Copyright © 2009 Arun K. Majumdar Recent research and development in Free-Space Laser Communications Lecture Series: 2 Brno University of Technology, Brno

Recent research and development in Free-Space Laser Communications

Lecture Series: 2

Brno University of Technology, Brno Czech RepublicDecember 1-6, 2009

Dr. Arun K. [email protected]

105 W. Mojave Rose Ave.Ridgecrest, California 93555,

USA

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

Background, need and recent R&D directions 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 links

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 space-

worthy 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

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

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

Strength of Turbulence, Cn2 parameter

• Structure Function (of a random variable, say refractive index):

• 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

3/22)( rCrD nn 00 Lrl

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, California2 Air Force Research Laboratory, Kirtland Air Force Base, New Mexico

3 QEI Technologies, Inc., Broomfield, Colorado4 R3, Inc., Albuquerque, New Mexico,

5 Air Force Research Laboratory, WPAFB, Ohio6 Boeing LTS, Inc., Kirtland AFB, New Mexico

7 DARPA /ATO, Arlington, Virginia

FREE-SPACE LASER COMMUNICATIONS VISPIE Optics & Photonics, 15-17 August, 2006 San Diego, California

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

- Rytov Variance, σr2

- Greenwood Frequency, fG

Optical remote sensing system detecting a point

source on the ground

H

Air-borne Imaging system

Aberrated wavefront

Spherical wave from point source

Turbulence

Point Source

Strength of Turbulence, Cn2 parameter

• Structure Function (of a random variable, say refractive index):

• 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

3/22)( rCrD nn 00 Lrl

Atmospheric Models• Hufnagel-Valley (HV) model:

where is the rms wind speed. Typical value of the parameter, A=1.7x10-14 m-2/3.

• Modified Hufnagel-Valley (MHV) model:

100exp

1500exp107.2

1000exp)10(

2700594.0)( 16105

22 h

Ahh

hhCn

100exp1090.1

1500exp1002.3

1000exp1016.8)( 151710542 hhh

hhCn

• SLC-Day model:

Cn2 = 0 0 m < h < 19 m

= 4.008 x 10^13h^-1.054 19 m < h < 230 m

= 1.300 x 10^-15 230 m < h < 850 m

= 6.352 x 10^-7h^-2.966 850 m < h < 7000m

= 6.209 x 10^-16h^-0.6229 7000 m <h < 20,000 m

CLEAR1 model:• Note: here h is altitude in kilometer above mean sea level

(MSL)22

10 )(log

13.223.1

ChBhAC

h

n

34.1013.2 h22

10 )(log ChBhACn

}]/)[(5.0exp{)(log 22210 FEhDChBhACn

where A= -10.7025, B= -4.3507 C= +0.8141

where A= -16.2897, B= +0.0335, C= -0.0134

where A= -17.0577, B= -0.0449, C= -0.0005 D= 0.6181, E= 15.5617, F= 3.4666

3034.10 h

Coherence length, r0

5/3

0

3/522

023/8

2

0 )(

6

11

6

5sin2

6sin

3

427

10

R

n R

rrdrCk

b

r

For Kolmogorov turbulence, the coherence length r0 of a spherical wave observed at slant range R from its point source is given by

884.65

6

5

242

6/5

b

2

0 k

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

5/3

0

23/523/50 /)1)((9.114

R

n R

rrdrCR

Rytov Variance:

R

nr R

rrrdrC

0

6/76/5

6/522 /1)(78.4

A critical time constant specifying the interval over which turbulence remains essentially unchanged derives from Greenwood

5/33/5

0

25/35/6 )()(sec31.2

R

nG rVrdrCf

Greenwood Frequency, fG :

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 temperature, wind speed and pressure.

• Relationship between Structure Function and Power Spectral Density: the structure function is related with the PSD in the inertial subrangeD(r) = 2(φ(0) - φ(r)) D(r) = Cx2 rp (0 < p < 2)

Cn2 = (79e-6* (p/T2))2 * Ct2

autocorrelation function= φ (r)

the autocorrelation function and the PSD are Fourier transform pairs

12

2sin

2

)1()( p

x kCpp

kW

RESULTS

Cn2 from scintillation measurements

1 6 . 6 1 6 . 8 1 7 1 7 . 2 1 7 . 4 1 7 . 6

1 0- 1 5

1 0- 1 4

1 0- 1 3

1 0- 1 2

Cn

2

M i s s i o n D a y / T i m e [ D a y s ]

Cn2 from Balloon (tethered-blimp)

measurements

Instruments3D-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

1 1018

1 1017

1 1016

1 1015

1 1014

1 1013

500

1000

1500

2000

2500

3000

raw datasmoothed dataplus 1 sigmaminus 1 sigma

Cn2 Profile

Cn2 (m^-2/3)

Alti

tude

(m

)

0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.61 10

18

1 1017

1 1016

1 1015

1 1014

MeasuredHufnagel-ValleyModified Hufnagel-ValleySLC-DayCLEAR1 Night

Cn2 Profile Comparison

Altitude (Km)

Cn2

(m

^-2/

3)

0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.61 10

18

1 1017

1 1016

1 1015

1 1014

MeasuredHufnagel-ValleyModified Hufnagel-ValleySLC-DayCLEAR1 Night

Cn2 Profile Comparison

Altitude (Km)

Cn2

(m

^-2/

3)

Comparison of ) Cn2 profile generated from tethered-blimp instrument measurement and various models.

