Recent research and development in
Free-Space Laser Communications
Dr. Arun K. Majumdar
a.majumdar@IEEE.org
105 W. Mojave Rose Ave.
Ridgecrest, California 93555,
USA
Lecture Series: 2
Brno University of Technology, Brno
Czech Republic
December 1-6, 2009
Copyright © 2009 Arun K. Majumdar
OUTLINE
• Background, need and recent R&D directions
• Basic Free-Space Optics (FSO) communication
system and parameters
• Some areas of current interest
• My own recent research and results
• Conclusions and recommendations for solving
problems of interest to the FSO community
Copyright © 2009 Arun K. Majumdar
Background, need and recent R&D directions
•
•
•
•
•
•
•
•
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Needs for improvements and advanced technologies
laser and hybrid (combination of laser and RF)
communications: advanced techniques and issues
advances in laser beam steering, scanning, and shaping
technologies
laser propagation and tracking in the atmosphere
atmospheric effects on high-data-rate free-space optical data
links (including pulse broadening)
long wavelength free-space laser communications
adaptive optics and other mitigation techniques for free-space
laser communications systems
techniques to mitigate fading and beam breakup due to
atmospheric turbulence/scintillation: spatial, temporal,
polarization, and coding diversity strategies, and adaptive
approaches
error correction coding techniques for the atmospheric channel
characterization and modeling of atmospheric effects
(aerosols, turbulence, fog, rain, smoke, etc.) on optical and RF
communication linksCopyright © 2009 Arun K. Majumdar
Background, need and recent R&D directions
(Continued…)
• communication using modulated retro-reflection
• terminal design aspects for free-space optical link (for
satellite- or land-mobile-terminals)
• integration of optical links in networking concepts (e.g.
inter-aircraft MANET)
• design and development of flight-worthy and spaceworthy optical communication links
• deep-space/ inter-satellite optical communications
• multi-input multi-output (MIMO) techniques applied to
FSO
• free space optical communications in indoor
environments
• underwater and UV communications: applications and
concepts of FSO in sensor networks for monitoring
climate change in the air and under water
Copyright © 2009 Arun K. Majumdar
Basic Free-Space Optics (FSO)
communication system and parameters
• A typical free-space laser communications
system
Communications Parameters
- Modulation Techniques for FSO communications
- Received signal-to-noise ratio (SNR)
- Bit-Error-Rate
Copyright © 2009 Arun K. Majumdar
Some areas of my current interest
• Atmospheric Turbulence Measurements over Desert site
relevant to optical communications systems
• Reconstruction of Unknown Probability Density Function
(PDF) of random Intensity Fluctuations from Higher-order
Moments
• Atmospheric Propagation Effects relevant to UV
Communications
Copyright © 2009 Arun K. Majumdar
Strength of Turbulence, Cn2 parameter
• Structure Function (of a random variable, say
refractive index):
Dn (r )  Cn r 2 / 3
2
l0  r  L0
• Measurements of the refractive index structure
function constant or Cn2 can be classified into
boundary-layer and free-atmosphere
measurements: the boundary layer can extend
from hundreds of meters to 2 km above the
surface
Copyright © 2009 Arun K. Majumdar
Atmospheric Turbulence Measurements over Desert site
using ground-based instruments, kite/tethered-blimp
platform and aircraft relevant to optical communications
and imaging systems: Preliminary Results
Arun K. Majumdar 1, Frank D. Eaton 2, Michael L. Jensen 3, Demos T.
Kyrazis 4, Bryce Schumm 5, Matthew P. Dierking 5, Marjorie A.
Shoemake 6, Dari Dexheimer 6, Jennifer C. Ricklin7
1 LCResearch,Inc., Agoura Hills, California
2 Air Force Research Laboratory, Kirtland Air Force Base, New Mexico
3 QEI Technologies, Inc., Broomfield, Colorado
4 R3, Inc., Albuquerque, New Mexico,
5 Air Force Research Laboratory, WPAFB, Ohio
6 Boeing LTS, Inc., Kirtland AFB, New Mexico
7 DARPA /ATO, Arlington, Virginia
FREE-SPACE LASER COMMUNICATIONS VI
SPIE Optics & Photonics, 15-17 August, 2006  San Diego, California
Copyright © 2009 Arun K. Majumdar
THEORETICAL CONCEPTS DESCRIBING
ATMOSPHERIC TURBULENCE EFFECTS
• The atmosphere is very complex and dynamic
system
• Understanding effects of atmospheric propagation is
absolutely necessary to design and develop
communications and imaging systems
• Various parameters relevant to imaging and
communication systems:
- Strength of Turbulence, Cn2 parameter
- Coherence length, r0
- Isoplanatic Angle, Ө0
2
Rytov
Variance,
σ
r
- Greenwood Frequency, fG
Copyright © 2009 Arun K. Majumdar
Optical remote sensing system detecting a point
source on the ground
Air-borne
Imaging
system
Aberrated
wavefront
H
Turbulence
Spherical wave from point
source
Point Source
Copyright © 2009 Arun K. Majumdar
Strength of Turbulence, Cn2 parameter
• Structure Function (of a random variable, say
refractive index):
Dn (r )  Cn r 2 / 3
2
l0  r  L0
• Measurements of the refractive index structure
function constant or Cn2 can be classified into
boundary-layer and free-atmosphere
measurements: the boundary layer can extend
from hundreds of meters to 2 km above the
surface
Copyright © 2009 Arun K. Majumdar
•
Atmospheric Models
Hufnagel-Valley (HV) model:
h 
h 
 


