Download Lecture 12: Communication Aspects of Atmospheric Optical Channel

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Lecture 12: Communication Aspects of Atmospheric Optical
Channel
12.1. Main Characteristics
Optical wireless communication is rapidly becoming a familiar part of modern
life [1, 2]. Over the last decade, there has been a steady increase in the number of
consumers requiring high capacity links. In the past, these customers were pleased with
tens of megabits per second, but nowadays near-gigabits per second links are required.
Banks, universities, offices, companies and government facilities all need communication
services for stationary and mobile applications. (The emerging technology of mobile
optical wireless communication is beyond the scope of this book and will not be
discussed in this chapter). High data rate communication applications range from next
generation internet and support for cellular infrastructure to last mile applications. Some
of the requirements of these new applications could be met by fiber optics or millimeter
wave wireless links. Fiber optics has been distributed in many cities in close proximity to
the backbone of the network. However, massive effort is required to bridge the distance
from the central switch to the client premises (this is termed the “last mile” problem) and
many difficulties need to be to overcome. In some cases it may not be possible or
practical, or it may be too time-consuming or costly to dig up main streets and lay down
fibers. In such cases a wireless solution can bridge the gap. Millimeter wave wireless
links provide medium data capacity for long ranges. However, the capacity is limited and
in some cases public health and safety considerations as well as heavy tariffs and
licensing fees make this selection less favorable. Additionally, the bureaucracy involved
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in obtaining permits can take months. As a result, in cases where high data rate is
required without any licensing and tariffs and the range is limited, optical wireless
communication (OWC) is the best solution (Fig. 12.1).
Fig. 12.1: A schematic illustration of an optical wireless communication network
courtesy of [1]
In addition, OWC is an excellent choice when a temporary solution is sought, or when an
unexpected redeployment of premises calls for the provision of instant communication
links. It is, of course, very important to design the system to operate in the eye-safe
regime in the interests of health and safety. After all, light in the infrared (IR) range has
been harmlessly endured since the beginning of human evolution. In some scenarios a
hybrid system is the optimum solution. A hybrid system includes an optical wireless
transceiver, a millimeter RF wireless transceiver, a monitoring system and a switch. The
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advantages of hybrid systems are a) all-weather operation and b) very high data rate most
of the time. The disadvantage is the complexity and the cost of the hybrid system. Most
of the time the system transmits high data rate information, but when the weather become
unstable, with a lot of haze or fog or very strong turbulence, the system switches to a
medium data rate and transmits the information by millimeter RF wireless transceiver.
The ability to work in all weather and to differentiate type/priority of the information
makes the system very reliable due to the facility that in the medium data rate mode we
transmit high priority information such as video streaming, browsing and voice calls,
while mail and backup are delayed. Following the previous discussion, the question
“why not utilize present electrical cable infrastructures, which can be used to bridge the
last mile gap?” remains open. Electrical cable communication infrastructure includes, for
example, asynchronous digital subscriber line (ADSL), power line communication (PLC)
or cable television (CATV) connectivity. However, the limited bandwidth of these
technologies and high leasing fees make them an inferior solution in comparison to
OWC. In many cities all over the world the flexibility of OWC systems (also termed
Free Space Optics – FSO) provides high-capacity connections to the fiber backbone to
home users. OWC can provide fiber-like performance using a very small, low weight
transceiver. In addition, the installation can take only a few hours without entailing any
licensing or fees. The installation process requires only electrical and communication link
connections to the two transceivers and simple alignment between them. The transceiver
could be placed on a rooftop, billboards, an electrical pillar, bridges, lampposts, or inside
offices near windows and an OWC system can be operative within hours. As the
importance and value of the information transferred in the system increases, the security
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features of OWC become more significant. The security features of OWC result from
narrow beam divergence angle of the transmitter, which prevents spill over of signal
energy to an unintended direction, which could be used to eavesdrop (small footprint).
Moreover, the narrow field of view of the receiver reduces the probability of interference
or jamming.
The main challenges in this field lie in extending the research work by providing
tailored solutions for signal degradation due to the atmospheric effects such as turbulence
and aerosol scattering. OWC is heralded as a unique communication technology for the
coming decade, although some challenges must still be overcome.
12.2. Link Budget
In this subsection, we describe the relation between the main parameters of the
transmitter, the channel and the receiver to the power of the received signal. We start
with the definition of the concept of the gain of a telescope that we use in the following
passage to describe the parameters of the transmitter and the receiver. It is clear that the
telescope is a passive element so the gain does not add any additional energy to the
signal. The gain is the ratio of the radiation intensity of a telescope in a given direction to
the intensity that would be produced by a telescope that radiates equally in all directions
and has no losses. Therefore, the gain describes how the energy is distributed in the
spatial domain.
The received power in the detector plane is given by [3]:
  
