A novel accurate and useful approximation of the well-known Beckmann distribution is presented here, which is used to model generalized pointing errors in the context of free-space optical (FSO) communication systems. We derive an approximate closed-form probability density function (PDF) for the composite gamma-gamma (GG) atmospheric turbulence with the pointing error model using the proposed approximation of the Beckmann distribution, which is valid for most practical terrestrial FSO links. This approximation takes into account the effect of the beam width, different jitters for the elevation and the horizontal displacement and the simultaneous effect of nonzero boresight errors for each axis at the receiver plane. Additionally, the proposed approximation allows us to delimit two different FSO scenarios. The first of them is when atmospheric turbulence is the dominant effect in relation to generalized pointing errors, and the second one when generalized pointing error is the dominant effect in relation to atmospheric turbulence. The second FSO scenario has not been studied in-depth by the research community. Moreover, the accuracy of the method is measured both visually and quantitatively using curve-fitting metrics. Simulation results are further included to confirm the analytical results.

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An unsuitable alignment between transmitter and receiver together with fluctuations in the irradiance of the transmitted optical beam due to the atmospheric turbulence can severely degrade the performance of free-space optical (FSO) systems. In this paper, cooperative FSO communications with decode-and-forward (DF) relaying and equal gain combining (EGC) reception over atmospheric turbulence and misalignment fading channels is analyzed in order to mitigate these impairments. Novel closed-form asymptotic bit error-rate (BER) expressions are derived for a 3-way FSO communication setup when the irradiance of the transmitted optical beam is susceptible to either a wide range of turbulence conditions (weak to strong), following a gamma-gamma distribution of parameters α and β , or pointing errors, following a misalignment fading model where the effect of beam width, detector size and jitter variance is considered. Obtained results provide significant insight into the impact of various system and channel parameters, showing that the diversity order is independent of the pointing error when the equivalent beam radius at the receiver is at least 2β 1/2 times the value of the pointing error displacement standard deviation at the receiver. It is contrasted that the available diversity order is strongly dependent on the relay location, achieving greater diversity gains when the diversity order is determined by β AC + β BC , where β AC and β BC are parameters corresponding to the turbulence of the source-destination and relay-destination links. Simulation results are further demonstrated to confirm the accuracy and usefulness of the derived results. site," URL http://functions.wolfram.com. 36. V. S. Adamchik and O. I. Marichev, "The algorithm for calculating integrals of hypergeometric type functions and its realization in REDUCE system," in Proc. Int. Conf. on Symbolic and Algebraic Computation, 212-224 (Tokyo, Japan, 1990).

Since free-space optical (FSO) systems are usually installed on high buildings and building sway may cause vibrations in the transmitted beam, an unsuitable alignment between transmitter and receiver together with fluctuations in the irradiance of the transmitted optical beam due to the atmospheric turbulence can severely degrade the performance of optical wireless communication systems. In this paper, asymptotic bit error-rate (BER) performance for FSO communication systems using transmit laser selection over atmospheric turbulence channels with pointing errors is analyzed. Novel closed-form asymptotic expressions are derived when the irradiance of the transmitted optical beam is susceptible to either a wide range of turbulence conditions (weak to strong), following a gamma-gamma distribution of parameters α and β, or pointing errors, following a misalignment fading model where the effect of beam width, detector size and jitter variance is considered. Obtained results provide significant insight into the impact of various system and channel parameters, showing that the diversity order is independent of the pointing error when the equivalent beam radius at the receiver is at least 2(min{α,β})(1/2) times the value of the pointing error displacement standard deviation at the receiver. Moreover, since proper FSO transmission requires transmitters with accurate control of their beamwidth, asymptotic expressions are used to find the optimum beamwidth that minimizes the BER at different turbulence conditions. Simulation results are further demonstrated to confirm the accuracy and usefulness of the derived results, showing that asymptotic expressions here obtained lead to simple bounds on the bit error probability that get tighter over a wider range of signal-to-noise ratio (SNR) as the turbulence strength increases.

A new upper bound on the capacity of power-and bandwidth-constrained optical wireless links over gamma-gamma atmospheric turbulence channels with intensity modulation and direct detection is derived when on-off keying (OOK) formats are used. In this free-space optical (FSO) scenario, unlike previous capacity bounds derived from the classic capacity of the well-known additive white Gaussian noise (AWGN) channel with uniform input distribution, a new closed-form upper bound on the capacity is found by bounding the mutual information subject to an average optical power constraint and not only to an average electrical power constraint, showing the fact that the input distribution that maximizes the mutual information varies with the turbulence strength and the signal-to-noise ratio (SNR). Additionally, it is shown that an increase of the peak-to-average optical power ratio (PAOPR) provides higher capacity values. Simulation results for the mutual information are further demonstrated to confirm the analytical results under several turbulence conditions.

Atmospheric turbulence produces fluctuations in the irradiance of the transmitted optical beam, which is known as atmospheric scintillation, severely degrading the performance over free-space optical (FSO) links. Additionally, since FSO systems are usually installed on high buildings, building sway causes vibrations in the transmitted beam, leading to an unsuitable alignment between transmitter and receiver and, hence, a greater deterioration in performance. In this paper, the outage probability as a performance measure for multiple-input/multiple-output (MIMO) FSO communication systems with intensity modulation and direct detection (IM/DD) over strong atmospheric turbulence channels with pointing errors is analyzed. Novel closed-form expressions for the outage probability as well as their corresponding asymptotic expressions are presented when the irradiance of the transmitted optical beam is susceptible to either strong turbulence conditions, following a negative exponential distribution, and pointing error effects, following a misalignment fading model where the effect of beam width, detector size and jitter variance is considered. Obtained results show that the diversity order is independent of the pointing error when the equivalent beam radius at the receiver is at least twice the value of the pointing error displacement standard deviation at the receiver. Simulation results are further demonstrated to confirm the analytical results. Additionally, since proper FSO transmission requires transmitters with accurate control of their beamwidth, asymptotic expressions here obtained for different diversity techniques are used to find the optimum beamwidth that minimizes the outage performance.

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In this work, the ergodic capacity performance for multiple-input/single-output (MISO) free-space optical (FSO) communications system with equal gain combining (EGC) reception is analyzed over gamma-gamma and misalignment fading channels, which are modeled as statistically independent, but not necessarily identically distributed (i.n.i.d.). Novel and analytical closed-form ergodic capacity expression is obtained in terms of H-Fox function by using the well-known inequality between arithmetic and geometric mean of positive random variables (RV) in order to obtain an approximate closed-form expression of the distribution of the sum of M gamma-gamma with pointing errors variates. In addition, we present an asymptotic ergodic capacity expression at high signal-to-noise ratio (SNR) for the ergodic capacity of MISO FSO systems. It can be concluded that the use of MISO technique can significantly reduce the effect of the atmospheric turbulence as well as pointing errors and, hence, provide significant capacity gain over the direct path link (DL). The impact of pointing errors on the MISO FSO system is also analyzed, which only depends on the number of laser sources and pointing error parameters. Moreover, it can be also concluded that the ergodic capacity performance is dramatically reduced as a consequence of the severity of pointing error effects. Simulation results are further demonstrated to confirm the analytical results.