Gamma-Gamma Turbulence Channels Research Articles

Performance analysis of fixed gain relay-assisted vertical UWOC systems with generalized misalignment fading model

Underwater wireless optical communication (UWOC) as a potential underwater transmission technology has attracted increasing attention due to its high speed, low delay, and wide range of applications. In addition to absorption and scattering, ocean turbulence fading and misalignment fading seriously affect system performance. Thus, the relay assistance methods have been presented as an effective technique for fading mitigation in optical channels. In this paper, we propose a fixed gain amplify-and-forward (AF) relay-assisted vertical UWOC system with a generalized misalignment fading model over multi-layer cascaded gamma-gamma turbulence channels. For the relay-assisted system, the cumulative distribution function (CDF) and the probability density function (PDF) of the end-to-end instantaneous signal-to-noise ratio (SNR) are derived with the help of the Meijer-G function and the bivariate Fox-H function. Subsequently, based on these statistical analyses of SNR, we derive the closed-form expressions of the outage probability and ergodic capacity. Furthermore, we provide a very tight asymptotic expression for the outage probability in terms of simple functions under high SNR, and the diversity order is analyzed. Finally, results from Monte Carlo simulations are used to validate our derived results. Numerical results for different relay position deployments and alignment error levels reveal that the relay-assisted vertical UWOC system performs better when the relay node is located near the source, while the increase of alignment error level can damage the system performance.

Performance analysis of OSSK-UWOC systems considering pointing errors and channel estimation errors.

In this paper, we present the bit error rate (BER) performance of the underwater wireless optical communication (UWOC) systems using the optical space shift keying (OSSK) on the gamma-gamma turbulent fading channel, which also considers pointing errors and channel estimation errors. Firstly, we develop the new expressions for the probability density function (PDF) based on the Gamma-Gamma distribution with error factors. Subsequently, we analyze the statistical characteristic of the difference in attenuation coefficients between two channels in the OSSK system, by which we provide analytical results for evaluating the average BER performance. The results show that the effective improvement of spectral efficiency (SE) and BER performance is achieved by rationally allocating the number of lasers and detectors in the system. The OSSK-UWOC system performs better when a narrow beam waist is used. Furthermore, the presence of channel estimation error brings the BER performance advantage to the system, and the system with a high channel estimation error (ρ = 0.7) shows a 4 dB improvement in signal-to-noise ratio (SNR) gain compared to the system with a low channel estimation error (ρ = 0.95). The findings in this paper can be used for the UWOC system design.

Generalized transmit laser selection for vertical underwater wireless optical communications over Gamma-Gamma turbulence channels.

Underwater wireless optical communication (UWOC) is a potential technology for high-speed and reliable underwater data transmission. In underwater environment, ocean turbulence has a strong impact on the performance of UWOC systems. Thus, transmission laser selection (TLS) is proposed as an effective technique for fading mitigation in turbulence channels. In this paper, we present a vertical UWOC system with generalized TLS (GTLS) in multi-layer cascaded Gamma-Gamma ocean turbulence channels. With GTLS, the transmitter is equipped with N laser sources and the nth source is selected for transmission. For the ideal case, the optimal laser source is selected, but in practice, a sub-optimal or worse source may be selected due to channel estimation and/or feedback errors. For the GTLS system, we derive an exact closed-form expression for outage probability. Furthermore, based on the outage probability expression, the diversity order and asymptotical diversity order expression are analyzed. Finally, we give simulation results to validate our analytical results. Numerical results show that the GTLS system performs better than the system without GTLS (i.e. N = 1). The number of cascade channel layers, the number of laser sources and the selection of source index significantly affect the performance of the GTLS system.

FSO Communications Over Doubly Inverted Gamma-Gamma Turbulence Channels With Nonzero-Boresight Pointing Errors

FSO Communications Over Doubly Inverted Gamma-Gamma Turbulence Channels With Nonzero-Boresight Pointing Errors

Proposal of Hybrid NOAM-MPPM Technique for Gamma-Gamma Turbulence Channel With Pointing Error and Different Deep Learning Techniques

Proposal of Hybrid <i>N</i>OAM-MPPM Technique for Gamma-Gamma Turbulence Channel With Pointing Error and Different Deep Learning Techniques

