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International Journal of Science and Advanced Technology (ISSN 2221-8386) Volume 1 No 5 July 2011http://www.ijsat.com

116

Performance Evaluation of Different Type of Channel

Models in FSO Communication

Bobby Barua

Assistant Professor, Department of EEE,Ahsanullah University of Science and Technology

Dhaka, Bangladesh

[email protected]

Mirza Moazzem Hossain

B.Sc. Engineering Student, Department of EEE,

Ahsanullah University of Science and Technology

Dhaka, Bangladesh

[email protected]

Md. Rezwan IslamB.Sc. Engineering Student, Department of EEE,

Ahsanullah University of Science and Technology,

Dhaka, Bangladesh

[email protected]

Md. Khairul BasharB.Sc. Engineering Student, Department of EEE,

Ahsanullah University of Science and Technology,

Dhaka, Bangladesh

[email protected]

Abstract - Atmospheric turbulence-induced fading is one of themain impairments affecting free-space optics (FSO)

communications. To design a high performance communicationlink for the atmospheric FSO channel, it is of great importance to

characterize the channel with proper model. An accurate PDF of

irradiance for a FSO channel is important when designing a laser

radar, active laser imaging, or a communications system to

operate over the channel. Parameters such as detector threshold

level, probability of detection, mean fade time, number of fades,

BER, and SNR are derived from the PDF and determine the

design constraints of the receiver, transmitter, and corresponding

electronics. There are many types of PDF models. This paper

investigates the most efficient PDF model which we should use.

Index Terms - Free space optics (FSO), probability of density

function (PDF), Irradiance (I), Scintillation index (S.I.).

.

I. INTRODUCTION

Free space optical (FSO) communications is a promising

technology capable of offering full-duplex gigabit rate

throughput (data, voice, and video simultaneously) in certain

applications and environment [1][3]. FSO offers a huge

license-free frequency spectrum using a single wavelength,

immunity to electromagnetic interference including

co/adjacent channel interference (due to a well defined narrow

beam size and no power spill), and high security [1], [4].FSO

is less affected by snow and rain, but can be severely affected by the atmospheric turbulence and fog. The earths

atmosphere has three main hurdles to overcome when using it

as a communication channel; absorption, scattering, and

turbulence. Absorption of optical waves results in

attenuation, it occurs throughout the visible and IR spectrum.

Absorption is a selective process and results from specific

molecules in the atmosphere having an absorption band at an

optical wavelength. Scattering occurs when a particle in the

atmosphere is on the same order of magnitude of the optical

wavelength [6, 7]. The interaction of the particle and light

wave causes an angular redistribution of a portion of the

radiated wave. Optical turbulence is a result of fluctuations inthe index of refraction along a propagation path. These

fluctuations distort the phase front and vary the temporal

intensity of an optical wave. The combination of these

atmospheric effects on an optical system can cause

phenomena such as beam spreading, image dancing, beam

wander, and scintillation [7].

The dominant noise source in an FSO communication system

is atmosphere-induced intensity and phase fluctuations;

scintillation. A larger aperture (collecting lens) can help

reduce scintillation effects and improve SNR. Design criteria

such as detector threshold level, probability of detection, mean

fade time, number of fades, and SNR require knowledge of theprobability density function (PDF) of the received irradiance

of the optical field. The PDF of the received irradiance is

nonstationary by nature and is dependent upon the

atmospheric turbulence parameters, transmitted beam

characteristics, and receiver design parameters; such as

aperture size and bandwidth. Nonetheless, an accurate PDF of

the received irradiance is necessary to build a robust and

reliable FSO communication.

II. SYSTEM MODEL

The major subsystems in an FSO communication system are

illustrated in Fig. 1. A source producing data input is to be

transmitted to a remote destination. This source has its output

modulated onto an optical carrier; typically laser, which is

then transmitted as an optical field through the atmospheric

channel. The important aspects of the optical transmitter

system are size, power, and beam quality, which determine

laser intensity and minimum divergence obtainable from the

system. At the receiver, the field is optically collected and
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detected, generally in the presence of noise WSK signal which

are then directly fed to a pair of photo detectors.

Modulator Driver Laser DiodeTransmit Optics

Receive OpticsPhoto DetectorAmplifierDemodulator

Source

Destination

Transmitter

Receiver

Atmospheric Channel

Fig1: Block diagram of FSO communication system.

