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

Szyszkowicz, Sebastian S.; Yanıkömeroğlu, Halim

doi:10.1109/glocom.2009.5426029

Cited by 5 publications

(13 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…3) The Distribution of I mW in (5): Third, we invoke the main results in [17][18], which indicate that the sum of multiple independent lognormal RVs can be well approximated by a power lognormal RV. Accordingly, in our case, since each I b , b ∈ {2, .…”

Section: A the Interference Analysismentioning

confidence: 78%

DNA-GA: A new approach of network performance analysis

Ding

Pérez

Mao

et al. 2016

2016 IEEE International Conference on Communications (ICC)

View full text Add to dashboard Cite

In this paper, we propose a new approach of network performance analysis, which is based on our previous works on the deterministic network analysis using the Gaussian approximation (DNA-GA). First, we extend our previous works to a signal-to-interference ratio (SIR) analysis, which makes our DNA-GA analysis a formal microscopic analysis tool. Second, we show two approaches for upgrading the DNA-GA analysis to a macroscopic analysis tool. Finally, we perform a comparison between the proposed DNA-GA analysis and the existing macroscopic analysis based on stochastic geometry. Our results show that the DNA-GA analysis possesses a few special features: (i) shadow fading is naturally considered in the DNA-GA analysis; (ii) the DNA-GA analysis can handle non-uniform user distributions and any type of multi-path fading; (iii) the shape and/or the size of cell coverage areas in the DNA-GA analysis can be made arbitrary for the treatment of hotspot network scenarios. Thus, DNA-GA analysis is very useful for the network performance analysis of the 5th generation (5G) systems with general cell deployment and user distribution, both on a microscopic level and on a macroscopic level. 1

show abstract

Section: A the Interference Analysismentioning

confidence: 78%

DNA-GA: A new approach of network performance analysis

Ding

Pérez

Mao

et al. 2016

2016 IEEE International Conference on Communications (ICC)

View full text Add to dashboard Cite

show abstract

“…. , B} is approximated by the Gaussian RV Q b , the sum of 10 1 10 Q b can be well approximated by a power lognormal RV [19]- [21] expressed aŝ I mW = 10 1 10 Q , where the PDF and CDF of Q can be respectively written as [19] …”

Section: Remarkmentioning

confidence: 99%

“…where the parameters λ, µ Q and σ Q are obtained from {µ Q b } and σ 2 Q b . The method to accomplish such task has been well addressed in [19]- [21]. In Appendix B, we provide an example to obtain λ, µ Q and σ Q based on [17], [20] and [21].…”

Section: Remarkmentioning

confidence: 99%

“…, 84} using (20). If the maximum value of ε is reasonably small, e.g., less than 0.01, then we can approximate I mW in (5) as a power lognormal RVÎ mW = 10 1 10 Q , where the PDF and the CDF of Q are given by (21) with the parameters λ, µ Q and σ 2 Q obtained from, e.g., Appendix B. The maximum values of the 83 R b -specific ε's for various r values are presented in Table V. From Table V, we can observe that, for all the investigated values of r, the maximum values of ε are below 0.01.…”

Section: B the Scenario With Multiple Interfering Cellsmentioning

confidence: 99%

See 1 more Smart Citation

Microscopic Analysis of the Uplink Interference in FDMA Small Cell Networks

Ding¹,

Liu²,

Mao³

et al. 2016

IEEE Trans. Wireless Commun.

View full text Add to dashboard Cite

In this paper, we analytically derive an upper bound on the error in approximating the uplink (UL) single-cell interference by a lognormal distribution in frequency division multiple access (FDMA) small cell networks (SCNs). Such an upper bound is measured by the Kolmogorov-Smirnov (KS) distance between the actual cumulative density function (CDF) and the approximate CDF. The lognormal approximation is important because it allows tractable network performance analysis. Our results are more general than the existing works in the sense that we do not pose any requirement on (i) the shape and/or size of cell coverage areas, (ii) the uniformity of user equipment (UE) distribution, and (iii) the type of multi-path fading. Based on our results, we propose a new framework to directly and analytically investigate a complex network with practical deployment of multiple BSs placed at irregular locations, using a power lognormal approximation of the aggregate UL interference. The proposed network performance analysis is particularly useful for the 5th generation (5G) systems with general cell deployment and UE distribution.

show abstract

“…The statistical analysis can also be found in Nelson and Doganaksoy (1995). Szyszkowicz and Yanikomeroglu (2009) and Liu et al (2008) proposed the use of power lognormal distributions to approximate lognormal sum distributions.…”

Section: Introductionmentioning

confidence: 99%