 h 
16
Cn (h)  0.00594  (10 5 h)10 exp  
  2.7  10 exp  
  A exp  

27
1000
1500
100
 






2
2
where  is the rms wind speed. Typical value of the
parameter, A=1.7x10-14 m-2/3.
•
Modified Hufnagel-Valley (MHV) model:
 h 
 h 
 h 
2
17
15
Cn (h)  8.16  1054 h10 exp  

3
.
02

10
exp


1
.
90

10
exp





 1000 
 1500 
 100 
Copyright © 2009 Arun K. Majumdar
•
SLC-Day model:
Cn2 = 0
0 m < h < 19 m
= 4.008 x 10^13h^-1.054
= 1.300 x 10^-15
= 6.352 x 10^-7h^-2.966
= 6.209 x 10^-16h^-0.6229
19 m < h < 230 m
230 m < h < 850 m
850 m < h < 7000m
7000 m <h < 20,000 m
Copyright © 2009 Arun K. Majumdar
CLEAR1 model:
• Note: here h is altitude in kilometer above mean sea level
(MSL)1.23  h  2.13
log 10 (Cn )  A  Bh  Ch2
2
where A= -10.7025, B= -4.3507 C= +0.8141
2.13  h  10.34
log 10 (Cn )  A  Bh  Ch
2
2
where A= -16.2897, B= +0.0335, C= -0.0134
10.34  h  30
log 10 (Cn )  A  Bh  Ch2  D exp{0.5[(h  E) / F ]2}
2
where A= -17.0577, B= -0.0449, C= -0.0005
D= 0.6181,
E= 15.5617, F= 3.4666
Copyright © 2009 Arun K. Majumdar
Coherence length, r0
For Kolmogorov turbulence, the coherence length r0 of a
spherical wave observed at slant range R from its point source is
given by


10 2

r0  
 27 4  sin   28 / 3 sin  5

3  6 
 6
 24  6 
b  2  
 5  5 


5/3

R
 k0 2  drCn 2 (r ) r  
2
0
R 
  11  
  b 

 6 
5/6
 6.884
Copyright © 2009 Arun K. Majumdar
k0 
2

3 / 5
Isoplanatic Angle, Ө0
• The isoplanatic patch, which defines the angle
within which the distortion over the turbulence
path will be essentially unchanged, is given by

r 5/3 2 
2
5/3
0  114.9 R  drCn (r )(1  ) /  
R
0


R
3 / 5
Rytov Variance:
R


 r 2  4.78 drCn 2 (r )r 5 / 6 1 
Greenwood Frequency, fG :
0
r

R
5/6
/ 7 / 6
A critical time constant specifying the interval over which turbulence remains
essentially unchanged derives from Greenwood 3 / 5
5/3
R