.interference, signal distortion, and background radiation. Theatmospheric free-space channel is a natural medium for

outdoor optical wireless communication and has generated

significant research attention in the past 10 years as a

complement to radio-frequency (RF) links. The free spaceoptical (FSO) atmospheric channel has a wide bandwidth and

may support many more users than an RF channel. To design

a high-performance communication link for the atmospheric

free-space optical (FSO) channel, it is of great importance to

characterize the channel through proper model. Several

models exist for the aggregate amplitude distribution, though

none is universally accepted, since the atmospheric conditions

obviously matter. Most prominent among the models are

analyzed in this paper.

III. THEORETICAL ANALYSIS

a. Rayleigh Distribution

The Rayleigh model is used to describe the channel gain. The

scintillation index for the Rayleigh situation is 1.The density

function of Rayleigh is more concentrated at low(deeply

faded) values.

The PDF for Rayleigh distribution is

2 2( ) exp , 0

2

I I f I I

(1)

Where,

I=Irradiance

2= Variance

b. Lognormal Distribution

The atmospheric turbulence impairs the performance of anFSO link by causing the received optical signal to vary

randomly thus giving rise to signal fading. The fading strength

depends on the link length, the wavelength of the optical

radiation and the refractive index structure parameter Cn2 of

the channel. The log-normal distribution is generally used to

model the fading associated with the weak atmospheric

turbulence regime [2, 8, 11]. This model is mathematically

tractable and it is characterized by the Rytov variance l2

The turbulence induced fading is termed weak when l2

< 1.2

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and this defines the limit of validity of the log-normal model

[8].

The Rytov variance can be calculated as

l2=1.23C

2n K

7/6L

11/6(2)

where,

L is the propagation distance

k is the wave number.

The log-normal models assumes the log intensity l of the laser

light traversing the turbulent atmosphere to be normally

distributed with a mean value of -l2/2.Thus the probability

density function of the received irradiance is given by [11,

12]:

2 2

0

1 22 2

(ln ( ) 2)1( ) exp , 0

2(2 )

i

i

i

I I f I I

I

(3)

Where

I represents the irradiance at the receiver

Io is the signal irradiance without scintillation.

c. Rician Distribution

The Rician distribution is observed when, in addition to the

multipath components, there exists a direct path between the

transmitter and the receiver. The Rician density function given

by [5] :

2 2

02 2 2

1( ) exp , 0

2

d d I k Ik f I I I

(4)

Where,

I represents the irradiance at the receiver

2=VARIANCE=1.23C

2n K7/6L11/6

K(dB)=10log10(Kd2/2

2)=Rician factor

d. Nakagami-m Distribution

It is possible to describe both Rayleigh and Rician fading with

the help of a single model using the Nakagami distribution [9].

The fading model for the received signal envelope, proposed

by Nakagami, has the pdf given by

2 1 2

2( ) exp , 0( ) 2

m m

mm I mI f I I

m

(5)

where,

(m) is the Gamma function

controls the spread of the distribution; =E{I2}

m is the shape factor ( m 0.5)

2 2

22 2

( )

E Im

E I E I

(6)

e. GammaGamma Distribution

The gamma-gamma turbulence model is based on the

modulation process where the fluctuationof light radiation

traversing turbulent atmosphere is assume to consist of small

scale (scattering) and large scale (refraction) effects. The

former is contributed by the eddies cells smaller than the

Fresnel zone or the coherence radius while the latter effect is

due to the turbulence eddies greater than the first Fresnel zone

or the scattering disk .The small scale eddies are assumed to

be modulated by the large scale eddies. Consequently, thereceived irradiance I is defined as the product of two

statistically independent random processesIx andIy, that is

I=IxIy (7)

Ix and Iy arise from the large scale and small scale turbulent

eddies respectively.

The gamma-gamma model for the probability density function

(pdf) of received irradiance fluctuation which is based on the

assumption that both the large and small scale effects are

governed by the gamma distribution is therefore derived as

( )( )/21

2( )

2( )( ) (2 ), 0

( ) ( ) f I I K I I

(8)

I is the signal intensity, (.) is the gamma function, and

K is the modified Bessel function of the second kind and

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. and are PDF parameters describing thescintillation experienced by plane waves, and in the case of

zero-inner scale.

If the optical radiation is assumed to be a plane wave, the twoparameters and that characterize the irradiance

fluctuation(scintillation) pdf are related to the atmospheric

conditions by

2

12 /5 7 / 6

1

0.49exp 1

(1 1.11 )R

R

(9)

2

12 / 5 5 / 6

1

0.51exp 1

(1 0.69 )R

R

(10)

where R2 is the Rytov variance given by

R

2=1.23C

2

n k7/6

L11/6

k = 2/is the optical wave number, L is propagationdistance, and Cn

2is the refractive index structure parameter,

which we assume to be constant for horizontal paths.

