Optical Wireless
Prof. Brandt-Pearce
Lecture 2
Channel Modeling
Channel Effects
Attenuation (Loss)
o Rayleigh scattering (atmospheric gases molecules)
o Mie scattering (aerosol particles)
 Beam divergence
 Pointing Loss
Atmospheric (refractive) turbulence
Beam wander
Background light (Sun)
Atmospheric attenuation: loss of part of optical energy when traversing
Attenuation is due to absorption and/or scattering
ml : molecular absorption coefficient
al : Aerosol absorption coefficient
 : Transmitted Power
 : Received Power
: Path Length
ml : molecular scattering coefficient
al : Aerosol scattering coefficient
An aerosol is a suspension of solid or liquid particles in a gaseous medium,
with size larger than a molecule.
Weather conditions and their visibility range values 1
Weather condition
Thick fog
Moderate fog
Light fog
Thin fog/heavy rain (25mm/hr)
Haze/medium rain (12.5mm/hr)
Clear/drizzle (0.25mm/hr)
Very clear
optics by Willebrand and Ghuman, 2002
Visibility range (m)
770 – 1000
1900 – 2000
2800 – 40000
18000 – 20000
23000 – 50000
Loss dB/km
Signal Attenuation coefficient at λ = 850 nm.
Thick fog
Clear air
 Low Clouds
– Very similar to fog
– May accompany rain and snow
 Rain
– Drop sizes larger than fog and wavelength of light
– Extremely heavy rain (can’t see through it) can take a link down
– Water sheeting on windows
 Heavy Snow
– May cause ice build-up on windows
– Whiteout conditions
 Sand Storms
– Likely only in desert areas; rare in the urban core
Attenuation due to Absorption
Absorption: the energy of a photon is taken by gas molecules or particles
and is converted to other forms of energies
This takes place when there is an interaction between the propagating
photons and molecules (present in the atmosphere) along its path
Primarily due to water vapor and carbon dioxide
Wavelength dependent
This leads to the atmosphere having transparent zones (range of
wavelengths with minimal absorptions) referred to as the transmission
It is not possible to change the physics of the atmosphere, therefore,
wavelengths adopted in FSO systems are basically chosen to coincide
with the atmospheric transmission windows
Attenuation due to Absorption
Atmospheric absorption transmittance at sea level over 1820 m
horizontal path1
optics by Willebrand and Ghuman, 2002
Attenuation due to Scattering
 Scattering: dispersion of a beam into other direction due to
particles in air
 This results in angular redistribution of the optical field with and
without wavelength dependence
 Depends on the radius of the particles
Two type of scattering:
Rayleigh scattering (Molecule): elastic scattering of light by
molecules and particulate matter much smaller than the wavelength of the
incident light.
 Mie Scattering (Aerosol): broad class of scattering of light by
spherical particles of any diameter.
 Scattering phase function at angle θ is (μ=cos θ)1
Zachor, A. S., “Aureole radiance field about a source in a scattering-absorbing medium,” Applied Optics,.)1978(
Rayleigh Scattering (Molecular)
 Elastic scattering of light by molecules and particulate matter much
smaller than the wavelength of the incident light.
 Rayleigh scattering intensity has a very strong dependence on the size
of the particles (it is proportional the sixth power of their diameter).
 It is inversely proportional to the fourth power of the wavelength of
light: the shorter wavelength in visible white light (violet and blue) are
scattered stronger than the longer wavelengths toward the red end of
the visible spectrum.
 The scattering intensity is generally
not strongly dependent on the
wavelength, but is sensitive to the
particle size.
 Responsible for the blue color of the
sky during the day
Rayleigh Scattering
 For a single molecule, the scattering phase function at angle θ is 1
ρ is the depolarization parameter
 A simplified expression describing the Rayleigh scattering 1
  : number of particles per unit volume
  : the cross-sectional area of scattering
Bucholtzr, A., “Rayleigh-scattering calculations for the terrestrial atmosphere,” Applied Optics 34.)1995(
Mie Scattering (Fog. Haze, Rain)
 Broad class of scattering of light by spherical particles of any
 The scattering intensity is generally not strongly dependent on the
wavelength, but is sensitive to the particle size.
 Mie scattering intensity for large particles is proportional to the
square of the particle diameter.
 Coincides with Rayleigh scattering in the special case where the
diameter of the particles is much smaller than the wavelength of
the light; in this limit, however, the shape of the particles no
longer matters.
 The scattering phase function at angle θ is 1
g: aerosol asymmetry parameter given by the mean cosine of the scattering angle
f: aerosol hemispheric backscatter fraction
Zachor, A. S., “Aureole radiance field about a source in a scattering-absorbing medium,” Applied Optics,.)1978(
Attenuation due to Beam Divergence
 One of the main advantages of FSO systems is the ability to transmit a
very narrow optical beam, thus offering enhanced security But due to
diffraction, the beam spreads out This results in a situation in which the
receiver aperture is only able to collect a fraction of the beam.
