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Prof. Brandt-Pearce

Lecture 2Channel Modeling

Optical Wireless Communications

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Attenuation (Loss)

AbsorptionScattering

o Rayleigh scattering (atmospheric gases molecules)o Mie scattering (aerosol particles)

Beam divergence Pointing Loss

Atmospheric (refractive) turbulence

Scintillation

Beam wander

Background light (Sun)

Channel Effects

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Atmospheric attenuation: loss of part of optical energy when traversing

atmosphere

: Transmitted Power : Received Power : Path Length

Attenuation is due to absorption and/or scattering

: molecular absorption coefficient : Aerosol absorption coefficient : molecular scattering coefficient : Aerosol scattering coefficient

An aerosol is a suspension of solid or liquid particles in a gaseous medium, with size larger than a molecule.

Attenuation

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Weather condition Visibility range (m) Loss dB/kmThick fog 200 300 Moderate fog 500 120Light fog 770 – 1000 25Thin fog/heavy rain (25mm/hr) 1900 – 2000 25Haze/medium rain (12.5mm/hr) 2800 – 40000 10Clear/drizzle (0.25mm/hr) 18000 – 20000 1Very clear 23000 – 50000 0.2

Weather conditions and their visibility range values 1

1Free-space optics by Willebrand and Ghuman, 2002

Attenuation

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Signal Attenuation coefficient at λ = 850 nm.

Th

ick fog

Clear air

Attenuation

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AttenuationLow 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

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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

windows

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

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Attenuation due to Absorption

Atmospheric absorption transmittance at sea level over 1820 m horizontal path1

1Free-space optics by Willebrand and Ghuman, 2002

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Attenuation due to ScatteringScattering: 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

1 Zachor, A. S., “Aureole radiance field about a source in a scattering-absorbing medium,” Applied Optics, (1978).

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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

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Rayleigh Scattering

For a single molecule, the scattering phase function at angle θ is 1

where

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

1 Bucholtzr, A., “Rayleigh-scattering calculations for the terrestrial atmosphere,” Applied Optics 34 (1995).

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Mie Scattering (Fog. Haze, Rain) Broad class of scattering of light by spherical particles of any

diameter.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 fraction1 Zachor, A. S., “Aureole radiance field about a source in a scattering-absorbing medium,” Applied Optics, (1978).

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Attenuation due to Beam DivergenceOne 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

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: 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:

Attenuation due to Beam Divergence Transmitter effective antenna gain:

: Receiver effective aperture areas

Free-space path loss:

: Path length For transmitted power , received power, , is (Friis transmission equation)

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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 areaAdditional 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 standThe ratio of the received beam spot size and detector area becomes

important Lenses and their focal length play an important role in determining the

spot sizeSmall spot size requires low receiver field of view (FoV)

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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

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Example

Typical link budget for 2.5 Gbps, 2 km link, and 1550 nm wavelength

Attenuation: Link Budget Example

“Optical Wireless Communication Systems: Channel Modelling with MATLAB”, Z.Ghassemlooy.

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TurbulenceBeam 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 information-

bearing optical beam which ultimately results in fading of the

received optical power

Results in increased bit-error-rate (BER) but not complete outage.

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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

Turbulence

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Turbulence

Atmospheric turbulence effects include

Beam wander: caused by a large-scale turbulence

Beam scintillation

In imaging detector they causes speckle pattern

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Turbulence – Experimental Results

Due to the turbulence a fluctuation is introduced on the received irradiance

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Turbulence

Y. Tian, S.G. Narasimhan, A. J. Vannevel ,Proc. of Computer Vision and Pattern Recognition (CVPR), Jun, 2012.

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

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Three most reported models for irradiance fluctuation in turbulent

channels:

Log-normal (weak regimes)

Gamma–gamma (weak-to-strong regimes)

K-distribution (very strong regimes)

Negative exponential (saturated regimes)

Turbulence

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Turbulence

Negative exponential

Values of α and β under different turbulence regimes: weak, moderate to strong and saturation

Gamma–gamma

Log-normal

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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

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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

Background Light

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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