Histogram of Cn2 : some typical examples

14.5 14 13.5 13 12.5 12 11.50

2

4

6

8

log10(Cn2 (m^-2/3))

FR

EQ

UE

NC

Y (

%)

15.5 15 14.5 14 13.5 13 12.50

5

10

log10(Cn2 (m^-2/3))

FR

EQ

UE

NC

Y (

%)

Table 1. Coherence length, r0, (cm)

Geometry of synthetic-aperture imaging system

Balloon Data HV Modified HV

SLC-Day CLEAR1

Air-borne sensor :Zenith Angle = 79.02 degRange (slant path length) = 7913 mWavelength λ= 1.55 μm

70.03±3.05 52.96 288.09 55.00 54.62

Table 2. Isoplanatic Angle,Ө0 (μrad)


Balloon Data

HV Modified HV SLC-Day CLEAR1


27.93 2.94 86.71 9.65 16.39

Table 3. Rytov Variance, σr2


Balloon Data

HV Modified HV SLC-Day CLEAR1


0.01 0.06 0.0009 0.02 0.02

Table 4. Greenwood Frequency, fG, (Hz)


Balloon Data

HV Modified HV

SLC-Day CLEAR1


20.62 108.69 5.94 42.39 33.29

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

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 913012 The Boeing Company, Directed Energy Systems, West Hills, CA 91304

FREE-SPACE LASER COMMUNICATIONS VIISPIE Optics & Photonics, 28-30 August, 2007 San Diego, California

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

- Probability of Fade Statistics

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

PROPOSED METHOD BASED ON HIGHER-

ORDER MOMENTS • Analytical techniques to reconstruct PDF from higher-

order 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

Gram-Charlier method:

8

1

22

)(2

]2/)[(exp)(

nnn xHC

mxxf

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


• sought-for PDF is given by a gamma PDF modulated by a series of generalized Laguerre polynomials:

0

)1( )()()(n

nng

xLWxfxf

)0( x )(xf gx is the random intensity is the gamma PDF

x22

2

xx

x

The generalized Laguerre polynomials are defined by

n

l

l

n l

x

ln

nxL

0

)1(

!

)(1)(

Using the orthogonality condition we can show that

n

l

ll

n llnl

xnW

0 )()!(!

)/()(!

is the intensity moment of order l lx


Test Probability Density Functions (Ideal Functions)• Log-Normal PDF (parameters and ):

2

2

2

)(log

2

1)(

I

eI

IpHigher-order Moments:

kk

k e

2221

•Rice-Nakagami PDF (parameters β and <I >):

II

IIII

Ip)1(

2)exp())1(

exp()1(

)( 0

Higher-order Moments: );1;1()]1(/)1([)exp())1(

( 11

kFkI

m kk

]1

[! 2

kk k

k higher-order cumulants:


• Gamma-Gamma distribution PDF ( parameters and ):

• Higher-order Moments:

0,)2()()(

)(2)( 12/)(

2/)(

IIKIIp

)()(

)()(

)(

1

kk

mkk

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 r = 1 :

Conservation of probability:

Thus the general result:

cumulative distribution function of x, CDF(x)

Thus, r = CDF(x).

otherwise

rforrp

0

101)(

0

1.1)( drdrrp

x

x

r

r

x

x

r

r

dxxPdrordxxPdrrp )(.1)()(0

x

x

dxxPr )(

x

dxxPxCDF )()(

RESULTS : Test PDFs (Analytical Functions)

Figure . Generalized Laguerre PDF fit :10,000 data points : Log Normal distribution, Moment Order = 6, parameters, mean = 1.0, sigma = 0.5

0 2 4 6 8 10 12 -0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45 generalized-Laguerre fit to log-Normal with 6 moments: 10000 data values

ideal PDF PDF fit

PDF(x)

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

0 1 2 3 4 5 6 7 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7 generalized-Laguerre fit to Rice-Nakagami with 8 moments: 3000 data values

ideal PDF PDF fit

Random Variable, x

PDF (x)


• Figure . Generalized Laguerre PDF fit :3,000 data values : Gamma-Gamma distribution, Moment Order = 6, parameters, alpha = 17.13, beta = 16.04

0 0.5 1 1.5 2 2.5 3 3.5 4 -0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4 generalized-Laguerre fit to gamma-gamma with 6 moments: 3000 data values

ideal PDF PDF fit

Random Variable, x

PDF (x)