2
6 / 5
3/ 5
f G  2.31 sec    drCn (r ) V (r ) 
 0

Copyright © 2009 Arun K. Majumdar
Cn2 from point measurements
Figure contains the Cn2 measurement probe. It's attached to an RM Young
anemometer so that it always faces into the wind. The black cylindrical object
is a Gill Windsonic that was actually used for our wind measurements. The
fine wire temperature probe (FWTP) :Small temperature variations along the
fine wire (1μm -5μm) probes at the ground level can be used to calculate the
temperature structure parameter (Ct2). From Ct2 the refractive index structure
parameter (Cn2) can be calculated using the local measurements of
© 2009 Arun K. Majumdar
temperature, wind speed andCopyright
pressure.
• Relationship between Structure Function and Power
Spectral Density: the structure function is related with the
PSD in the inertial subrange
D(r) = 2(φ(0) - φ(r))
D(r) = Cx2 rp (0 < p < 2)
autocorrelation function= φ (r)
the autocorrelation function and the PSD are Fourier transform pairs
(1  p )
p
2
W (k ) 
sin
C x k   p 1
2
2
Cn2 = (79e-6* (p/T2))2 * Ct2
Copyright © 2009 Arun K. Majumdar
RESULTS
Copyright © 2009 Arun K. Majumdar
Copyright © 2009 Arun K. Majumdar
Copyright © 2009 Arun K. Majumdar
Copyright © 2009 Arun K. Majumdar
Cn2 from scintillation measurements
1 0
C n 2
1 0
1 0
1 0
-1 2
-1 3
-1 4
-1 5
1 6 .6
1 6 .8
1 7
M is s io n
1 7 .2
1 7 .4
D a y / T im e [ D a y s ]
Copyright © 2009 Arun K. Majumdar
1 7 .6
Cn2 from Balloon (tethered-blimp)
measurements
Instruments
3D-CTA/TC: A 3D Constant Temperature Anemometer
(CTA)/ThermoCouple
system is used to provide 2 kHz measurements of all 3 velocity
components and temperature.A separate 3D sonic anemometer unit is
used for in-flight calibration of the 3D-CTA/TC
Copyright © 2009 Arun K. Majumdar
Cn2 Profile
3000
2500
Altitude (m)
2000
1500
1000
500
18
1 10
1 10
17
raw data
smoothed data
plus 1 sigma
minus 1 sigma
1 10
1 10
Cn2 (m^-2/3)
16
15
1 10
Copyright © 2009 Arun K. Majumdar
14
1 10
13
Valley
Hufnagel-Valley
Comparison of ) Cn2 profile generated from tetheredblimp instrument measurement and various models.
Cn2 (m^-2/3)
Night
1 10
14
1 10
15
1 10
16
1 10
17
1 10
18
Cn2 Profile Comparison
0.8
1
1.2
Measured
Hufnagel-Valley
Modified Hufnagel-Valley
SLC-Day
CLEAR1 Night
1.4
1.6
1.8
Altitude (Km)
2
2.2
Copyright © 2009 Arun K. Majumdar
2.4
2.6
Histogram of Cn2 : some typical examples
FREQUENCY (%)
8
6
4
2
0
14.5
14
13.5
13
12.5
log10(Cn2 (m^-2/3))
14.5
14
13.5
log10(Cn2 (m^-2/3))
12
11.5
FREQUENCY (%)
10
5
0
15.5
15
Copyright © 2009 Arun K. Majumdar
13
12.5
Table 1. Coherence length, r0, (cm)
Geometry of syntheticBalloon Data HV
aperture imaging system
Air-borne sensor :
Zenith Angle = 79.02
deg
Range (slant path
length) = 7913 m
Wavelength λ= 1.55 μm
70.03±3.05
52.96
Modified
HV
SLC-Day
CLEAR1
288.09
55.00
54.62
Table 2. Isoplanatic Angle,Ө0 (μrad)
Geometry of syntheticaperture imaging
system
Balloon
Data
HV
Modified HV
SLC-Day
CLEAR1
Air-borne sensor :
Zenith Angle = 79.02
deg
Range (slant path
length) = 7913 m
Wavelength λ= 1.55
μm
27.93
2.94
86.71
9.65
16.39
Copyright © 2009 Arun K. Majumdar
Table 3. Rytov Variance, σr2
Geometry of syntheticaperture imaging
system
Balloon
Data
HV
Modified HV
SLC-Day
CLEAR1
Air-borne sensor :
Zenith Angle = 79.02
deg
Range (slant path
length) = 7913 m
Wavelength λ= 1.55
μm
0.01
0.06
0.0009
0.02
0.02
Table 4. Greenwood Frequency, fG, (Hz)
Geometry of
