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1 Prof. Brandt- Pearce Lecture 2 Channel Modeling Optical Wireless Communication s

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Prof. Brandt-Pearce

Lecture 2

Channel Modeling

Optical Wireless Communications

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Attenuation (Loss)

Absorption

Scattering

Rayleigh scattering (atmospheric gases molecules)

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 conditionVisibility range (m)Loss dB/kmThick fog200 300 Moderate fog 500120Light fog 770 100025Thin fog/heavy rain (25mm/hr)1900 200025Haze/medium rain (12.5mm/hr) 2800 4000010Clear/drizzle (0.25mm/hr)18000 200001Very clear23000 500000.2

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 = 850 nm.

Thick fog

Clear air

Attenuation

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Attenuation

Low Clouds

Very similar to fog

May accompany rain and snow

Rain

Drop sizes larger than fog and wavelength of light

Extremely heavy rain (cant 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 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): elasticscattering of light by molecules andparticulate mattermuch 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 is (=cos )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)

Elasticscattering of light by molecules andparticulate mattermuch 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 is 1

where

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 is 1

g: aerosol asymmetry parameter given by the mean cosine of the scattering angle

f: aerosol hemispheric backscatter fraction

1 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 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

: 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:

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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 area

Additional power penalty is usually incurred due to lack of perfect alignment of the transmitter and receiver

For short FSO links (