José María Garrido-Balsells

A Unifying Statistical Model for Atmospheric Optical Scintillation

In this paper we develop a new statistical model for the irradiance fluctuations of an unbounded optical wavefront (plane and spherical waves) propagating through a turbulent medium under all irradiance fluctuation conditions in homogeneous, isotropic turbulence. The major advantage of the model is that leads to closed-form and mathematically-tractable expressions for the fundamental channel statistics of an unbounded optical wavefront under all turbulent regimes. Furthermore, it unifies most of the proposed statistical models for the irradiance fluctuations derived in the bibliography providing, in addition, an excellent agreement with the experimental data.

Impact of pointing errors on the performance of generalized atmospheric optical channels

Recently, a new and generalized statistical model, called M or Málaga distribution, was proposed to model the irradiance fluctuations of an unbounded optical wavefront (plane and spherical waves) propagating through a turbulent medium under all irradiance fluctuation conditions in homogeneous, isotropic turbulence. Málaga distribution was demonstrated to have the advantage of unifying most of the proposed statistical models derived until now in the bibliography in a closed-form expression providing, in addition, an excellent agreement with published plane wave and spherical wave simulation data over a wide range of turbulence conditions (weak to strong). Now, such a model is completed by including the adverse effect of pointing error losses due to misalignment. In this respect, the well-known effects of aperture size, beam width and jitter variance are taken into account. Accordingly, after presenting the analytical expressions for the combined distribution of scintillation and pointing errors, we derive its centered moments of the overall probability distribution. Finally, we obtain the analytical expressions for the average bit error rate performance for the M distribution affected by pointing errors. Numerical results show the impact of misalignment on link performance.

On the capacity of M-distributed atmospheric optical channels.

In this Letter, closed-form expressions of ergodic capacity, outage probability, and outage rate are derived for an atmospheric optical communication link using intensity modulation and direct detection with unbounded optical wavefront propagating through a homogeneous and isotropic turbulent medium. The optical scintillation of the received signal is modeled with the recently proposed Málaga or M turbulence distribution. By taking advantage of this unifying statistical model, the expressions here presented are valid for all possible irradiance fluctuation conditions, leading to direct relationships between turbulence parameters and link capacity performance.

Physical-Layer Security in Free-Space Optical Communications

The communication between two legitimate peers in the presence of an external eavesdropper is studied from a physical-layer security perspective in the context of free-space optical (FSO) communications. We discuss viable mechanisms to eavesdrop the communication and study the effect of random optical irradiance fluctuations inherent to FSO communications on the probability of achieving a secure transmission. We observe that the joint effect of laser-beam divergence and turbulence-induced fading on the received irradiance, under certain conditions, allows an external eavesdropper close to the legitimate receiver to compromise the communication. Interestingly, we also observe that an eavesdropper placed close to the legitimate transmitter can easily compromise the communication by taking advantage of the larger attenuation suffered by the signal when propagating through the FSO link.

An efficient rate-adaptive transmission technique using shortened pulses for atmospheric optical communications

In free space optical (FSO) communication, atmospheric turbulence causes fluctuation in both intensity and phase of the received light signal what may seriously impair the link performance. Additionally, turbulent inhomogeneities may produce optical pulse spreading. In this paper, a simple rate adaptive transmission technique based on the use of variable silence periods and on-off keying (OOK) formats with memory is presented. This technique was previously proposed in indoor unguided optical links by the authors with very good performance. Such transmission scheme is now extensively analyzed in terms of burst error rate, and shown in this paper as an excellent alternative compared with the classical scheme based on repetition coding and pulse-position modulation (PPM), presenting a greater robustness to adverse conditions of turbulence.

Numerical model for the temporal broadening of optical pulses propagating through weak atmospheric turbulence

In atmospheric optical communications, propagating pulses may be influenced by pulse spreading owing to turbulence, above all in scenarios characterized by sand and/or dust atmosphere. The long-term temporal broadening of a space-time Gaussian pulse propagating along a horizontal path through weak optical turbulence is modeled by the behavior of a Gaussian filter, where its cutoff frequency is related to the physical parameters of the link. Thus, it could be incorporated in a direct way to a numerical simulation model.

Novel formulation of the ℳ model through the Generalized-K distribution for atmospheric optical channels.

