1. International Journal of ElectronicsJOURNAL OF ELECTRONICS AND
INTERNATIONAL and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 1, January (2014), © IAEME
COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET)
ISSN 0976 – 6464(Print)
ISSN 0976 – 6472(Online)
Volume 5, Issue 1, January (2014), pp. 105-112
© IAEME: www.iaeme.com/ijecet.asp
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IJECET
©IAEME
STUDY OF DIFFERENT ATMOSPHERIC CHANNEL MODELS
Dhaval Shah1,
1, 2, 3
Bhavin Nayak2,
Dharmendra Jethawani3
(Electronics & Communication Department, Nirma University, Ahmedabad, India)
ABSTRACT
In this paper various channel models of free space optics have been studied. Lognormal,
Negative Exponential and Gamma-Gamma are the mainly discussed in this paper. It is observed that
for low turbulence the Lognormal model is widely accepted while for high turbulence Negative
exponential model is used. The Gamma-Gamma model is used for low to high turbulence. The pdf
(probability distribution function) and BER vs SNR plot of these three channel models are described
in this paper.
Keywords: Bit error rate, Free-space optics, OOK (On-Off Keying), pdf (probability distribution
function), Scintillation Index (SI), SNR (Signal to Noise Ratio) and turbulence.
I. INTRODUCTION
In recent years, free space optical communication has gained significant importance in
terrestrial applications, deep space/inter-satellite and satellite- to-ground communication. Optical
communication links can be deployed for satellite-to-satellite cross links, up-and-down links between
space platforms, aircraft, ships and other ground platforms and among mobile and stationary
terminals. FSO communication is an attractive solution for “last mile” problem so as to bridge the
gap between end user and fiber optic infrastructure already deployed. Other applications of FSO are
to create a MAN (Metropolitan Area Network), enterprise/local area network connectivity, optical
fiber backup, backhaul for wireless cellular network and redundant links to search and rescue
operations. FSO communication technology makes use of unregulated spectrum (i.e., license free),
has extremely high bandwidth, and supports higher data rates (making it cost effective) [1]. Other
attractive features like inherent security, easy and quick deploy ability further increase the demand
for these systems.
Atmospheric conditions prominently affect the performance of FSO system making them
highly susceptible to degrading effects of atmospheric turbulence and pointing errors [2] [4-5].
Aerosol scattering effects caused by rain, snow and fog can reduce the link performance of FSO.
Sway of high rise buildings which in turn is caused due to thermal expansion, dynamic wind loads
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2. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 1, January (2014), © IAEME
and big earthquakes are the major factor causing pointing errors. Another most important impairment
in the FSO system performance is the atmospheric turbulence. In homogeneity in the temperature
and pressure fluctuations leads to variations in the refractive index, results in atmospheric turbulence.
Atmospheric turbulence causes the random fluctuations of the phase and intensity of the received
signal known as channel fading. Intensity fluctuations caused by channel fading leads to an increase
in the system’s bit error rate (BER)[7]. Over the years, a number of statistical channel models have
been proposed to describe weak or strong atmospheric-induced turbulence fading [1]. In this respect,
the log normal model, has been proved accurate enough for weak turbulence, the gamma-gamma and
the I–K distribution models for weak to strong turbulence, while the K and the negative exponential
(NE) ones, are suitable for strong turbulence [8-9].
For an FSO communication link with IM/DD (Intensity modulated/ Direct detection), the
laser beam propagates along a horizontal path through a channel with additive white Gaussian noise
(AWGN). The channel is assumed to be memory less, stationary and ergodic. Different atmospheric
channels have been discussed in section II. The BER vs SNR performance curve is explained in
section III. Then some conclusions are driven in the section IV.
II. VARIOUS STATISTICAL ATMOSPHERIC TURBULENCE MODEL
The statistical channel model is given by:
y = sx + n = ηIx + n
(1)
where y is the signal at the receiver, s = ηI is the instantaneous intensity gain, η is the effective
photo-current conversion ratio of the receiver, I is the normalized irradiance, x is the modulated
signal (and takes values “0” or “1”), and n is the AWGN with zero mean and variance N0/2[10].