PR  PT GT TT 
 T A G R TR TF
 4Z 
2
(12.1)
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where PT is the transmitter optical power, GT is the laser transmitter telescope gain TT is
the optics efficiency of the transmitter, is the laser wavelength, Z is the distance
between the laser transmitter and the optical receiver. The term in brackets is the free
space loss, TA is the atmospheric transmission, GR is the optical receiver telescope gain,
TR is the optics efficiency of the receiverand TF is the filter transmission.
Figure 12.2 depicts the normalized received power as a function of distance. It is
easy to see that as the distance increases the power decreases according to the power of
two.
Fig. 12.2: Normalized received power as a function distance
We use results from work done reported in [2] to analysis of the gain of the transmitter.
In the analysis the authors assume that Cassegrain telescope is used and the laser emits a
circular, single mode TEM-beam (Fig. 12.3). Ref. [2] gives the transmitter telescope gain
based on the previous assumption
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 2a 
GT  ,  ,  , X   
 gT  ,  ,  , X 
  
2
(12.2)
where ,  are system parameters, X is parameter describing off axis distribution, and 
includes near fields and defocusing effects as defined below:


a
(12.3)

b
a
(12.4)
X  k a sin 1 
 k a 2  1
(12.5)
1
  
  
  R
2



(12.6)
where  is the wave length of the light, a is the radius of the aperture primary mirror, b is
the radius of the secondary mirror,  is the distance from the axis according to the e 2 time decay of the intensity of the laser radiation in the spatial domain, 1 is the
observation angle, k=2/, R is the curvature of the phase front at the telescope aperture
and
gT  ,  ,  , X   2
 exp  ju exp   u J o X u 
1
2
0.5
2
du
2
(12.7)
2
In order to simplify (12.7) we assume the special case of far field, on axis observation
such that
gT  ,0,  ,0 
2

2
exp   exp    
2
2
2 2
(12.8)
It is possible to maximize the on axis gain in the far field using the following relation
  1.12  1.3 2  2.12 4
(12.9)
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Fig. 12.3: Cassegrain telescope
Formula (4.9) gives the maximum on axis gain for the aperture to beam-width ratio for a
general obscuration and is accurate to within 41% for y < 0.4.
 2a 
GT  10 log 
  10 log gT  ,0,  ,0
  
2
[dB]
(12.10)
In the analysis of the gain of the receiver telescope similar assumptions are made; a
Cassegrain telescope is used , but in this case we assume that the receiver is placed far
away from the transmitter so that plane waves impinge on the receiver aperture
Ref. [3] gives the receiver telescope gain based on the previous assumption


