On the scattering-induced fading for optical wireless links through seawater: statistical characterization and its applications.

Recent research has shown that an accurate underwater channel characterization is necessary for underwater optical wireless communication (UOWC) in order to improve its current limitations related to the achievable data rate and the link distance, as required in undersea optical networks. This paper presents a new statistical model to characterize the scattering effect in terms of a fading never considered before. In this way, the probability density function of the scattering-induced fading channel is derived by means of a Gamma distribution by using only one degree of freedom in clear ocean and coastal waters. The developed fading model is employed to compute the performance of UOWC systems in terms of bit error rate and outage probability along with turbulence-induced fading modeled by a Weibull distribution. The results prove that smaller diversity order values are achieved when scattering-induced fading is the dominant effect, i.e., when the condition σ s2>1ß 1 is satisfied, where σ s2 and ß1 are parameters related to the Gamma and Weibull distributions, respectively. Moreover, the optical power penalty due to scattering-induced fading is analytically evaluated in several turbulence conditions to provide a deeper insight. Optical power penalty values of up to 6 dB and 9 dB are achieved when compared with no scattering scenarios at moderate distances for clear ocean and coastal waters. As a key feature, scattering should be always considered in terms of fading for future designs of advanced UOWC systems. The analytical results are verified by Monte Carlo simulations.

Capacity of underwater optical wireless communication systems over salinity-induced oceanic turbulence channels with ISI.

Point-to-point underwater optical wireless communication (UOWC) links are mainly impaired by scattering due to impurities and turbidity in the open water, resulting in a significant inter-symbol interference (ISI) that limits seriously both channel capacity and the maximum practical information rate. This paper conducts, for the first time, the channel capacity analysis of UOWC systems in the presence of ISI and salinity-induced oceanic turbulence when the undersea optical channel is accurately modeled by linear discrete-time filtering of the input symbols. In this way, novel upper and lower bounds on channel capacity and mutual information are developed for non-uniform on-off keying (OOK) modulation when different constraints are imposed on the channel input. The results show that the capacity-achieving distribution, which is computed through numerical optimization, is discrete and depends on the optical signal-to-noise-ratio (SNR). Moreover, a non-uniform input distribution significantly improves the channel capacity of such systems affected by ISI and oceanic turbulence, especially at low optical SNR. Monte Carlo techniques are employed to test the developed bounds for different undersea optical channels with one, two and three casual ISI coefficients.

Impact of angular pointing error on BER performance of underwater optical wireless links.

Even in clear ocean water, underwater optical wireless communication (UOWC) is impaired not only by absorption and scattering, but also by oceanic turbulence and dynamic pointing errors which result in a fading channel, degrading the bit error rate (BER) performance. In this paper, for the first time, we quantify analytically the trade-off between geometric loss and misalignment in underwater scattering channels. A novel geometric loss model is developed which is used to compute the average BER in the presence of absorption and scattering over salinity-induced oceanic turbulence channels. Our findings suggest that UOWC systems are less sensitive to angular pointing errors due to jitter since scattering is able to alleviate such a fading effect at the expense of a higher attenuation due to geometric spread. Monte Carlo simulation results are further included to verify the developed BER expression which is valid over a wide range of signal-to-noise-ratio (SNR). Finally, the impact of inter-symbol interference (ISI) is also quantified by measuring the optical power penalty.

Secure communication for FSO links in the presence of eavesdropper with generic location and orientation.

When the beam waist at the receiver is significantly larger than the receiver size, free-space optical (FSO) links may be vulnerable to some optical tapping risks at the physical layer. In this paper, we conduct a new framework for the analysis of the secrecy performance in terms of the secrecy outage probability (SOP) of FSO systems affected by gamma-gamma (GG) turbulence-induced fading channels with pointing errors. As a key feature, we evaluate the SOP in the presence of an external eavesdropper with generic location and orientation. For that reason, a new misalignment error model is proposed to consider a non-orthogonal optical beam with respect to the photodetector plane at the eavesdropper's receiver, where the effective area is determined by a rotated ellipse. New approximate and asymptotic solutions at high signal-to-noise-ratio (SNR) for the secrecy performance are obtained in closed-form, which are verified by exact Monte Carlo simulations. By using the developed expressions, we analyze in greater detail some effects such as the SNR of the eavesdropper's channel, the normalized beamwidth at the receiver-side, and the location and orientation of the eavesdropper on the secrecy performance for different turbulence conditions.