 The remaining uncollected beam then results in beam divergence loss
Attenuation due to Beam Divergence
 Transmitter effective antenna gain:
: Diffraction limited beam divergence angle in radians
  : Aperture diameter
 In diffuse channels and FSO networks,  is non-diffraction limited and
determined by transmitter optics
: Radiation solid angle
 Receiver effective antenna gain:
 : Receiver effective aperture areas
 Free-space path loss:
  : Path length
 For transmitted power  , received power,  , is (Friis transmission equation)
Attenuation due to the Pointing Loss
 When the received signal is not centered on the detector, a part of
received signal may fall outside the detector area
 Additional power penalty is usually incurred due to lack of perfect
alignment of the transmitter and receiver
 For short FSO links (<1 km), this might not be an issue
 For longer link ranges, this can certainly not be neglected
 Misalignments could result from building sway or strong wind effect on
the FOS link head stand
 The ratio of the received beam spot size and detector area becomes
 Lenses and their focal length play an important role in determining the
spot size
 Small spot size requires low receiver field of view (FoV)
Total Link Loss
 Atmospheric link with receive spot larger than the receive aperture:
ηt: transmit optics efficiency
ηA: transmit aperture illumination efficiency
At: effective area of transmit optics
Ar: effective area of receive optics
ηr: receive optics efficiency
Ltp; transmit pointing loss
Lrp: receive pointing loss
Latm: atmospheric loss
Lpol: polarization mismatch
L: link length
Attenuation: Link Budget Example
Typical link budget for 2.5 Gbps, 2 km link, and 1550 nm wavelength
“Optical Wireless Communication Systems: Channel Modelling
with MATLAB”, Z.Ghassemlooy.
 Beam spreading and wandering due to propagation through air
pockets of varying temperature, density, and index of refraction.
 Almost mutually exclusive with fog attenuation.
 The interaction between the laser beam and the turbulent medium
results in random phase and amplitude variations of the informationbearing optical beam which ultimately results in fading of the
received optical power
 Results in increased bit-error-rate (BER) but not complete outage.
Atmospheric turbulence results in random fluctuation of the
atmospheric refractive index
Lens-like eddies result in a randomized interference effect between
different regions of the propagating beam causing the wavefront to be
distorted in the process
 Atmospheric turbulence effects include
 Beam wander: caused by a large-scale turbulence
 Beam scintillation
 In imaging detector they causes speckle pattern
Turbulence – Experimental
 Due to the turbulence a fluctuation is introduced on the received irradiance
 A measure of irradiance fluctuations can be given by the scintillation index:
 For weak fluctuations, it is proportional, and for strong fluctuations, it is
inversely proportional to the Rytov variance:
is the refractive-index structure parameter
Y. Tian, S.G. Narasimhan, A. J. Vannevel ,Proc. of Computer Vision and Pattern Recognition (CVPR), Jun, 2012.
Three most reported models for irradiance fluctuation in turbulent
 Log-normal (weak regimes)
 Gamma–gamma (weak-to-strong regimes)
 K-distribution (very strong regimes)
Negative exponential (saturated regimes)
Values of α and β under different turbulence
regimes: weak, moderate to strong and saturation
Negative exponential
Mitigating Turbulence Effects
 Multiple Transmitters Approach
(Courtesy Jaime Anguita: Ref. Jai Anguita, Mark A. Neifeld and Bane Vasic, “Multi-Beam Space-Time Coded Communication
Systems for Optical Atmospheric Channels,” Proc. SPIE, Free-Space Laser Communications VI, Vol. 6304, Paper # 50, 2006)
Aperture averaging and multiple beams is effective in reducing
scintillation, improving performance
Adaptive Optics approach can be incorporated to mitigate turbulence
effects for achieving free space laser communications
Background Light
 In FSO systems is divided into two types
 Localized point sources, such as the Sun
 Irradiance (power per unit area):
 W(λ): the spectral radiant emittance of the sun
 Extended sources, such as sky or lighting in urban areas
 Irradiance:
 N(λ): spectral radiance of the sky
 Ω: photodetector’s field of view angle in radians
 Celestial bodies such as stars affect deep space FSO systems
Other Effects
 There can be other effects
 Dispersion: wavelength dependence of refraction index can
cause optical signals with different wavelengths travel with
different speed.
 Multipath: reflections can occur for low altitude beams,
especially from sea surface for shipboard applications and for
underwater FSO links
 Nonlinearity: strong transmitted powers can cause nonlinear
effects in the channel

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