Optical wireless communication (OWC) refers to transmission in unguided propagation media through the use of optical carriers, i.e., visible, infrared (IR), and ultraviolet (UV) bands. In this survey, we focus on outdoor terrestrial OWC links which operate in near IR band. These are widely referred to as free space optical (FSO) communication in the literature. FSO systems are used for high rate communication between two fixed points over distances up to several kilometers. In comparison to radio-frequency (RF) counterparts, FSO links have a very high optical bandwidth available, allowing much higher data rates. They are appealing for a wide range of applications such as metropolitan area network (MAN) extension, local area network (LAN)-to-LAN connectivity, fiber back-up, backhaul for wireless cellular networks, disaster recovery, high definition TV and medical image/video transmission, wireless video surveillance/monitoring, and quantum key distribution among others. Despite the major advantages of FSO technology and variety of its application areas, its widespread use has been hampered by its rather disappointing link reliability particularly in long ranges due to atmospheric turbulence-induced fading and sensitivity to weather conditions. In the last five years or so, there has been a surge of interest in FSO research to address these major technical challenges. Several innovative physical layer concepts, originally introduced in the context of RF systems, such as multiple-input multiple-output communication, cooperative diversity, and adaptive transmission have been recently explored for the design of next generation FSO systems. In this paper, we present an up-to-date survey on FSO communication systems. The first part describes FSO channel models and transmitter/receiver structures. In the second part, we provide details on information theoretical limits of FSO channels and algorithmic-level system design research activities to approach these limits. Specific topics include advances in modulation, channel coding, spatial/cooperative diversity techniques, adaptive transmission, and hybrid RF/FSO systems.

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Survey on Free Space Optical Communication: A Communication Theory Perspective

▪ AbstractThe coexistence in the deep ocean of a finite, stable stratification, a strong meridional overturning circulation, and mesoscale eddies raises complex questions concerning the circulation energetics. In particular, small-scale mixing processes are necessary to resupply the potential energy removed in the interior by the overturning and eddy-generating process. A number of lines of evidence, none complete, suggest that the oceanic general circulation, far from being a heat engine, is almost wholly governed by the forcing of the wind field and secondarily by deep water tides. In detail however, the budget of mechanical energy input into the ocean is poorly constrained. The now inescapable conclusion that over most of the ocean significant “vertical” mixing is confined to topographically complex boundary areas implies a potentially radically different interior circulation than is possible with uniform mixing. Whether ocean circulation models, either simple box or full numerical ones, neither explic...

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Vertical mixing, energy, and the general circulation of the oceans

The authors describe carbon system formulation and simulation characteristics of two new global coupled carbon–climate Earth System Models (ESM), ESM2M and ESM2G. These models demonstrate good climate fidelity as described in part I of this study while incorporating explicit and consistent carbon dynamics. The two models differ almost exclusively in the physical ocean component; ESM2M uses the Modular Ocean Model version 4.1 with vertical pressure layers, whereas ESM2G uses generalized ocean layer dynamics with a bulk mixed layer and interior isopycnal layers. On land, both ESMs include a revised land model to simulate competitive vegetation distributions and functioning, including carbon cycling among vegetation, soil, and atmosphere. In the ocean, both models include new biogeochemical algorithms including phytoplankton functional group dynamics with flexible stoichiometry. Preindustrial simulations are spun up to give stable, realistic carbon cycle means and variability. Significant differences...

GFDL’s ESM2 Global Coupled Climate–Carbon Earth System Models. Part I: Physical Formulation and Baseline Simulation Characteristics

We investigate the performance and design of free-space optical (FSO) communication links over slow fading channels from an information theory perspective. A statistical model for the optical intensity fluctuation at the receiver due to the combined effects of atmospheric turbulence and pointing errors is derived. Unlike earlier work, our model considers the effect of beam width, detector size, and jitter variance explicitly. Expressions for the outage probability are derived for a variety of atmospheric conditions. For given weather and misalignment conditions, the beam width is optimized to maximize the channel capacity subject to outage. Large gains in achievable rate are realized versus using a nominal beam width. In light fog, by optimizing the beam width, the achievable rate is increased by 80% over the nominal beam width at an outage probability of 10-5. Well-known error control codes are then applied to the channel and shown to realize much of the achievable gains.

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Outage Capacity Optimization for Free-Space Optical Links With Pointing Errors

We develop a model for the probability density function (pdf) of the irradiance fluctuations of an optical wave propagating through a turbulent medium. The model is a two-parameter distribution that is based on a doubly stochastic theory of scintillation that assumes that small-scale irradiance fluctuations are modulated by large-scale irradi- ance fluctuations of the propagating wave, both governed by indepen- dent gamma distributions. The resulting irradiance pdf takes the form of a generalized K distribution that we term the gamma-gamma distribution. The two parameters of the gamma-gamma pdf are determined using a recently published theory of scintillation, using only values of the refractive-index structure parameter C n (or Rytov variance) and inner scale l 0 provided with the simulation data. This enables us to directly calculate various log-irradiance moments that are necessary in the scaled plots. We make a number of comparisons with published plane wave and spherical wave simulation data over a wide range of turbu- lence conditions (weak to strong) that includes inner scale effects. The gamma-gamma pdf is found to generally provide a good fit to the simu- lation data in nearly all cases tested. © 2001 Society of Photo-Optical Instrumen-

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Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media