Novel approximation of misalignment fading modeled by Beckmann distribution on free-space optical links.

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.

Impact of nonzero boresight pointing error on ergodic capacity of MIMO FSO communication systems.

A thorough investigation of the impact of nonzero boresight pointing errors on the ergodic capacity of multiple-input/multiple-output (MIMO) free-space optical (FSO) systems with equal gain combining (EGC) reception under different turbulence models, which are modeled as statistically independent, but not necessarily identically distributed (i.n.i.d.) is addressed in this paper. Novel closed-form asymptotic expressions at high signal-to-noise ratio (SNR) for the ergodic capacity of MIMO FSO systems are derived when different geometric arrangements of the receive apertures at the receiver are considered in order to reduce the effect of nonzero inherent boresight displacement, which is inevitably present when more than one receive aperture is considered. As a result, the asymptotic ergodic capacity of MIMO FSO systems is evaluated over log-normal (LN), gamma-gamma (GG) and exponentiated Weibull (EW) atmospheric turbulence in order to study different turbulence conditions, different sizes of receive apertures as well as different aperture averaging conditions. It is concluded that the use of single-input/multiple-output (SIMO) and MIMO techniques can significantly increase the ergodic capacity respect to the direct path link when the inherent boresight displacement takes small values, i.e. when the spacing among receive apertures is not too big. The effect of nonzero additional boresight errors, which is due to the thermal expansion of the building, is evaluated in multiple-input/single-output (MISO) and single-input/single-output (SISO) FSO systems. Simulation results are further included to confirm the analytical results.

Ergodic capacity analysis for DF strategies in cooperative FSO systems.

This paper focuses on the ergodic capacity analysis in the context of cooperative free-space optical (FSO) systems when the line of sight is available. Novel asymptotic closed-form expressions for the ergodic capacity corresponding to two different decode-and-forward (DF) strategies are obtained for a cooperative FSO communication system. Here, the atmospheric turbulence is modeled by a gamma-gamma distribution of parameters α and ß which allows to study a wide range of turbulence conditions (moderate-to-strong) as well as the effect of the misalignment with zero boresight. It is demonstrated that cooperative communications are able to achieve not only a better performance in terms of the error rate performance as well as outage probability than direct transmission, but also in terms of the channel capacity in the context of FSO systems without much increase in hardware. In this way, a 3-way FSO communication setup is considered, in which the cooperative protocol can be applied to achieve a greater ergodic capacity compared to a direct transmission. It can be concluded that a greater and robust capacity strongly dependent on the relay location is achieved compared to a direct transmission without cooperative communication when line of sight is available. Here, the line of sight is taken into account in order to achieve a significant robustness under different turbulence conditions and more severe pointing errors regardless of the relay location. Simulation results are further demonstrated to confirm the accuracy and usefulness of the derived results.

Novel space-time trellis codes for free-space optical communications using transmit laser selection.

In this paper, the deployment of novel space-time trellis codes (STTCs) with transmit laser selection (TLS) for free-space optical (FSO) communication systems using intensity modulation and direct detection (IM/DD) over atmospheric turbulence and misalignment fading channels is presented. Combining TLS and STTC with rate 1 bit/(s · Hz), a new code design criterion based on the use of the largest order statistics is here proposed for multiple-input/single-output (MISO) FSO systems in order to improve the diversity order gain by properly chosing the transmit lasers out of the available L lasers. Based on a pairwise error probability (PEP) analysis, closed-form asymptotic bit error-rate (BER) expressions in the range from low to high signal-to-noise ratio (SNR) are derived when the irradiance of the transmitted optical beam is susceptible to moderate-to-strong turbulence conditions, following a gamma-gamma (GG) 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 diversity orders of 2L and 3L when simple two-state and four-state STTCs are considered, respectively. Simulation results are further demonstrated to confirm the analytical results.