Hybrid MPPM-BB84 Quantum Key Distribution Over FSO Channel Considering Atmospheric Turbulence and Pointing Errors

Nowadays, a high level of security is required for the transmission of critical information. Quantum Key Distribution (QKD) systems are considered the best option to protect such information. Many studies have shown the efficiency of the QKD optical fiber inspired by M-ary pulse position modulation (MPPM). Free-Space Optical (FSO) links provide an efficient and effective data transmission system. However, cumulative effects of laser beam divergence, misalignment, and turbulence-induced fading on the received irradiance in the FSO link might allow an external eavesdropper located near the authorized receiver to break the transmission under certain conditions. This paper introduces the development of an FSO system based on the MPPM and the BB84 protocol (MPPM-BB84) over the Gamma-Gamma (GG) turbulence channel with pointing errors. Time Binning is implemented using MPPM to increase system security and reduce the quantum bit error rate (QBER). The system security is investigated under photon number splitting attack and excess noise. Closed-form expressions for asymptotic expressions of the average symbol error probability (SER), raw key rate (RKR), and secret key rate (SKR) are introduced. Moreover, the Monte-Carlo simulations are then used to prove the validity of the analytical results. The optimal values for the average photon number per pulse (to achieve the maximum RKR and SKR) for each symbol length can guarantee the stability of the FSO system under different weather conditions. Smaller symbol lengths are more tolerant of detector loss. The proposed system supports linking distances from 1 km to 3 km while keeping the SKR almost constant.

Design and Performance Analysis of Probabilistically Shaped QAM Signals for Coherent FSO Systems with Gamma-Gamma Turbulence Channels

Probabilistic shaping (PS) is a promising technique to approach the Shannon limit. In this paper, we design a practical coded modulation scheme based on PS to improve the capacity of coherent free-space optical (FSO) links with quadrature amplitude modulation (QAM), where the fading channel follows the Gamma-Gamma distribution. The aim of this paper is to optimize the probability mass function (PMF) of the QAM signal points to achieve the maximum channel capacity. Due to the complexity of the objective function, the heuristic algorithm was employed to solve the optimization problem. To the best of the authors’ knowledge, the closed-form pairwise error probability (PEP) is first derived with the non-uniform signals under the turbulence channel. In addition, we measure the average symbol error rate (SER) and post-FEC bit error rate (BER) by the Monte Carlo simulation method. The numerical simulation results of both capacity and BER show that the proposed PS scheme is better than the uniform distribution. The post-FEC BER results show that the proposed PS scheme provides significant gains compared with the uniform scheme.

Error rate analysis of few-mode fiber based free-space optical communication.

Few-mode fiber (FMF) based receiver emerges as a promising solution for free-space optical (FSO) communication due to its excellent performance in the presence of turbulence. We propose a theoretical model that uses the coupling efficiency of FMF to evaluate the performance of FMF-based FSO system in the presence of turbulence. The series solutions and asymptotic solutions to bit-error rate (BER) of such system are derived for maximal-ratio combining (MRC) scheme and equal gain combining (EGC) scheme over the Gamma-Gamma turbulence channels. Simulation results show that for the FMF-based FSO system, the asymptotic BER of MRC and EGC are highly accurate in the large transmitted optical power regimes.

Free-Space Optical Communication Using Non-Mode-Selective Photonic Lantern-Based Coherent Receiver

A free-space optical communication system using non-mode-selective photonic lantern (PL) based coherent receiver is studied. Based on the simulation of photon distribution, the power distribution at the single-mode fiber end of the PL is quantitatively described as a truncated Gaussian distribution over a simplex. The signal-to-noise ratios (SNRs), bit-error rate (BER), and outage probability of PL based receiver using selection combining (SC), equal-gain combining (EGC), and maximal-ratio combining (MRC) over Gamma-Gamma turbulence channels are analyzed and compared with the single-mode fiber (SMF) receiver and multimode fiber (MMF) receiver. We demonstrate that EGC is the most suitable combining for PL based receiver because the PL power distribution has limited influence on the BER and outage probability when EGC is used and can greatly affect the BER and outage probability when SC is used. Numerical results show that PL based receiver with EGC requires 6 dB less SNR than the SMF receiver and 5.5 dB less SNR than the MMF receiver at BER of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−6</sup> in moderate turbulence.