A. Lognormal Model
Lognormal distribution is widely used model for the probability density function (pdf) of the
irradiance due to its simplicity in terms of mathematical calculation. This turbulence model is only
applicable to weak turbulence conditions and for propagation distances less than 100 m. Considering
lognormal model, the pdf of the received optical field I is given as f (I ) [3].
f (I) = √ଶగఙమ exp ൤െ
ଵ
ூ
ሺ௟௡ሺூሻି௠೔ሻమ
మ
ଶఙ೔
൨, I ≥ 0
(2)
where mi is the mean and σi the standard deviation of ln(I).
ଶ
The scintillation index as a function of variance is given by [3] ߪௌூ =݁ ఙ೔ െ 1. Hence
ଶ
ଶ
ଶ
ߪ௜ = ln(ߪௌூ +1) and for a given scintillation index, one may compute ߪ௜ . For weak turbulence, SI
falls in the range of [0, 0.75]. As the strength of turbulence increases, multiple scattering effects
should be taken into consideration. In such cases, lognormal statistics exhibit large deviations
compared to experimental data. The detection and fade probabilities which are mainly based on tails
of the pdf are not accurately analyzed as lognormal pdf underestimates the behavior as compared
with experimental results. This in turn affects the accuracy of performance analysis.
మ
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3. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 1, January (2014), © IAEME
Fig.1: Lognormal distribution pdf
SNR can be calculated by {4 ܴ2ܲ2/(ߪ1+ߪ0)2}. Where, R is responsivity of receiver, P is
transmitted power and σ1 and σ0 are standard deviation of noise currents for symbols ‘1’ and ‘0’.
Using this equation, SNR v/s. BER relationship can be plotted as shown in Fig.2.
Fig.2: Lognormal distribution BER v/s. SNR curve
B. Negative Exponential Model
In case of strong irradiance fluctuations where link length spans several kilometers, number
of independent scatter become large [3]. In that case, signal amplitude follows a Rayleigh
distribution which in turn leads to a negative exponential statistics for the signal intensity (square of
field amplitude). This is given by [6]
p(I) = ூ exp ቀെ ூ ቁ, I ≥ 0
ଵ
బ
of 1).
ூ
బ
(3)
ଶ
where Io is the mean radiance (average photon count per slot). Here ߪௌூ =1 (or in the vicinity
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4. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 1, January (2014), © IAEME
1
0.9
0.8
0.7
P(I)
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.5
1
1.5
2
2.5
3
Intensity (I)
3.5
4
4.5
5
Fig.3: Negative Exponential Distribution pdf
The analysis of the negative exponential channel model was done in MATLAB
(MATrixLABouratory software) and the BER vs. SNR curve was analyzed in it.[8]Also, from that
analysis’ reference, the lognormal and gamma-gamma channel model was analyzed in MATLAB
software.
To develop the negative exponential channel model in MATLAB, the random input bit
pattern was generated at the transmitter end by using OOK (On-Off Keying) modulation scheme.
After that the generated bit pattern are passed through the channel with noise and attenuation (i.e.
y=hx+n).[9] Now, this generated output will be having the PDF distributed in the negative
exponential manner. For that we used the ‘random’ function to generate the bit-pattern (input to this
function is y i.e. noise added and attenuated signal) with the negative exponentially manner.
The equations used for finding out the BER and SNR are given below. [8]
ௌ
Spontaneous SNR γ =
Average SNR µ =
ௌ௔௩௚
ே
=
ሺఎ୍ሻమ
ே௢
(4)
=
ሺఎழ୍வሻమ
ே௢
(5)
ே
Average BERPav = ‫׬‬଴ ܲ ሺ‫ܫ‬ሻ ݂ሺ‫ ܫ‬ሻ݀‫ܫ‬
ା∞
ሺఎூሻ
=ଶ ‫ ݂ܿݎ݁ ׬‬ቀଶ
଴
ଵ
ା∞
√ே௢
ቁ ݂ሺ‫ ܫ‬ሻ݀‫ܫ‬
(6)
Using eq.(1),(2) and (3), the plot of BER vs. SNR curve was generated in MATLAB.
Also, the same result for the other channel model (Lognormal and Gamma-Gamma) can be obtained
using the same algorithm used in this case of negative exponential channel model.