On the capacity of MISO FSO systems over gamma-gamma and misalignment fading channels.

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.

Impact of relay placement on diversity order in adaptive selective DF relay-assisted FSO communications.

The impact of relay placement on diversity order in adaptive selective decode-and-forward (DF) cooperative strategies is here investigated in the context of free-space optical (FSO) communications over atmospheric turbulence channels with pointing errors when line of sight is available. The irradiance of the transmitted optical beam here considered is susceptible to moderate-to-strong turbulence conditions, following a gamma-gamma (GG) distribution together with a misalignment fading model where the effect of beam width, detector size and jitter variance is considered. Novel closed-form approximate bit error-rate (BER) expressions are obtained for a cooperative FSO communication setup with N relays, assuming that these relays are located in an area similar to an annulus around source or destination node. An analytical expression is here found that determines the best selection criterion based on the knowledge of the channel state information (CSI) of source-relay or relay-destination links in order to significantly increase the diversity order corresponding to the cooperative strategy under study. It is concluded that the highest diversity order is achieved when the relation ß(SR(min)) > ß(SD) + ß(R(min)D) is satisfied, wherein ß(SR(min)), ß(R(min)D) and ß(SD) are parameters corresponding to the atmospheric turbulence conditions of source-relay and relay-destination link with the greatest scintillation index, and source-destination link, respectively.

Transmit alternate laser selection with time diversity for FSO communications.

In this paper, a new transmit alternate laser selection (TALS) scheme for FSO communication systems using intensity modulation and direct detection (IM/DD) over atmospheric turbulence and misalignment fading channels is presented when limited time diversity is available in the turbulent channel. Assuming channel state information (CSI) at the transmitter and receiver and a time diversity order (TDO) limited, we propose the transmit diversity technique based on the rotating selection of TDO out of the available L lasers corresponding to the optical paths with greater values of scintillation. Implementing repetition coding with blocks of TDO information bits, each information bit will be retransmitted TDO times using the TDO largest order statistics in an alternating way. Closed-form asymptotic bit error-rate (BER) expressions are derived when the irradiance of the transmitted optical beam is susceptible to moderate-to-strong turbulence conditions, following a gamma-gamma (GG) distribution, and pointing error effects, following a misalignment fading model where the effect of beam width, detector size and jitter variance is considered. Fully exploiting the potential time-diversity TDO available in the turbulent channel, a significant diversity gain is achieved, providing a diversity order of (2L + 1 - TDO)TDO/2.

Adaptive selective relaying in cooperative free-space optical systems over atmospheric turbulence and misalignment fading channels.

In this paper, a novel adaptive cooperative protocol with multiple relays using detect-and-forward (DF) over atmospheric turbulence channels with pointing errors is proposed. The adaptive DF cooperative protocol here analyzed is based on the selection of the optical path, source-destination or different source-relay links, with a greater value of fading gain or irradiance, maintaining a high diversity order. Closed-form asymptotic bit error-rate (BER) expressions are obtained for a cooperative free-space optical (FSO) communication system with Nr relays, when the irradiance of the transmitted optical beam is susceptible to either a wide range of turbulence conditions, following a gamma-gamma distribution of parameters α and ß, or pointing errors, following a misalignment fading model where the effect of beam width, detector size and jitter variance is considered. A greater robustness for different link distances and pointing errors is corroborated by the obtained results if compared with similar cooperative schemes or equivalent multiple-input multiple-output (MIMO) systems. Simulation results are further demonstrated to confirm the accuracy and usefulness of the derived results.

Improved BDF relaying scheme using time diversity over atmospheric turbulence and misalignment fading channels.