synthetic-aperture
imaging system
Balloon
Data
HV
Modified
HV
SLC-Day
CLEAR1
Air-borne sensor :
Zenith Angle = 79.02
deg
Range (slant path
length) = 7913 m
Wavelength λ= 1.55
μm
20.62
108.69
5.94
42.39
33.29
Copyright © 2009 Arun K. Majumdar
SUMMARY AND CONCLUSIONS
• New results of atmospheric turbulence measurements
over desert site using ground-based instruments and
tethered-blimp platform are presented
• An accurate model of the complex optical turbulence
model for profile is absolutely necessary to analyze and
predict the system performance of free-space laser
communications and imaging systems
• Because of the complexity and variability of the nature of
atmospheric turbulence, accurate measurements of
turbulence strength parameters are essential to design
the system for operating over a wide range
Copyright © 2009 Arun K. Majumdar
Reconstruction of Probability Density Function of
Intensity Fluctuations Relevant to Free-Space Laser
Communications through Atmospheric Turbulence
Arun K. Majumdar 1, Carlos E. Luna 2, and Paul S. Idell 2
1
LCResearch, Inc., Agoura Hills, CA 91301
2 The Boeing Company, Directed Energy Systems, West Hills, CA 91304
FREE-SPACE LASER COMMUNICATIONS VII
SPIE Optics & Photonics, 28-30 August, 2007  San Diego, California
Copyright © 2009 Arun K. Majumdar
Background and need to reconstruct Probability
Density Functions (PDF)
• The performance of a lasercom system can be
significantly diminished by turbulence-induced
scintillation resulting from beam propagation through the
atmosphere
• scintillation can lead to power losses at the receiver and
eventually to fading of the received signal below a
prescribed threshold.
• reliability of a laser communication system
• subject of the statistics of the irradiance fluctuations in
turbulent atmosphere is still, unsettled and in need of
additional fundamental understanding and developments
• Relevance to Free-space Laser Communications –
- Bit-Error-Rate (BER) Performance
- ProbabilityCopyright
of Fade
© 2009Statistics
Arun K. Majumdar
EXISTING METHODS
•
•
Construct a histogram from the data and
compare it to known PDF’s to model the
random process
Calculate the moments of the data and
compare them to moments of known
PDF’s
Copyright © 2009 Arun K. Majumdar
PROPOSED METHOD BASED ON HIGHERORDER MOMENTS
• Analytical techniques to reconstruct PDF from higherorder moments - estimate the PDF by data moments of
order up to 8th
• PDFs under consideration represent some practical
situations such as fluctuations of laser intensity when
propagated through atmospheric turbulence and are
non-Gaussian in nature
• two similar methods which were attempted initially:
Gram-Charlier expansion and Edgeworth series
expansion
[( x  m) 2 / 2 2 ]
f ( x)  exp
Gram-Charlier method:  2
Copyright © 2009 Arun K. Majumdar
8
C
n 1
n
 H n ( x)
PROPOSED METHOD BASED ON HIGHER-ORDER MOMENTS
• Edgeworth series expansion is obtained to construct the
PDF from the cumulants of higher-orders
• Both the Gram-Charlier series Edgeworth series
expansion have poor convergence properties
• The proposed generalized Laguerre polynomial
expansion method did not have any divergent or
oscillatory problems to reconstruct the PDF
Copyright © 2009 Arun K. Majumdar
PROPOSED METHOD BASED ON HIGHER-ORDER MOMENTS
• sought-for PDF is given by a gamma PDF modulated by
a series of generalized Laguerre polynomials:

f ( x )  f g ( x )  W n Ln
(  1)
n 0
x is the random intensity
  x 
(
x
)

(0  x   )
f g (x)
 x 2

 x2    x 2
The generalized Laguerre polynomials are defined by
Ln
(  1)
 n    1 ( x) l

( x)   
l 0  n  l
 l!
n
Using the orthogonality condition we can show that
(  /  ) l  x l 
Wn  n !(  )
l  0 l !( n  l )! (   l )
n
 xl 
is the gamma PDF
is the intensity moment
order
l K. Majumdar
Copyrightof
© 2009
Arun
PROPOSED METHOD BASED ON HIGHER-ORDER MOMENTS
Test Probability Density Functions (Ideal Functions)
• Log-Normal PDF (parameters  and ):
p( I ) 
1
2    I

e
(log I   ) 2
2 2
Higher-order Moments:
k  e
1 2 2
k   k
2
•Rice-Nakagami PDF (parameters β and <I >):
p( I ) 
  (1   ) 
(1   )
(1   )
exp( 
 I )  exp(   )  I 0 2
I
I
I

I



Higher-order Moments: mk  (
higher-order cumulants:
I k
)  exp(   )  [(k  1) / (1)] 1 F1 (k  1;1;  )
(   1)
1
 k  k!  [   ]
k
2k
Copyright © 2009 Arun K. Majumdar
PROPOSED METHOD BASED ON HIGHER-ORDER MOMENTS
• Gamma-Gamma distribution PDF ( parameters  and  ):
2( ) (   ) / 2 (   ) / 2 1
p( I ) 
I
 K   (2 I ) ,
( )(  )
•
Higher-order Moments: mk 
1
( ) k

(k   )  ( k   )
( )  (  )
Copyright © 2009 Arun K. Majumdar
I 0
Simulation
• By generating random variables which follow a given
PDF
• The applying our theory of reconstruction of PDF using
these randomly generated variables
• define uniform variables p(r) drawn from a standard
probability density function that is uniform between r = 0
and pr(r=) 1 1: for 0  r  1


 0
 p(r )dr  1.dr
otherwise
Conservation of probability:
 p(r )dr   P( x)dx
r

x
r  
x  
or
1
0
r
x
r 0
x  
1.dr   P( x)dx
Thus the general result:
x
r
 P( x)dx
x  
Copyright © 2009 Arun K. Majumdar
cumulative distribution function of x, CDF(x)
x
CDF ( x) 
 P( x)dx