In this paper, a novel and deeper physical interpretation on the recently published Málaga or ℳ statistical distribution is provided. This distribution, which is having a wide acceptance by the scientific community, models the optical irradiance scintillation induced by the atmospheric turbulence. Here, the analytical expressions previously published are modified in order to express them by a mixture of the known Generalized-K and discrete Binomial and Negative Binomial distributions. In particular, the probability density function (pdf) of the ℳ model is now obtained as a linear combination of these Generalized-K pdf, in which the coefficients depend directly on the parameters of the ℳ distribution. In this way, the Málaga model can be physically interpreted as a superposition of different optical sub-channels each of them described by the corresponding Generalized-K fading model and weighted by the ℳ dependent coefficients. The expressions here proposed are simpler than the equations of the original ℳ model and are validated by means of numerical simulations by generating ℳ -distributed random sequences and their associated histogram. This novel interpretation of the Málaga statistical distribution provides a valuable tool for analyzing the performance of atmospheric optical channels for every turbulence condition.

850-nm hybrid fiber/free-space optical communications using orbital angular momentum modes.

Light beams can carry orbital angular momentum (OAM) associated to the helicity of their phasefronts. These OAM modes can be employed to encode information onto a laser beam for transmitting not only in a fiber link but also in a free-space optical (FSO) one. Regarding this latter scenario, FSO communications are considered as an alternative and promising mean complementing the traditional optical communications in many applications where the use of fiber cable is not justified. This next generation FSO communication systems have attracted much interest recently, and the inclusion of beams carrying OAM modes can be seen as an efficient solution to increase the capacity and the security in the link. In this paper, we discuss an experimental demonstration of a proposal for next generation FSO communication system where a light beam carrying different OAM modes and affected by ℳ turbulence is coupled to the multimode fiber link. In addition, we report a better and more robust behavior of higher order OAM modes when the intermodal dispersion is dominant in the fiber after exceeding its maximum range of operation.

Spatially correlated gamma-gamma scintillation in atmospheric optical channels

In this paper, novel analytical closed-form expressions are derived for the probability density function of the sum of identically distributed correlated gamma-gamma random variables that models an optical atmospheric channel communication with receiver spatial diversity. The mathematical expressions here proposed provide a general procedure to obtain information about the scintillation effects induced by turbulence over a diversity reception scheme implementing equal-gain combining method. Both, validity and accuracy of the obtained statistical distribution are corroborated by comparing the analytical results to numerical results obtained by Monte-Carlo simulations. These simulations are particularized for constant, exponential and circular correlation models, corresponding to three different receivers spatial configurations. In addition, the extreme situations of no correlation and fully correlated received signals are also studied. The presented expressions lead to a simple and easy-to-compute analytical procedure of analyzing atmospheric optical communications systems with correlated spatial diversity.

A Computationally Efficient Numerical Simulation for Generating Atmospheric Optical Scintillations

Atmospheric optical communication has been receiving considerable attention recently for use in high data rate wireless links (Juarez et al., 2006; Zhu & Kahn, 2002). Considering their narrow beamwidths and lack of licensing requirements as compared to microwave systems, atmospheric optical systems are appropriate candidates for secure, high data rate, cost-effective, wide bandwidth communications. Furthermore, atmospheric free space optical (FSO) communications are less susceptible to the radio interference than radio-wireless communications. Thus, FSO communication systems represent a promising alternative to solve the last mile problem, above all in densely populated urban areas. Then, applications that could benefit from optical communication systems are those that have platforms with limited weight and space, require very high data links and must operate in an environment where fiber optic links are not practical. Also, there has been a lot of interest over the years in the possibility of using optical transmitters for satellite communications (Nugent et al., 2009). This chapter is focused on how to model the propagation of laser beams through the atmosphere. In particular, it is concerned with line-of-sight propagation problems, i.e., the receiver is in full view of the transmitter. This concern is referred to situations where if there were no atmosphere and the waves were propagating in a vacuum, then the level of irradiance that a receiver would observe from the transmitter would be constant in time, with a value determined by the transmitter geometry plus vacuum diffraction effects. Nevertheless, propagation through the turbulent atmosphere involves situations where a laser beam is propagating through the clear atmosphere but where very small changes in the refractive index are present too. These small changes in refractive index, which are typically on the order of 10−6, are related primarily to the small variations in temperature (on the order of 0.1-1◦C), which are produced by the turbulent motion of the atmosphere. Clearly, fluctuations in pressure of the atmosphere also induces in refractive index irregularities. Thus, the introduction of the atmosphere between source and receiver, and its inherent random refractive index variations, can lead to power losses at the receiver and eventually it produces spatial and temporal fluctuations in the received irradiance, i.e. turbulence-induced signal power fading (Andrews & Phillips, 1998); but this random variations in atmospheric refractive index along the optical path also produces fluctuations in other wave parameters such as phase, angle of arrival and frequency. Such fluctuations can produce an increase in the 7