The pdf of irradiance fluctuation is valid for all turbulence

scenarios from weak to strong and the values of and at

any given regime can be obtained from the above equation.Inthis work, the values of the log intensity variance l

2

corresponding to the weak, moderate and strong atmospheric

turbulence regimes are given in Table I [11]

TABLE:1

f. The Negative Exponential Distribution

In the limit of strong irradiance fluctuations (i.e. in saturation

regime and beyond) where the link length spans several

kilometers, the number of independent scatterings becomes

large . This saturation regime is also called the fully developed

speckle regime. The amplitude fluctuation of the field

traversing the turbulent medium in this situation is generally

believed and experimentally verified to obey the Rayleigh

distribution implying negative exponential statistics for theirradiance. That is:

0 0

1( ) exp , 0

I f I I

I I

(11)

Where E[I] = Io is the mean received irradiance. During the

saturation regime, the value of the scintillation index,S.I1.

L

IV.RESULTS AND DISCUSSION

Following the analytical approach presented in section III, we

evaluate the probability density function for different type ofchannel model. The simulations are performed using Matlab.

The influence of scintillation is modeled assuming different

channel distribution function and an ideal photon counting

receiver is employed.

0 0.5 1 1.5 2 2.5 3 3.5 40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

IRRADIANCE

PROB

ABILTY

DENSITY

FUNCTION

RAYLEIGH MODEL

Fig 2: Plot ofprobability density function vs. irradiance for

Rayleigh Model.

TURBULENCE REGIME

PARAMETER WEAK MODERATE STRONG

R2 0.2 1.6 3.5

11.6 4.0 4.2

10.1 1.9 1.4

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The plot of the probability density functions in Fig. 2 for

Rayleigh case with typical value of scintillation index (S.I)and turbulence strength.

0 2 4 6 8 10 120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

IRRADIANCE

PROBABILTY

DENSITY

FUNCTION

LOGNORMAL MODEL


Lognormal Model.

The plot of Fig. 3 shows the probability density functions for

lognormal case with typical value of scintillation index (S.I)

and turbulence strength. Fig. 4 shows the plot of theprobability density function for Rician model. From the figureit is found that, the probability density function is maximum

with the irradiance value of 1.1.

0 0.5 1 1.5 2 2.5 3 3.5 40

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

IRRADIANCE

PROBABILTY

DENSITY

FU

NCTION

RICIAN MODEL


Rician Model.

0 0.5 1 1.5 2 2.5 3 3.5 40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

IRRADIANCE

PROBABILTY

DENS

ITY

FUNCTION

NAKAGAMI MODEL


Nakagamim Model.

The plot of Fig. 5 and Fig. 6 shows the probability densityfunctions with respect to the irradiance for nakagami-m model

and gamma-gamma model respectively. . From the figure it is

clear that, the probability density function is maximum with

the irradiance value of 0.7 for nakagami-m model and 0.53 for

gamma-gamma model..

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0 0.5 1 1.5 2 2.5 3 3.5 4

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

IRRADIANCE

PROBABILTY

DENSITY

FUNCTION

GAMMA GAMMA MODEL


Gamma-gamma Model.

0 0.5 1 1.5 2 2.5 3 3.5 40

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

IRRADIANCE

PROBABILTY

DENSITY

FUNCTION

NEGATIVE EXPONENTIAL MODEL


Negative Exponential Model.

Fig. 4 shows the plot of the probability density function fornegative exponential model. From the figure it is clear that the

optimum value of probability density function is found at

negative region. The plots ofprobability density function for

different type of channel models are shown on the Fig. 8.

From the overall analysis of the plots it is clear that the

probability density function is found at negative exponential

model. But the maximum value is occurred at negative region.

0 0.5 1 1.5 2 2.5 3 3.5 40

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

IRRADIANCE

PROBABILITY

DENSITY

FUNCT

ION

COMPARISON OF DIFFERENT CHANNEL MODELS

RAYLEIGH

CHI-SQUARE

LOGNORMAL

NAKAGAMI

RICIAN

NEGATIVE EXPONENTIAL

GAMMA GAMMA

Fig 8: Plots ofprobability density function vs. irradiance for

different channel model.

V. CONCLUSION

We have analysed different type of channel models used in

FSO communication for the turbulence under consideration of

S.I1. It should be noted that the channel models such as the

Rayleigh, Log-normal, Rician and Nakagami-m distribution

are valid from weak to strong turbulence regime but the

Gammagamma model performs better for all regimes from

weak to strong turbulence region. The negative exponentialmodel is also valid for the same limit of Gamma-gamma

model but the optimum value is occurred at negative region.So finally our decision is to prefer gamma-gamma modelunder weak to strong turbulence regime as channel model for

FSO communication.

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