RESULTS : Test PDFs (Analytical Functions)
generalized-Laguerre fit to log-Normal with 6 moments: 10000 data values
0.45
ideal PDF
PDF fit
0.4
0.35
PDF(x)
0.3
0.25
0.2
0.15
0.1
0.05
0
-0.05
0
2
4
6
8
10
12
Random Variable, x
Figure . Generalized Laguerre PDF fit :10,000 data points : Log Normal distribution,
Moment Order = 6, parameters, mean = 1.0, sigma = 0.5
Copyright © 2009 Arun K. Majumdar
RESULTS : Test PDFs (Analytical Functions)
generalized-Laguerre fit to Rice-Nakagami with 8 moments: 3000 data
0.7 values
ideal PDF
PDF fit
0.6
0.5
0.4
PDF (x)
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
Random Variable, x
Figure . Generalized Laguerre PDF fit :3,000 data values : Rice Nakagami distribution,
Moment Order =8, parameters, mean = 1.5, beta = 0.5
Copyright © 2009 Arun K. Majumdar
RESULTS : Test PDFs (Analytical Functions)
generalized-Laguerre fit to gamma-gamma with 6 moments: 3000 data values
1.4
ideal PDF
PDF fit
1.2
1
0.8
PDF (x)
0.6
0.4
0.2
0
-0.2
0
0.5
1
1.5
2
2.5
3
3.5
4
Random Variable, x
•
Figure . Generalized Laguerre PDF fit :3,000 data values : Gamma-Gamma
distribution, Moment Order = 6, parameters, alpha = 17.13, beta = 16.04
Copyright © 2009 Arun K. Majumdar
RESULTS : Simulation using 5000 data samples
generated randomly to follow a given distribution
generalized-Laguerre fit to data LN5000 with 6 moments:
0.35 5000 data values
fit
nrm
0.3
histogram
Figure . Simulation with 5000 data points : PDF Fit: Log Normal distribution,
Moment Order = 6, generalized Laguerre fit, parameters, mean = 1.0, sigma = 0.5
0.25
PDF
0.2
0.15
0.1
generalized-Laguerre fit to data LN5000 with 6 moments:
5000 data values
fit
nrm
0.9
histogram
0.8
1
0.05
0
0.050
2
4
6
8
Intensity
10
0.7
12
0.6
CDF
Figure . Simulation with 5000 data points : CDF Fit: Log Normal distribution,
Moment Order = 6, generalized Laguerre fit, parameters,
mean = 1.0, sigma = 0.5
0.5
0.4
0.3
0.2
0.1
0
0
2
4
Copyright © 2009 Arun K. Majumdar
6
8
Intensit
y
10
12
RESULTS : Simulation using 5000 data samples
generated randomly to follow a given distribution
generalized-Laguerre fit to Rice-Nakagami with 6 moments:
0.7 5000 data values
fit
Figure . Simulation with 5000 data points : PDF Fit: Rice Nakagami distribution,
Moment Order = 6, generalized Laguerre fit, parameters, mean = 1.5, beta = 0.5
nrm histogram
0.6
0.5
PDF
0.4
0.3
0.2
generalized-Laguerre fit to Rice-Nakagami with 6 moments:
1 5000 data values
fit
nrm
0.9
histogram
0.8
0.1
0
0
1
2
3
4
Intensity
5
6
7
0.7
0.6
CDF C 0.5
D
F
0.4
Figure . Simulation with 5000 data points : CDF Fit: Rice Nakagami distribution,
Moment Order = 6, generalized Laguerre fit, parameters, mean = 1.5, beta = 0.5
0.3
0.2
0.1
0
0 K. Majumdar
1
2
Copyright © 2009 Arun
3
4
Intensit
Intensity
y
5
6
7
RESULTS : Simulation using 5000 data samples
generated randomly to follow a given distribution
generalized-Laguerre fit to data GG5000 with 6 moments:
1.4
fit
Nrm
histogram
1.2
Figure . Simulation with 5000 data points : PDF Fit: Gamma-Gamma distribution,
Moment Order = 6, generalized Laguerre fit, parameters, alpha = 17.13, beta = 16.04
1
0.8
0.6
0.4
generalized-Laguerre fit to data GG5000 with 6 moments:
1
0.2
fit
nrm
0.9
0
0.8
-0.2
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Intensity
y
0.7
0.6
0.5
Figure . Simulation with 5000 data points : CDF Fit: Gamma-Gamma distribution,
Moment Order = 6, generalized Laguerre fit, parameters, alpha = 17.13, beta = 16.04
0.4
0.3
0.2
0.1
0
0
0.5
1
1.5
2
2.5
Intensity
Copyright © 2009 Arun K. Majumdar
3
3.5
4
4.5
5
CONCLUSIONS AND SUMMARY
• A new method of reconstructing and predicting an
unknown probability density function (PDF) is presented
• The method is based on a series expansion of
generalized Laguerre polynomials and generates the
PDF from the data moments without any prior knowledge
of specific statistics, and converges smoothly
• We have applied this method to both the analytical
PDF’s and simulated data, which follow some known
non-Gaussian test PDFs such as Log-Normal, RiceNakagami and Gamma-Gamma distributions
• Results show excellent agreement of the PDF fit was
obtained by the method developed
