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An comparitive study of exponential and i-k distribution channel model

An Comparitive study of Exponential and I-K Distribution Channel Model

Heleena J1, Shamona G Bert2

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1PG Scholar”,Ponjesly College of Engineering”,Nagercoil

2PG Scholar”,Ponjesly College of Engineering”,Nagercoil.

Abstract—Free Space Optical(FSO) Communication provides better speed, dense spatial reuse, high bandwidth, secure and license free communication.FSO finds its applications in last mile access, military access”,fibre backup and so on.In this paper the optical signal transmitted is assumed to be affected by turbulence and pointing errors. Exponential Distribution is used to model the strong turbulence effect. I-K distribution is used to model weak to strong blustery channels The performance of the channel models is studied in terms of the Bit Error Rate (BER) and the comparison is presented.

Keywords— I-k Channel”,Pointing Errors”,Atmospheric Turbulence”,Negative Exponential”,Intensity Modulation


An effective transmission system should have high bandwidth”,low BER”,power efficient”,data security”,low cost and easy installation.FSO ia information transmission syatem which has all the above mentioned effects.FSO uses optical sources like LASER’s or LED’s for data transmission and photodetector for reception.FSO is capable of transmitting 2.5Gbps.FSO overcomes the disadvantages of fibre optics.Fibre optics requires permission for digging whereas FSO is an license free technology and there is no need of digging.

Eventhough FSO has most of the advantages there are some factors which affect the performance of the systemThe factors includefog”,absorption”,scattering.physical obstructions”,scintillation”,building sway and atmospheric blustery”,

In this paper, the Intensity Modulation/Direct Detection(IM/DD) FSO link with On-Off Keying(OOK) is assumed to be affected by the joint effects of atmospheric turbulence modeled by channel models and pointing errors.The performance is studied in terms of BER.Negative Exponential Channel Model and I-K Distribution Channel Model is used and the comparison between the channel models is presented.

System and Channel Model

In the FSO system using IM/DD with OOK “,the laser beams propagate through the turbulence channel.The received signal is expressed as

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where x is the transmitted signal ie)OOK modulated signal having values 0 and 1.I is the normalized irradiance and it is considered as the product of two random factors ie)

Where It is the turbulence effect and Ip is the pointing error effect.



) (






) (








Turbulence channel




) (




Receiver optical

) (


) (



Figure)FSO Block Diagram

Exponential Channel Model:

The proability density function of the exponential channel model is given by


The Negative Exponential Channel model is used in strong atmospheric blustery conditions. The pointing error effect is also considered along with the turbulence effect.The proability density function (PDF) of the pointing error is given by


is the ratio between beam waist at the receiver to the standard deviation at the receiver ie).

The combined channel state is given by

Where (3)


The integral is solved in terms of Meijer function.Meijer function is the standard built in function in software packages”,

I-K Distribution Channel:

The PDF of the I-K Distribution channel is given by

( 5)

The pdf of pointing errors is given in equation (2).The combined channel state equation is given by


On substituting (4) and (5) in (6) and solving the integral in

terms of Meijer function the combined channel state is derived.

BER of the FSO Link

BER and Signal to Noise Ratio(SNR) are used to access the quality of the transmission syatem.The BER is the ratio of number of error bits to the total transmitted bits.The BER is expressed as




The BER for the OOK modulation is given by

; is the instantaneous SNR.It can also be written as”,


On substituting (8) and (9) in (7)


On using approximation”,



From equation (12) and (13) the average BER for Negative Exponential Channel is given by”,


From the equations (12) and (6) the average BER for the I-K channel Model is given by”,

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The FSO Link uses a receiver with diameter of 0.10 m.The value for the ratio of beam waist and standard deviation is given as 9.The value for wz is taken as 0.12.These assumptions are considered in both Negative Exponential and I-K Distribution Channels”,Figure1 shows the plot between SNR and BER for the Negative Exponential Channel Model.Figure 2 shows the plot between the SNR and BER of the I-K Channel model.

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Figure 1)SNR vs BER plot for Exponential channel

[image: ]

Figure 2)BER vs SNR Plot of I-K Channel

In the Negative Exponential channel model, Bit Error Rate is higher when compared to the I-K distribution channel model.Moreover, Exponential channel model can be used only in the strong turbulence cases wheras I-k channel can be used in both strong and weak blustery conditions. Thus I-k channel model is more efficient when compare to the Exponential channel model.


The BER Performance of the FSO Link with the joint effects of turbulence and ponting errors is studied in case of both Negative Exponential channel and I-K Distribution channe


The BER Performance of the FSO link with the joint effects of turbulence and pointing errors is studied in case of exponential and I-K distribution channel model, Both the results shows that the blustery and pointing errors has an severe performance degradation. But when comparison is made the BER in I-K Distribution model is reduced than the Negative Exponential channel model.Eventhough the BER is not completely reduced. So considerations must be taken on turbulence and pointing errors effect.


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