Prof. Brandt-Pearce Lecture 2 Channel Modeling

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

2. Channel Effects • 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)

3. Attenuation • 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 sizelarger than a molecule.

4. Attenuation Weather conditions and their visibility range values 1 1Free-space optics by Willebrand and Ghuman, 2002

5. Attenuation Signal Attenuation coefficient at λ = 850 nm. Thick fog Clear air

6. 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 (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

7. 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 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

8. Attenuation due to Absorption Atmospheric absorption transmittance at sea level over 1820 m horizontal path1 1Free-space optics by Willebrand and Ghuman, 2002

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

10. 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

11. 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 1Bucholtzr, A., “Rayleigh-scattering calculations for the terrestrial atmosphere,” Applied Optics 34 (1995).

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

13. 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

14. 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 (Friistransmission equation)

15. 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 important • Lenses and their focal length play an important role in determining the spot size • Small spot size requires low receiver field of view (FoV)

16. 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 16

17. Attenuation: Link Budget Example 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.

18. Turbulence • 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 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.

19. Turbulence • 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

20. Turbulence • Atmospheric turbulence effects include • Beam wander: caused by a large-scale turbulence • Beam scintillation • In imaging detector they causes speckle pattern

21. Turbulence – Experimental Results 21

22. Turbulence • 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.

23. Turbulence • 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)

24. Turbulence Values of α and β under different turbulence regimes: weak, moderate to strong and saturation Log-normal Negative exponential Gamma–gamma

25. 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

26. 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 emittanceof the sun • Extended sources, such as sky or lighting in urban areas • Irradiance: • N(λ): spectral radiance of the sky • Ω: photodetector’sfield of view angle in radians • Celestial bodies such as stars affect deep space FSO systems

27. 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