• The utility of reconstructed PDF relevant to free-space
laser communication is pointed out
Copyright © 2009 Arun K. Majumdar
Atmospheric Turbulence Effects in the
Solar blind Ultraviolet (SBUV)region
• Research Data not easily available in the literature, specifically in
this wavelength region (most work on the effects of optical
turbulence has been done for visible or near-infrared wavelengths)
• But, the effects of atmospheric turbulence can severely degrade
performance of UV systems
• Can be a limiting factor for UV systems operating near the Ground
where turbulence is greatest
• Rytov solution to the wave equation: log-amplitude variance scales
as wavelength to the -7/6 power, which implies that the effects of
scintillation are two to three times greater in the SBUV than in the
visible
• Also implies that the log-amplitude variance in the SBUV would
become saturated at levels of turbulence approximately half those
required to cause saturation of visible light
• Thus, UV radiation should be much susceptible to turbulence
effects than visible light
Copyright © 2009 Arun K. Majumdar
Some turbulence results at SBUV
Daniel Hutt & David Tofsted, Optics & Laser Technology,vol.32, 39-48 (2000)
Time plot of turbulence structure parameter Cn2 and UV scintillation index σI2
UV scintillation vs. logamplitude variance
Measured UV scintillation vs. Cn2
Copyright © 2009 Arun K. Majumdar
Probability density function for intensity
Tatarskii’s Normalized intensity
fluctuations spectrum
D.W.Goodwin and A.J.Lindop, OPTICA
ACTA, Vol.23, no.4, 257-263 (1976)
Copyright © 2009 Arun K. Majumdar
Attenuation/Scattering Effects in UV region
Gary Shaw, et al: Proc.SPIE Vol. 6231,62310C(2006)
Jeffery Puschel & Robert Bayse:
http://ieeexplore.ieee.org/iel2/172/4485/00177806.pdf
Debbie Kedar & Shlomi Arnon, Applied Optics, Vol. 45,
No.33, 20 Nov. 2006
Copyright © 2009 Arun K. Majumdar
Summary of SBUV propagation
• Scattering effects for high data-rate laser communications in the
SBUV can cause pulse broadening, and consequently limit the
available bandwidth.
• The effects of atmospheric turbulence can be a limiting factor for
SBUV systems operating near the ground where turbulence is
greatest.
• Depending on the scenario (such as slant path, range, operating
platforms, etc.), the combined effects of scattering and turbulence
must be taken into account to evaluate the communications
performance.
Copyright © 2009 Arun K. Majumdar
Why UV – Uniqueness and
Devices
Spectrum
Unique Channel Characteristics
 Solar blind (=200-280nm)  high SNR
 High scattering  NLOS (relaxed PAT)
 High absorption  covert and jamming-proof
 High bandwidth (potentially high rate)
Recent Advances in Enabling Technologies
 UV LEDs (DARPA’s past SUVOS program, s-et.com)
 High fidelity UV PMTs (Hamamatsu, PerkinElmer)
 UV APDs (DARPA’s on-going DUVAP program)
 Solar blind filters
(OfilSystems.com)
Copyright
© 2009 Arun K. Majumdar
UV Eye & Skin Safety (ICNIRP)
18
Exposure Limits (mJ/cm2)
16
UV LED (divergence 5):
0.5mJ/9.62mm^2 = 5.2mJ/cm2 at focus
Safe distance: 5cm away from LED <3mJ/cm2
14
12
10
(270nm, 3mJ/cm2)
8
6
4
2
0
225
235
245
255
265
275
285
295
305
Wavelength (nm)
Close proximity: UV protective eyewear,
faceshield,
and
gloves, and adhesive backed warning signs
Copyright
© 2009clothing
Arun K.
Majumdar
Typical Tx/Rx Configurations
Three scenarios in each of LOS and NLOS cases:
(1) smallest bandwidth but lowest pointing requirements
(2) medium bandwidth
(3) largest bandwidth,
certain
pointing
Copyright © 2009
Arun K.
Majumdar
Atmospheric Channel Attenuation
Inverse square law [Allard’1876] I exp(  K r ) / r 2
0
e
Coefficients [Reilly’76]
molecular
S: Scattering
A: Absorption
m: molecular
a: aerosol
Extinction coeff
unit: km-1
aerosol
total
 (nm)
KSm
KAm
Km
KSa
KAa
Ka
KS
KA
Ke
200
0.95
7.2
8.12
1.6
0.49
2.1
2.6
7.7
10.2
250
0.34
0.79
1.12
1.5
0.24
1.7
1.8
1.0
2.8
300
0.15
0.02
0.17
1.4
0.10
1.5
1.6
0.12
1.7
Scattering angular distribution (phase function)
 Isotropic, modified Rayleigh, Henyey-Greenstein
3
1  3   (1   )  2 
P Ray (  ) 
Rayleigh:
16 (1  2 )
particle size <<