C. Gamma-Gamma Model
Andrews et. al. [7] introduced the modified Rytov theory and proposed gamma-gamma pdf as
a useful mathematical model for atmospheric turbulence. This modified Rytov theory defines the
optical field as a function of perturbations which are due to large scale and small scale atmospheric
effects. The
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5. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 1, January (2014), © IAEME
Fig.4: BER vs. SNR curve of Negative Exponential Channel Model in MATLAB
normalized irradiance is given as I= IxIy where Ix and Iyarise from large scale and small scale
turbulent eddies and each of them follows gamma distribution. This gives the gamma-gamma pdf as
݂ሺ‫ܫ‬ሻ ൌ
ଶሺఈఉሻሺഀశഁሻ/మ ഀశഁିଵ
‫ ܫ‬మ Κఈିఉ ൫2ඥߙߚ‫ܫ‬൯,
ΓሺఈሻΓሺఉሻ
‫ܫ‬൐0
(7)
Where Ka(.) is the modified Bessel function of second kind of order a. α and β are the
effective number of small scale and large scale eddies of the scattering environment. These
parameters are directly related to atmospheric conditions according to [7]
ିଵ
ߙ ൌ ቂexp ቀሺଵା଴.ଵ଼ௗమା଴.ହ଺ఞభమ/ఱ ሻళ/లቁ െ 1ቃ
଴.ସଽఞమ
ߚ ൌ ቂexp ቀሺଵା଴.ଽௗమ ା଴.଺ଶௗమఞభమ/ఱ ሻఱ/ల ቁ െ 1ቃ
଴.ହଵఞమ ሺଵା଴.଺ଽఞభమ/ఱ ሻషఱ/ల
ିଵ
(8)
(9)
D. K channel model
This statistical model is used in strong turbulence condition. Here, SI is nearly 1 and the
value of log intensity variance is between 3 and 4.
This channel model can be considered as a product of two independent models-Exponential
and Gamma[11]. This model provides Excellent agreement between theoretical and experimental
values [11].
Pdf for the instantaneous electrical SNR, γ, at the receiver can be given by[12],
ഁశభ
ഁషయ
ఉ మ ఊ ర
Pγ(γ) = ௰ሺఉሻ
ഁశభ
క ర
‫ܭ‬ఉିଵ ቌ2ඨߚ ට ቍ
ఊ
క
(10)
Where β is related to the effective number of discrete scatterers., while Γ(.) is the Gamma
function. Kν(.) is the modified Bessel function of the second kind of order ν. ξ is average electrical
SNR at the receiver.
Which is given by ξ=ሺߟ‫ܧ‬ሾ‫ܫ‬ሿሻଶ ⁄ܰ଴.
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6. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 1, January (2014), © IAEME
Here one Bessel function is used which is denoted by K. Therefore this channel model is
known as K channel model. Based on Eq.(10), following result can be obtained in form of BER vs.
SNR for different values of β.
K distribution lacked the numerical computation in closed form. Also, it could not easily
relate the mathematical parameters with atmospheric turbulence and therefore it had limited
application and utilization.
Fig .5 BER performance of K channel for different values of β
E. I-K channel model
This channel model can be used in both scenarios, weak turbulence and strong turbulence.
Moreover it has less complexity than gamma-gamma channel model. So, this channel model is
gamma
generally used. Pdf for the instantaneous electrical SNR, γ, at the receiver can be given by [13-14].
,
(11)
Where Iν (.) is the modified Bessel function of the first kind of order ν, while α and ρ are the
distribution’s parameters and represent the effective number of scatters and a coherence parameter,
respectively [15-17].
Here, it has been assumed that our channel is fast fading[18-20]. When the fluctuations of the
fading[18 20].
signal intensity are supposed to be very rapid, and thus there is a difference from one symbol to
another, the channel can be characterized as fast fading, while these fluctuations are very slow
compared to the bit rate of the link, as slow. For the cases of high bit rate transmission, the channel
can be characterized as slow fading. Therefore channel can be considered as quasi-static[18].
quasi static[18].
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7. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 1, January (2014), © IAEME
Here, it has also been assumed that, the field of the optical wave is modeled as the sum of a
coherent (deterministic) component and a random component.
Here, the important parameter is ρ. The parameter ρ is a measure of the power ratio of mean
intensities of the coherent and random components of the field. For extremely weak scattering, ρ is
relatively large since the field is dominated by the coherent component. The power ratio decreases as
the strength of turbulence increases. By properly selecting values of α and ρ, both the weakscattering regime and the strong-scattering regime can be obtained.
Two kinds of Bessel functions are used symmetrically here, which are indicated by I and K.
There this channel model is referred to as I-K.