A novel bit-detect-and-forward (BDF) relaying scheme based on repetition coding with the relay is proposed, significantly improving the robustness to impairments proper to free-space optical (FSO) communications such as unsuitable alignment between transmitter and receiver as well as fluctuations in the irradiance of the transmitted optical beam due to the atmospheric turbulence. Closed-form asymptotic bit-error-rate (BER) expressions are derived for a 3-way FSO communication setup. Fully exploiting the potential time-diversity available in the relay turbulent channel, a relevant better performance is achieved, showing a greater robustness to the relay location since a high diversity gain is provided regardless of the source-destination link distance.

Asymptotic error-rate analysis of FSO links using transmit laser selection over gamma-gamma atmospheric turbulence channels with pointing errors.

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 ß, 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,ß})(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.

Outage performance of MIMO FSO links over strong turbulence and misalignment fading channels.

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.

Rate-adaptive FSO links over atmospheric turbulence channels by jointly using repetition coding and silence periods.

In this paper, a new and simple rate-adaptive transmission scheme for free-space optical (FSO) communication systems with intensity modulation and direct detection (IM/DD) over atmospheric turbulence channels is analyzed. This scheme is based on the joint use of repetition coding and variable silence periods, exploiting the potential time-diversity order (TDO) available in the turbulent channel as well as allowing the increase of the peak-to-average optical power ratio (PAOPR). Here, repetition coding is firstly used in order to accommodate the transmission rate to the channel conditions until the whole time diversity order available in the turbulent channel by interleaving is exploited. Then, once no more diversity gain is available, the rate reduction can be increased by using variable silence periods in order to increase the PAOPR. Novel closed-form expressions for the average bit-error rate (BER) as well as their corresponding asymptotic expressions are presented when the irradiance of the transmitted optical beam follows negative exponential and gamma-gamma distributions, covering a wide range of atmospheric turbulence conditions. Obtained results show a diversity order as in the corresponding rate-adaptive transmission scheme only based on repetition codes but providing a relevant improvement in coding gain. Simulation results are further demonstrated to confirm the analytical results. Here, not only rectangular pulses are considered but also OOK formats with any pulse shape, corroborating the advantage of using pulses with high PAOPR, such as gaussian or squared hyperbolic secant pulses. We also determine the achievable information rate for the rate-adaptive transmission schemes here analyzed.

Average capacity of FSO links with transmit laser selection using non-uniform OOK signaling over exponential atmospheric turbulence channels.

A new upper bound on the capacity of power- and bandwidth-constrained optical wireless links using selection transmit diversity over exponential atmospheric turbulence channels with intensity modulation and direct detection is derived when non-uniform on-off keying (OOK) formats are used. In this strong turbulence free-space optical (FSO) scenario, average capacity is investigated subject to an average optical power constraint and not only to an average electrical power constraint when the transmit diversity technique assumed is based on the selection of the optical path with a greater value of irradiance. Simulation results for the mutual information are further demonstrated to confirm the analytical results for different diversity orders.

Space-time trellis coding with transmit laser selection for FSO links over strong atmospheric turbulence channels.

Atmospheric turbulence produces fluctuations in the irradiance of the transmitted optical beam, which is known as atmospheric scintillation, severely degrading the link performance. In this paper, a scheme combining transmit laser selection (TLS) and space-time trellis code (STTC) for multiple-input-single-output (MISO) free-space optical (FSO) communication systems with intensity modulation and direct detection (IM/DD) over strong atmospheric turbulence channels is analyzed. Assuming channel state information at the transmitter and receiver, we propose the transmit diversity technique based on the selection of two out of the available L lasers corresponding to the optical paths with greater values of scintillation to transmit the baseline STTCs designed for two transmit antennas. Based on a pairwise error probability (PEP) analysis, results in terms of bit error rate are presented when the scintillation follows negative exponential and K distributions, which cover a wide range of strong atmospheric turbulence conditions. Obtained results show a diversity order of 2L-1 when L transmit lasers are available and a simple two-state STTC with rate 1 bit/(s .Hz) is used. Simulation results are further demonstrated to confirm the analytical results.