2 
2
1 g 
1
0.5(3  1)  Mie:
P Mie (  ) 

f
3
3
particle size /10
2
2 
4  1  g 2  2 g  2
1

g






ksRay Ray
ksMie Mie
  cos 
P(  ) 
P ( Copyright
)  © 2009
P (Arun
 ) K. Majumdar
ks
ks
Total:
weighted sum
Path Loss Model
 ke r (sin 1  sin  2 ) 
96r sin 1 sin  2 (1  cos ) exp 

2
sin

Pt
s


L 
Pr
ks P (cos( s )) Ar122 sin  s (12sin 2  2  22 sin 2 1 )
1
2
 L   (1 ,2 , 1 , 2 )r (1 ,2 ,1 ,2 ) e (1 ,2 ,1 ,2 ) r
V
s
r1
r2
1
2
Tx
1
2
r
Pt f r 

Quantum-limited BER: BER  0.5exp 

Copyright © 2009 Arun K. Majumdar
 L(hc /  ) R 
Rx
BER vs. SNR (OOK)
1.0E+0
1.0E-1
BER
1.0E-2
1.0E-3
1.0E-4
1.0E-5
Predicted BER
Measured BER
1.0E-6
1
10
SNR
200s
pulse,
variable
and 2, r =25m
Copyright
© 2009
Arun K.1Majumdar
100
Multiple Scattering Model for
Communications
•
(Reference: Haipeng Ding, Gang Chen, Arun K. Majumdar, Brian M. Sadler, Zhengyuan
Xu,”Modeling of Non-Line-of-Sight Ultraviolet Scattering Channels for Communications,”, IEEE
Journal on Selected Areas in Communications, Vol. 27, No.9, December 2009.)
• Based on photon tracing
– Expected channel impulse response obtained by computing
“photon arrival probabilities” and “associated propagation delay”
at the receiver
– Reliable prediction of NLOS path loss at small to medium
elevation angles (more accurate than single scattering theory)
– Predicted impulse response determines the channel bandwidth
Copyright © 2009 Arun K. Majumdar
NLOS UV communications link geometry
Receiver
Transmitter
Copyright © 2009 Arun K. Majumdar
Monte Carlo Impulse Response Model
= Rayleigh scattering co-efficient
= Mie scattering co-efficient
= absorption co-efficient
= total scattering
co--efficient
= extinction co-efficient
Simulate the multiple scattering process as s succession of elementary events
whose probability laws are known. Light is decomposed into a set of photons and
an individual photon migration process is modeled by the physical law that
governs this photon’s position migration. An emitted source photon moves a
distance
to a new location, where it may be scattered and absorbed with a
certain probability. The photon is repeatedly migrated until it either reaches the
receiver or its survival probability is smaller than the threshold value whereupon it
is considered lost.
Copyright © 2009 Arun K. Majumdar
Monte Carlo Impulse Response Model (contd..)
• STEPS:
• For each photon:
– 1. Compute the photon’s emission direction and its initial
survival probability
– 2. compute the propagation path length to the next scatter,
calculate the arrival probability, and update the survival
probability
– 3. repeat step.2 by using photon’s new direction model until
the photon’s survival probability is below the threshold (lost
photon), otherwise the photon successfully arrives at the
receiver
Repeat the process for N photons:
Sum the probabilities of the photons that reach at the receiver
at the same time
channel response time due to N
photons
after normalization by all photons’ energy
gives the “impulse response”
Copyright © 2009 Arun K. Majumdar
Simulated Impulse response for multiple and
single scattering conditions
Copyright © 2009 Arun K. Majumdar
Experimental verification of Monte Carlo path loss
prediction and parametric impulse response
Parametric model (Gamma
function) :
3-DB bandwidth:
Copyright © 2009 Arun K. Majumdar
Summary, Conclusions and
Recommendations for Future Research
• Measurement of atmospheric turbulence parameters are
essential for predicting lasercom system performance
• Need accurate model for PDF of intensity fluctuations
through atmospheric turbulence: necessary for
communication system design for achieving better
system performance
• Non-line-of-sight UV communications to develop new
technology for short-range secure communications:
concepts applied also to underwater optical
communications
Copyright © 2009 Arun K. Majumdar