 2a 
2
GR  10 log 
  10 log 1    10 log 



2
[dB]
(12.11)
where for direct detection
2
D 
1  2
RD k
2 Fs

0
J1 u   J1 u 2 du
u
(12.12)
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Additionally, FS is the F number of telescope defined as
FS 
f
D
(12.13)
where f is the focal length of the telescope and d is the diameter of the entrance pupil.
Analyzing (4.11) indicates that the first term is for an ideal unobscured telescope
gain, the second term describe the loss due to blockage of the incoming light by the
central obscuration and the third term represents the losses in direct detection due to the
spillover of signal energy beyond the detector boundary. Figure 12.4 depicts an ideal
telescope gain as a function of wavelength. It is easy to see that one order of magnitude
increase in wavelength reduces the gain by 20dB.
Fig. 12.4: Ideal telescope gain as a function of wavelength.
It is easy seen that one order of magnitude increase in wavelength reduce the gain in
20dB.
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12.3. Link Key Parameters Prediction
One of the important parameters that describes the atmosphere is the power attenuation.
During the last decades, many methods have been developed to calculate the attenuation
based on meteorological data. One of the most popular methods takes advantage of
visibility data that is regularly recorded at airports with very good temporal resolution
(once every 30 minutes or less). The visibility is defined by several terminology sets that
are very similar based on visual measurement or attenuation at 0.55m wavelength as
function of range at which image contrast drops to 0.02 and is given by [2]
VS   1 ln( 1 / 0.02)  3.912 /  ,
(12.14)
where  is the scattering coefficient and VS is in km.
From (12.14) and [5, 6] the link attenuation is given by the following relation
  exp[
 3.91   qS
(
) Z],
VS
0.55
(12.15)
where q S is size distribution parameter for scattering particles and Z is the propagation
range in km. q S may typically be 1.6 for high visibility ( VS > 50 km), 1.3 for average
visibility (6 km < VS < 50 km) and 0.585 V S1 / 3 for low visibility ( VS < 6 km) .
It is easy to show that , the attenuation coefficient of the link, is given by
 
1
Ln( )
Z
(12.16)
Attenuation is caused by atmospheric aerosol and molecular scattering and absorption. It
can be expressed as
  m  m a  a
(12.17)
where α are absorption coefficients and β are scattering coefficients; subscript “m” refers
to molecules and subscript “a” to aerosol particles.
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The scattering and absorption coefficients are given by
   a Na
(12.18)
   s Ns
(12.19)
and
where σ is cross-section parameters [m2] and N is particle concentration [1/m3]; subscript
“a” refer to absorption and subscript “s” to scattering.
12.4. Mathematical and Statistical Description of Signal Fading
In many optical wireless communication systems the received signal fades during typical
operation conditions. The signal fade is a stochastic process caused by atmospheric
turbulence.
12.4.1. Statistical description of turbulence
Turbulence is phenomenon that describe random changes in the atmospheric refractive
index in the spatial and temporal domains. This phenomenon is due to the temperature
difference between the atmosphere, the ocean, the ground and to the Earth’s revolution.
The stationary refractive index n of the atmosphere is a function of temperature, pressure,
wavelength, and humidity. For a marine atmosphere [6]
77 p  7.53 10 3
q  6
n0  1 

7733
1 
10
T 
T
2
(12.20)
where p is air pressure (millibars), T is temperature (K), q is specific humidity (gm-3), and
 is wavelength.
In order to deal with the stochastic behavior of the refraction index we use
Kolmogorov's theory [7-9]. One of the main parameters in this theory is Cn2. Cn2 is the
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refractive index structure constant which helps us to describe the fade statistics. Fried
developed an analytic model to describe this constant [8], and later an improved model
named after its proposers, Hufnagel and Stanley, become more acceptable [6, 12]. The
latter model is given by:
2
Cn2


10
h   0.00594 v  105 h exp   h   2.7 1016 exp   h   A exp   h 
 27 
 1000 
 1500 
 100 
(12.21)
where h is the altitude, v is the wind speed and A is the nominal value of C n2 0 at zero
altitude. At ground level C n2 0 typically range between 1.7 10-14 during daytime (strong
turbulence) and 10-16 at night (weak turbulence).
When the channel is short or the turbulence is weak, the mathematical model for
the covariance (over channel length L) for a plane wave in Kolmogorov turbulence is
given by [7]:
7
5
 2  6
 X2 L   0.56   C n2 u L  u  6 du ,
   0
L
(12.22)
in addition, for a spherical wave it is given by:
7
5
5
 2  6
 u 6
 X2 L   0.56   C n2 u   L  u  6 du .
   0
 L
L
(12.23)
The turbulence coherence diameter d0 in Kolmogorov turbulence is given for a plane
wave by
2L


