addition, analytic approximation formulas retain qualitative model information and preserve an explicit dependence of the results on the underlying parameters. Many approximate methods can be categorized by their scope into three classes: generally correlated [7][8][9][10], independent [11][12][13][14], and independent and identically distributed [15,16]. The probability density function of the correlated log-normal especially is carried out to propose various approximations of the sum distribution.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Volatility Effects on Correlated Log-Normal Random Variables

2017

Advances in Mathematical Physics

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The transition density function plays an important role in understanding and explaining the dynamics of the stochastic process. In this paper, we incorporate an ergodic process displaying fast moving fluctuation into constant volatility models to express volatility clustering over time. We obtain an analytic approximation of the transition density function under our stochastic process model. Using perturbation theory based on Lie-Trotter operator splitting method, we compute the leading-order term and the first-order correction term and then present the left and right skew scenarios through numerical study.

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Channel Characterization

2015

Wireless Communications

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A Simple Bound on the Outage Probability With Lognormally Distributed Interferers

Cited by 51 publications

References 5 publications

Fitting the Modified-Power-Lognormal to the Sum of Independent Lognormals Distribution

Fitting the Modified-Power-Lognormal to the Sum of Independent Lognormals Distribution

Stochastic Volatility Effects on Correlated Log-Normal Random Variables

Channel Characterization

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