RESULTS : Simulation using 5000 data samples generated randomly to follow a given distribution

0 2 4 6 8 10 12 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

generalized-Laguerre fit to data LN5000 with 6 moments: 5000 data values

fit nrm histogram

Intensity

CDF

0 2 4 6 8 10 12 -0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

PDF

Intensity

generalized-Laguerre fit to data LN5000 with 6 moments: 5000 data values

fit nrm 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

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 1 2 3 4 5 6 7 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

PDF

Intensity

generalized-Laguerre fit to Rice-Nakagami with 6 moments: 5000 data values

fit nrm histogram

0 1 2 3 4 5 6 7 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

CDF

Intensity

generalized-Laguerre fit to Rice-Nakagami with 6 moments: 5000 data values

fit nrm histogram

Intensity

CDF

Figure . Simulation with 5000 data points : PDF Fit: Rice Nakagami distribution, Moment Order = 6, generalized Laguerre fit, parameters, mean = 1.5, beta = 0.5

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 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 - 0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Intensity

y

generalized - Laguerre fit to data GG5000 with 6 moments:

fit Nrm histogram

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Intensity

generalized - Laguerre fit to data GG5000 with 6 moments:

fit nrm

Figure . Simulation with 5000 data points : PDF Fit: Gamma-Gamma distribution, Moment Order = 6, generalized Laguerre fit, parameters, alpha = 17.13, beta = 16.04

Figure . Simulation with 5000 data points : CDF Fit: Gamma-Gamma distribution, Moment Order = 6, generalized Laguerre fit, parameters, alpha = 17.13, beta = 16.04

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, Rice-Nakagami 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

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

Some turbulence results at SBUV

Time plot of turbulence structure parameter Cn2 and UV scintillation index σI

2

Measured UV scintillation vs. Cn2

UV scintillation vs. log-amplitude variance

Daniel Hutt & David Tofsted, Optics & Laser Technology,vol.32, 39-48 (2000)

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)

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

http://ieeexplore.ieee.org/iel2/172/4485/00177806.pdf

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.

Why UV – Uniqueness and Devices

Unique Channel CharacteristicsSolar blind (=200-280nm) high SNRHigh scattering NLOS (relaxed PAT)High absorption covert and jamming-proofHigh bandwidth (potentially high rate)

Recent Advances in Enabling TechnologiesUV 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)

Spectrum

UV Eye & Skin Safety (ICNIRP)

0

2

4

6

8

10

12

14

16

18

225 235 245 255 265 275 285 295 305

Wavelength (nm)

Ex

po

su

re L

imit

s (

mJ

/cm

2)

(270nm, 3mJ/cm2)

UV LED (divergence 5): 0.5mJ/9.62mm^2 = 5.2mJ/cm2 at focusSafe distance: 5cm away from LED <3mJ/cm2

Close proximity: UV protective eyewear, faceshield, clothing and gloves, and adhesive backed warning signs

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

Atmospheric Channel Attenuation

(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

molecular aerosol totalS: ScatteringA: Absorptionm: moleculara: aerosolExtinction coeffunit: km-1

Coefficients [Reilly’76]

23( ) 1 3 (1 )

16 (1 2 )RayP

Scattering angular distribution (phase function)Isotropic, modified Rayleigh, Henyey-Greenstein

3

2

2 2

32 2 2

1 1 0.5(3 1)( )

4 1 2 1

Mieg

P fg g g

( ) ( ) ( )Ray Mie

Ray Mies s

s s

k kP P P

k k

Rayleigh:particle size <<

Mie:particle size /10

20 exp( ) /eI K r rInverse square law [Allard’1876]

cos Total:weighted sum

Path Loss Model

1 2

2 2 1

2 1 21

2 2 2 21 2

(sin sin )96 sin sin (1 cos )exp

2 sin

(cos( )) sin (12sin sin )

e

st

r s s r s

k rr

PL

P k P A

0.5exp( / )

t f rPBER

L hc R

Rx1 2

r1 r2

V

1

2

r

Tx

s

Quantum-limited BER:

1 2 1 2 1 2 1 21 2 1 2

( , , , ) ( , , , )( , , , ) rL r e

BER vs. SNR (OOK)

200s pulse, variable 1 and 2, r =25m

1.0E-6

1.0E-5

1.0E-4

1.0E-3

1.0E-2

1.0E-1

1.0E+0

1 10 100

BE

R

SNR

Predicted BER

Measured BER

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

NLOS UV communications link geometry

Transmitter Receiver

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.

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”

Simulated Impulse response for multiple and single scattering conditions

Experimental verification of Monte Carlo path loss prediction and parametric impulse response

Parametric model (Gamma function) :

3-DB bandwidth:

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

Documents

Copyright © 2009 Arun K. Majumdar Recent research and development in Free-Space Laser Communications Lecture Series: 2 Brno University of Technology, Brno