 2 
d 0 L   1.45   C n2 u du 
   0


and for a spherical wave by

3
5
,
(12.24)
12
5


2L
3 2
2

u





d 0 L   1.45     C n u du 


   0 L



3
5
(12.25)
In order to analyze the temporal effect of the atmospheric turbulence the frozen air
model is used. In this model, it is assumed that the eddy pattern is stationary when it
passes over the receiver plane, hence turbulence coherence time can be expressed as [11]:
0 
d0
,
v
(12.26)
where v is the wind velocity perpendicular to the beam propagation direction. In the
following sub sections, we describe the lognormal, the Gamma- Gamma and the Kprobability density distribution functions. The non-Kolmogorov turbulence channel is
described in previous lectures.
12.4.2. Log Normal probability density function
The lognormal probability density function describes the scintillation and signal fading
statistics for weak turbulence. The transmitted pulse propagates through a large number
of elements of the atmosphere, each causing an independent, identically distributed
(I.I.D) phase delay and scattering. Using the Central Limit Theorem (CLT) indicates that
the marginal distribution of the log-amplitude is Gaussian [10],
  X  EX 2 

f X X  
exp  
2


2
2

2 x
x


1
(12.27)
where X is the log-amplitude fluctuation,  X2 is the variance and E[X] is the ensemble
average of log-amplitude X . X is assumed to be a homogeneous, isotropic and
independent Gaussian random variable.
The light intensity I as a function of X is given by
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I  I 0 exp 2 X  EX 
(12.28)
where Io is the normalized signal light intensity
The density distribution function of intensity, I, is lognormal [10]:
 ln I   ln I 0 2 

f I I  
exp  
2


2
8 x
2 I 2 x


1
(12.29)
In Fig. 12.5 a longnormal PDF as a function of the intensity for  x2  1 and ln I   3 is
shown. As can be seen this function has one peak near the origin of the axes and then
sharp drop for increasing of I.
Figure 12.5: Lognormal density distribution function as a function of the intensity.
12.4.3. Gamma - Gamma density distribution function
The Gamma Gamma distribution describes well a wide range of turbulence conditions
from weak to strong. The gamma distribution is a family of curves based on two
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parameters. The chi-square and exponential distributions, are derived from the GammaGamma distribution when one of the two Gamma parameters is fixed. The Gamma
Gamma PDF is given by
t  t
2 t  t  2
f I I  
I
 t  t 
t  t
2
1


K t   t 2  t  t I , I>0
(12.30)
where Kt-t(x) is the modified Bessel function of the second kind of order -. The αt
and βt are the effective number of small scale and large scale eddies of the scattering
environment and (x) is gamma function.
The parameters t and t a represent the effective number of large-scale cells of the
scattering process and the effective number of small-scale cells respectively. The
parameters αt and βt are given by [12,13]
 
 
 
0.49 x 2
 
 t  exp 
7
12  6
 
  1  0.18d 2  0.56 x 5 

  

 
 
 
 
  1
 
 
 
 
1
(12.31)
5
 
12   6

 
2
  0.51x 1  0.69 x 5 
 


 t  exp 
7
12  6
 
  1  0.9d 2  0.62d 2 x 5 

  

 
 
 
 
  1
 
 
 
 
1
(12.32)
where
7 11
x 2  0.5Cn2 k 6 L 6
(12.33)
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 kD2 

d  

4
L


(12.34)
where D is the diameter of the receiver collecting lens aperture and k is the wave number.
The Gamma function is given by

 z    t z 1e t dt
(12.35)
0
The recursive relation of gamma function is
z  1  zz 
(12.36)
and, if z is a positive integer
z   z 1!
(12.37)
12.4.4. K- probability density distribution function
The first non Gaussian field models to gain wide acceptance for a variety of applications
under strong fluctuation conditions were the family of K distribution, providing excellent
models for predicting amplitude or irradiance statistics in a variety of experiments
involving radiation scattered by turbulent media. The K-PDF has been successfully used
to model atmospheric turbulence deep into saturation and it is given by
f I I  
2
 n 
 n 1
n
 n 1  n 1
2
I
2
2

K n 1 
 n I 


(12.38)
where I denotes the optical signal intensity, and
n 
2
1
 si2
(12.39)
where 2si is the scintillation index defined as
 si2
 
