A Statistical Model for the 2g, Gsm Communication System in Uttarakhand Using Multiple Regression...

7/27/2019 A Statistical Model for the 2g, Gsm Communication System in Uttarakhand Using Multiple Regression Technique Ijest11!03!07-139

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A STATISTICAL MODEL FOR THE 2G,

GSM COMMUNICATION SYSTEM IN

UTTARAKHAND USING MULTIPLEREGRESSION TECHNIQUE

Meenal SharmaAssistant Professor

GRD-IMT, [email protected]

Rakesh MohanProfessor, deptt of mathematics

DIT, Dehradun

[email protected]

Abstract

This paper introduces a statistical model by using the statistical methods in 2G,GSM communication system.

Multiple regression formula is to calculate path loss. It is assumed that hb,W and are three statistical variables.

We use nakagami distribution to model hb,W and uniform distribution to model .

Key Words- 2G, GSM, Multiple regression, nakagami distribution, uniform distribution.

1.Introduction

Regression analysis is a popular multivariate analysis methodology in many sciences. It has been used typically

in a multivariate environment[3]. The strength of regression analysis is the ability to capture multiple

relationships simultaneously. We use multiple regression techniques in wireless communication technology

from the first (1G) to fourth (4G) generations. It is not apply the multiple regression formula in every urban and

suburban area, because the average rooftop level hb, the road width W and the road angle .may be different.

The statistical approach can solve above problems. In many studies the formula be used indifferent areas, but

only one parameter is variable in each simulation. In this study three parameters rooftop level, road width, and

the road angle are estimated at the same time. It will more applicable in the real circumstances. Numerous

probability distribution techniques like Rayleigh ,Rician, Gaussian, uniform etc are there to calculate the path

loss in different conditions. The rician distribution occurs frequently in the applied sciences. It had been studied

often in the content of wireless communication. This paper use Nakagami distribution. The Nakagami

distribution function is selected because it can be reduced to Gaussian distribution, Rayleigh distribution and

rice distribution. The physical characteristics of the building and the street width have these distribution.

However, it is not appropriate to apply the multiple regression formula in every urban and suburban area ,

Meenal Sharma et al. / International Journal of Engineering Science and Technology (IJEST)

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Table-1

Distance(m) Path loss Path loss

=45 =90

500 200.45 195.72

1000 213.09 208.37

1500 220.49 215.76

2000 225.73 221.01

2500 229.80 225.08

3000 233.135 228.41

3500 235.94 231.22

4000 238.38 231.22

4500 240.53 235.80

5000 242.53 237.72

Fig.1 the variation of path loss as a function of d

b. the estimation of some parameters in regression formula

the regression formula can predict the path loss for suburban areas on 2G frequency. In this study, the variation

boundaries of three parameters are hB W and evaluated at the same time. We assume that the parameters of hB

W and are evaluated at the same time.We assume that the parameters of hB W and in (2) are static. This

paper use nakagami distribution to model hB ,W and uniform distribution to model The nakagami distribution

function has the probability density function[5]

Fx (x) = e


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With shape parameter and scale parameter 1, for x 1. If x has a nakagami distribution with parameters

and, then x2 has a gamma distribution with shape parameter m and scale parameter .

If = 1 , the nakagami distribution is reduced to Rayleigh distribution[6] whose probability density function is

Fx (x) =

e

If =1k

2k1 , the nakagami distribution reduced to Rice distribution whose PDF is [7]

Fx (x) =

e

Io

Where Io(z) is the modified Bessel function of the first kind with order zero.

If , the Nakagami distribution is reduced to Gaussian distribution whose PDF is [8]

Fx (x) =

e

3.The simulation result

The path loss of the regression formula is simulated at the frequency of 900 MHz. In the simulation the

average rooftop level hB, the road width W and the road angle are modeled as random variable because these

parameters are not constancy at different areas.

There are two sets of parameter which are used in simulation. In fig.4 and fig.5

We calculate PDF and CDF for the path loss. We use the following distribution for hB W and.

- Nakagami distribution function for hB with shape parameter and scale parameter=1.

- Nakagami distribution function for W with =1, =1.

- uniform distribution function for with the range from 0 to 2.

Fig 4 Probability distribution function for path loss


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Fig 5 cumulative distribution function for path loss

In fig.6 and fig.7 to calculate PDF and CDF for path loss we use

- Nakagami distribution function for hB with shape parameter =100 and scale parameter=3.

- Nakagami distribution function for W with , =1.

- uniform distribution function for with the range from 0 to 2.

The parameters hB W and can choose other values according to the different circumstances.

Fig6 Probability density function for path loss

Fig7 Cumulative distribution function for path loss


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Apart from this we also calculate the other quantities which are required for error correction in digital

communication system. These quantities are the level crossing rate and the average duration of fades.

For level crossing rate and average duration of fades it is assumed that the vehicle circles the base station at the

rate of 36 km per hour. All three parameters , W and are variables at the same time, where- ,conforms to Nakagami distribution function with and W= 1.- W confirms to Nakagami distribution function with = 1, = 1.

- is modeled with the uniform distribution function with range from 0 to 2.

Fig 8 and fig 9 show the level crossing rate and the average duration of fade of the regression formula.

Fig 8 level crossing rate

Fig 9 average duration of fade

IV. Conclusion-

This paper proposes a statistical model for 2G,GSM communication system based on the multiple regression

formula, which can be used to predict the path loss in suburban areas. The probability density function,

cumulative distribution function, level crossing rate and the average duration of fade are studied combining the


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statical analysis with the multiple regression formula. The model introduced in this paper is a useful tool for the

design and analysis of data transmission scheme of the 2G mobile communication system.

REFERENCES

[1] KoshiroKITAO,ShinichiI Chitsubo.Path Loss Prediction Formulain Urban Area for the Fourth-Generation MobileCommunicationSystemsIEICETrans.Commun., Vol.e91-b, No.6, pp.0916-8516 2008.

[2] S.Sakagami,K,Kuboi,MobilePropagation Loss Prediction forArbitrary Urban Environment,IEICETrans.Commun.,Vol.J74-B-No.1,pp.17-25,Jan.1991.

[3] Jeonghoon Ahn, Beyond Single Equation Regression Analysis: Path Analysis andMulti-Stage Regression Analysis AmericanJournal of Pharmaceutical Education Vol. 66, Spring 2002

[4] S.R.Saunders B.G.Evans. A physical-statistical model for land mobilesatellite propagation in built-upareas[J]. Proc.ICAP97 EdinburghUK, 1997,:2.44-2.47.

[5] SaadAlAhmadi,Halim,Yanikomeroglu,On the approximation of the generalized-k distribution by na gamma distribution for modelingcomposite fading channel, IEEE Translation on wireless communications vol 9,issue 2, pages 706-713 ISSN: 1536-1276, 2010.

[6] Karmeshu and Rajeev Aggarwal, Efficiency of Rayleigh-inverse Gaussian distribution over k- distribution for wireless fadingchannel, volume 7 issue 1,page 1-7, 2006.

[7] Mohammad siraj and soumen kanrar, Performance of modeling wireless network in realistic environment, IJCN, Volume 2, Issue 1,2010

[8] Gaussian function, From Wikipedia, the free encyclopedia


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A Statistical Model for the 2g, Gsm Communication System in Uttarakhand Using Multiple Regression...

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