An extended random medium is modeled by a set of 2-D thin Gaussian phase-changing screens with phase power spectral densities appropriate to the natural medium being modeled. Details of the algorithm and limitations on its application to experimental conditions are discussed, concentrating on power-law spectra describing refractive-index fluctuations of the neutral atmosphere. Inner and outer scale effects on intensity scintillation spectra and intensity variance are also included. Images of single realizations of the intensity field at the observing plane are presented, showing that under weak scattering the small-scale Fresnel length structure of the medium dominates the intensity scattering pattern. As the strength of scattering increases, caustics and interference fringes around focal regions begin to form. Finally, in still stronger scatter, the clustering of bright regions begins to reflect the large-scale structure of the medium. For plane waves incident on the medium, physically reasonable inner scales do not produce the large values of intensity variance observed in the focusing region during laser propagation experiments over kilometer paths in the atmosphere. Values as large as experimental observations have been produced in the simulations, but they require inner scales of the order of 10 cm. Inclusion of an outer scale depresses the low-frequency end of the intensity spectrum and reduces the maximum of the intensity variance. Increasing the steepness of the power law also slightly increases the maximum value of intensity variance.

Intensity images and statistics from numerical simulation of wave propagation in 3-D random media

The energy and action flow through the small-scale part of the oceanic internal wave field is modeled by use of the eikonal technique, which is not subject to a weak interaction assumption. Both Monte Carlo calculations and a simplified model are presented and found to agree. It is found that the action flows toward slightly higher frequency (and thus the waves gain energy), in striking contrast to weak interaction predictions of a strong frequency decrease. The energy dissipation scales with depth as N2 cosh−1 (N/f), in agreement with measurements. The overall level is, however, a factor of 4 smaller than measurements. Possible sources of this discrepancy are discussed. A comparison is made with previous theoretical approaches for the depth dependence of dissipation.

Energy and action flow through the internal wave field: An eikonal approach

We analyze the pattern of phase and amplitude variations of seismic waves across the NORSAR array on a statistical basis in order to determine the statistical distribution of heterogeneities under NORSAR. Important observables that have been analyzed in the past are the phase (or travel time) and log amplitude variances and the transverse coherence functions (TCFs) of phase and amplitude fluctuations. We propose and develop the theory and methods of using other observables to reduce the degree of nouniqueness and increase the spatial resolution of the analysis. Most important are the angular coherence functions (ACFs), which characterize quantitatively the change in the pattern of fluctuations across the array from one incoming angle (or beam) to another and which have a different sensitivity to the depth distribution of heterogeneities than the TCFs. A combination of the ACFs and TCFs allows estimation of the power spectra of the P wave speed variations under the array as a function of depth. We use data for phase fluctuations from 104 incident beams and amplitude fluctuations from 185 beams with 2-Hz center frequency at NORSAR to calculate the three ACFs and three TCFs (of phase, log amplitude, and their cross coherence). The measured rms travel time fluctuation is 0.135 s, and the rms log amplitude fluctuation is 0.41. The half-coherence widths of the ACFs are 3° for log amplitude and 9° for phase. The half-coherence widths of the TCFs are 18 km for phase and less than the minimum separation between the elements of the array for log amplitude. In order to account for these features of the data, we adopt a two-overlapping-layer model for lithospheric and asthenospheric heterogeneities underneath NORSAR, with spectra that are band-limited between the wavelengths of 5.5 and 110 km. Our best model has an upper layer with a flat power spectrum extending from the surface to about 200 km, and a lower layer with a K−4 power spectrum extending from 15 to 250 km. The latter spectrum corresponds to an exponential correlation function with scale larger than the observation aperture (110 km). The rms P wave speed variations the in the range 1–4%. The small scale heterogeneities may be attributed to clustered cracks or intrusions; the larger-scale wavespeed heterogeneities are temperature or compositional heterogeneities that may be related to chemical differentiation, or dynamical processes in the boundary layer of mantle convection.

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Small-scale structure in the lithosphere and asthenosphere deduced from arrival time and amplitude fluctuations at NORSAR

We have calculated intensity spectra and variances for waves emanating from a point source and propagating through extended three-dimensional random media by simulation. Spectra of the medium fluctuations considered were power-law, power-law with inner scale, and Gaussian spectra. The simulations covered the regimes of weak fluctuations and strong focusing, including the peak of the intensity variance and beyond. The intensity variances are substantially larger than both the corresponding results for plane-wave incidence and the theoretical calculations for point sources by other authors. Our simulation results agree reasonably closely with the results of laserpropagation experiments over kilometer-length paths in the atmosphere.

Simulation of point-source scintillation through three-dimensional random media

We have carried out numerical simulations of waves traversing a three-dimensional random medium with Gaussian statistics and a power-law spectrum with inner-scale cutoff. The distributions of irradiance on the final observation screen provide the probability-density function (PDF) of irradiance. For both initially plane and initially spherical waves the simulation PDF’s in the strong-fluctuation regime lie between a K distribution and a log-normal-convolved-with-exponential distribution. We introduce a plot of the PDF of scaled log-normal irradiance, on which both the exponential and the lognormal PDF’s are universal curves and on which the PDF at both large and small irradiance is shown in detail. We have simulated a spherical-wave experiment, including aperture averaging, and find agreement between the simulated and the observed PDF’s.

Stanley M. Flatté

Papers

Intensity images and statistics from numerical simulation of wave propagation in 3-D random media

Energy and action flow through the internal wave field: An eikonal approach

Small-scale structure in the lithosphere and asthenosphere deduced from arrival time and amplitude fluctuations at NORSAR

Simulation of point-source scintillation through three-dimensional random media

Probability-density functions of irradiance for waves in atmospheric turbulence calculated by numerical simulation