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

2. 2  Attenuation (Loss) Absorption Scattering 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

3. 3 Attenuation

4. 4 Weather conditionVisibility range (m)Loss dB/km Thick fog200 300 Moderate fog500120 Light fog 770 – 100025 Thin fog/heavy rain (25mm/hr)1900 – 200025 Haze/medium rain (12.5mm/hr) 2800 – 4000010 Clear/drizzle (0.25mm/hr)18000 – 200001 Very clear23000 – 500000.2 Weather conditions and their visibility range values 1 1 Free-space optics by Willebrand and Ghuman, 2002 Attenuation

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

6. 6  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. 7   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

8. 8 Atmospheric absorption transmittance at sea level over 1820 m horizontal path 1 1 Free-space optics by Willebrand and Ghuman, 2002

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

10. 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. 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 1 Bucholtzr, A., “Rayleigh-scattering calculations for the terrestrial atmosphere,” Applied Optics 34 (1995).

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

13. 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. 14 Attenuation due to Beam Divergence  Transmitter effective antenna gain:

15. 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. 16 Total Link Loss  Atmospheric link with receive spot larger than the receive aperture:  η t : transmit optics efficiency  η A : transmit aperture illumination efficiency  A t : effective area of transmit optics  A r : effective area of receive optics  η r : receive optics efficiency  L tp ; transmit pointing loss  L rp : receive pointing loss  L atm : atmospheric loss  L pol : polarization mismatch  L: link length

17. 17 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.

18. 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. 19  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

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

21. 21 Turbulence – Experimental Results

22.  Due to the turbulence a fluctuation is introduced on the received irradiance 22 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

23.  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) 23 Turbulence

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

25. 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. 26  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

27. 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