III. CONCLUSION
In the future, FSO will become important medium of information exchange due to its
numerous advantages. In this type of wireless communication atmospheric conditions play an
important role in transmission system setup. Proper turbulence model must be used while designing
the channel model. For weak turbulence scenario lognormal distribution is used, for strong
turbulence scenario K distribution must be used while I-K distribution model is used for weak to
strong turbulence scenario and it has less complexity than gamma-gamma channel model.
IV. REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
Jolly Parikh, “Study on Statistical Models of Atmospheric Channel for FSO Communication
Link”, International Conference On Current Trends In Technology, Nuicone – 2011
S. Arnon, “Optical Wireless Communications”, Encyclopaedia of Optical Engineering,
Marcel Dekker Inc., 2003.
Kamran Kiasaleh, “Performance of APD-Based, PPM free-space optical communication
systems in atmospheric turbulence”. IEEE Transactions on Communications, vol. 53,
pp.1455-1461, 2005.
A.A. Farid, S. Hranilovic, Outage capacity optimization for free-space optical links with
pointing errors, J. Lightwave Technol. 25 (7) (2007) 1702–1710.
A.K. Majumdar, Free-space laser communication performance in the atmospheric channel, J.
Opt. FiberCommun. Res. 2 (2005) 345–396.
T. Ohtsuki, “Performance analysis of atmospheric optical PPM CDMA systems,” J.
Lightwave Technol. , vol. 21, no. 2, pp. 406–411, Feb. 2003.
L. C. Andrews, R. L. Phillips, and C. Y. Hopen, “Laser beam scintillation with applications”,
SPIE Press, 2001.
A. Al-Habash, L.C.Andrews and R.L.Phillips, “Mathematical model for the irradiance
probability density function of a laser beam propagating through turbulent media”, Opt. Eng.,
vol. 40, pp.1554-1562, 2001.
S. Karp, R. Gagliardi, S.E. Moran, and L.B Stotts, Optical Channels, Plenum, NY, 1988.
Gagliardi, R. M., and Karp, S., Optical Communications, 2nd edition, John Wiley & Sons,
Inc., 1995.
O. Bouchet et.al, “Free Space Optics: Propagation and Communication”, Wiley, 2006.
SANDALIDIS, H. G., TSIFTSIS, T. A. Outage probability and ergodic capacity of freespace optical links over strong turbulence. Electronics Letters, 2008, vol. 44, no. 1, p. 46 - 47.
ANDREWS, L. C., PHILIPS, R. L. I-K distribution as a universal propagation model of laser
beams in atmospheric turbulence. Journal of the Optical Society of America A, 1985, vol. 2,
no. 2, p. 160 – 163.
111

8. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 1, January (2014), © IAEME
[14] ANDREWS, L. C., PHILIPS, R. L. Mathematical genesis of the IK distribution for random
optical fields. Journal of the Optical Society of America A, 1986, vol. 3, no. 11, p. 1912 1919.
[15] ANDREWS, L. C., PHILIPS, R. L. I-K distribution as a universal propagation model of laser
beams in atmospheric turbulence. Journal of the Optical Society of America A, 1985, vol. 2,
no. 2, p. 160 - 163.
[16] ANDREWS, L. C., PHILIPS, R. L. Mathematical genesis of the IK distribution for random
optical fields. Journal of the Optical Society of America A, 1986, vol. 3, no. 11, p. 1912 1919.
[17] LETZEPIS, N., FABREGAS, A. G. Outage probability of the free space optical channel with
doubly stochastic scintillation. IEEE Transactions on Communications, 2009, vol. 57, no. 10.
[18] SIMON, M. K., ALOUINI, M. S. Digital Communications over Fading Channels. Wiley
Interscience, 2000.
[19] NISTAZAKIS, H. E., TOMBRAS, G. S., TSIGOPOULOS, A. D., KARAGIANNI, E. A.,
FAFALIOS, M. E. Capacity estimation of optical wireless communication systems over
moderate to strong turbulence channels. Journal of Communications and Networks, 2009,
vol. 11, no. 4, p. 387 - 392.
[20] BELMONTE, A., KAHN, J. M. Capacity of coherent free space optical links using
atmospheric compensation techniques. Optics Express, 2009, vol. 17, no. 4, p. 2763 - 2773.
[21] Mazin Ali A. Ali, “Characterization of Fog Attenuation for Free Space Optical
Communication Link”, International Journal of Electronics and Communication Engineering
& Technology (IJECET), Volume 4, Issue 3, 2013, pp. 244 - 255, ISSN Print: 0976- 6464,
ISSN Online: 0976 –6472.
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