E I2
 2 1
E I 
(12.40)
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12.5. Mitigating Atmospheric Turbulence Effects
From the previous subsection, it is clear that turbulence affect dramatically the
performance of any optical wireless system. However, several methods can be used to
mitigate the effect of the turbulence. The obvious one is to adapt the transmitter power so
as that the SNR will kept at constant value, however there is some probability that the
beam will wonder outside the receiver field of view and as results the power adaptation
could not help. In addition, high power laser transmitter could create hazard to human
vision system therefore this solution is bounded by the maximum laser exposure
regulation. Another method is to use multiple transmitter which transmit the information
to the receiver through multiple uncorrelated spatial channel as a result the probability
that the turbulence outage the communication reduce dramatically this method is similar
to the concept of diversity in RF communication. The same thing could be done in the
receiver side where the signal from multiple receivers is combining in some optimal way.
Another method to mitigate the turbulence effect is to use bigger aperture in the receiver.
Bigger aperture in the receiver collect bigger chunk of the received spot. Due to the fact
the turbulence is a stochastic process bigger chunk of the received spot increase the
efficiency averaging process. The last method that we discuss here is the adaptive optics.
Adaptive optics is a method that sense the wave front of the receive signal and than based
on this information use adaptable mirror to cancel the effect of the turbulence on the
wave front. Mathematically it describe as spatial inverse filter for the turbulence.
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12.6. Performance of an OWC as a Function of Wavelength
OWC is emerging technology that has many applications in areas, such as business and
offices connection, urban short wireless link and in inters university campuses
communication owing to its unique combination of characteristics: license- and tariff-free
bandwidth allocation, low power consumption, extremely high data rate, rapid
deployment time and low weight and size. However, the major weakness of OWC in
terrestrial applications is the threat of downtime caused by bad weather conditions, such
as fog and haze. The main mechanism that effect light photon propagate through fog and
haze is scattering by atmospheric aerosols which deflect randomly the propagate photons
to directions other than intend. Consequently, less power is received and the
communication system performance degraded. This phenomenon encourages many
researcher to look for wavelength which minimize the scattering effect.
12.7. Solar-Blind Ultraviolet Communication
As light propagates through the atmosphere, it will be absorbed or scattered by molecules
and aerosols [4, 21-24]. Since these mechanisms are highly wavelength sensitive, the
transmission of light at two different wavelengths through a given propagation channel
differs significantly. Usually, radiation wavelengths that are heavily absorbed by
atmospheric particles are avoided in optical wireless communication systems to minimize
beam attenuation and consequent power requirements. However, background radiation at
the transmitted wavelength, particularly due to solar radiance during daytime operation,
produces background shot noise that contaminates the desired signal to noise ratio. To
combat background shot noise the receiver FOV and the filter are designed to be narrow
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[22]. However, we can use the fact that the spectrum of solar irradiance reaching the
ground is far from uniform. Notably, almost all the solar radiation in the spectral region
around 200–280 nm is absorbed by ozone in the upper atmosphere. Hence virtually no
background noise would be encountered when the transmission wavelength is in this
region, which is known as “solar-blind ultraviolet,” and very large FOV receivers can be
used. Additionally, considerable scatter by atmospheric particles occurs at very short
wavelengths. This enables the establishment of a non-line-of-sight communication
regime, in which the atmospheric particles act as reflective elements and close a link
between non-aligned transmitter-receiver pairs. Mentioned above is shown in Fig. 12.6
Multi-scattering
environment
Cluster of
sensor nodes
Transmitting
node
Receiving nodes
Fig. 12.6: Possible scenario; microsensors strewn ad hoc on the ground self-orientate to
face vertically upwards. Communication is achieved by virtue of backscatter from multiscattering environment (courtesy of [22]).
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It can be seen clearly from Fig. 12.6 that, for a given transmitter beam divergence and
transmitter-receiver separation, a larger receiver FOV would result in a larger intersection
of the beam and FOV cones, and more backscattered optic power from the transmitter
would reach the receivers. Similarly, an increased transmitter beam divergence would
enlarge the intersection area. In conclusion, an optical wireless system operating in the
solar-blind ultraviolet spectral range could achieve non line of sight (NLOS)
communication by means of backscatter from atmospheric particles and use large FOV
receivers to collect the scatter power.
References
0. D. Kedar and S. Arnon, "Urban optical wireless communication network: The main
challenges and possible solutions," in the IEEE Optical Communications
Supplement to IEEE Communications Magazine, pp. S1-S7, 2004.
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