Finite-SNR Diversity Gain Analysis of FSO Systems over Gamma-Gamma Fading Channels With Pointing Errors

Free space optical (FSO) communication systems are subject to turbulence-induced fading as a result of fluctuations in the refractive index. Gamma-Gamma (GG) distribution is commonly used in the literature to characterize moderate-to-strong turbulence conditions. The performance of FSO systems is further degraded by pointing error-induced fading as a result of building sways. While the asymptotic analysis presented in earlier works is important to understand the maximum diversity gains of FSO systems attainable over fading channels, such gains might not be available in practical range of signal-to-noise ratio (SNR). Furthermore, different systems with the same asymptotic slope may have different slopes in the range of finite SNR values. In this paper, we consider a multiple-input multiple-output (MIMO) FSO system with intensity modulation and direct detection (IM/DD). We derive approximate expression for the finite-SNR diversity order over GG turbulence channels in the presence of pointing errors. We also investigate convergence speed to full diversity. We provide numerical results to demonstrate the accuracy of our derivations and corroborate on our analytical findings.

Efficient and Secure Bit-Level Chaos Security Algorithm for Orbital Angular Momentum Modulation in Free-Space Optical Communications

Currently, secure multimedia applications are becoming a very hot research topic, specifically over the Internet and wireless communication networks due to their rapid progress. Several researchers have implemented various chaotic image and video encryption algorithms to achieve data stability and communication security. This paper presents a novel bit-level video frame cryptosystem that is dependent on the piecewise linear chaotic maps (PWLCMs). It is implemented for orbital angular momentum (OAM) modulation over different turbulence channels. Firstly, the mathematical model for the bit error rate (BER) of OAM modulation is derived over the gamma-gamma turbulence channel. After that, a comparison between the theoretical results from Mathematica and the simulation results from MATLAB for different turbulence strengths, signal-to-noise ratios (SNRs), and propagation distance values is presented to assure that there is a perfect match. The proposed video cryptosystem is checked using entropy analysis, histogram testing, attack analysis, time analysis, correlation testing, differential analysis, and other quality and security evaluation metrics. The simulation results and the performance analysis confirm that the proposed cryptosystem is reliable and secure for video frame encryption, and communication with different turbulence conditions in free space.

Closed-Form Density Matrices of Free-Space Optical Quantum Communications in Turbulent Channels

A closed-form expression is derived for the received density matrix of the free-space optical quantum communication over the gamma-gamma turbulence channels. A truncation method based on root-mean-square error is proposed to facilitate the calculation of the received density matrix. The required minimum matrix size and minimum number of terms for calculating the received density matrix under various channel conditions are obtained. These results can provide a benchmark for choosing these two parameters in practical implementations. The computation efficiency of the proposed truncation method can be more than 30 times higher than that of the integration method. Besides, we find a convergent property of the required minimum number of terms in the truncation method as the number of signal photons increases.

EVOLUTION OF FREE SPACE OPTICAL SYSTEM BASED ON SUBCARRIER INTENSITY MODULATION OVER SOME DEGREE OF TURBULENT

The use of Binary Phase Shift Keying (BPSK) Subcarrier Intensity Modulation (SIM) in a Gamma-gamma turbulent atmospheric channel was used to study the behavior of Free-Space Optical (FSO) communication system. Subcarrier Intensity Modulation was used to obviate a requirement for an adaptive threshold detector. At the receiver, direct detection was used and each subcarrier is subsequently demodulated clearly. The optimal Maximum Ratio Combining (MRC), the Equal Gain Combining (EGC), and the Selection Combining (SC) was used to combine the received signals linearly. Combining diversity made the effect of irradiance fading less severe. The Bit Error Rate (BER) equations are gotten by putting both the Additive White Gaussian Noise and Gamma-gamma intensity fluctuations into consideration. The simulation results show that at any given Bit Error Rate (BER), the performance of MRC was exceptional compared to the other two techniques. The overall results also put forward the model capability of reducing atmospheric turbulence especially for the 5G wireless network in the terrestrial link.

Tractable Optical Channel Modeling Between UAVs

More recently, the research on potential use of free-space optical (FSO) link as a powerful communication link between unmanned aerial vehicles (UAVs) has created much interest in academia and industry. Due to the need of higher number of UAV-based FSO links relative to the conventional ground-based FSO links, the optimum design of UAV-based FSO system parameters (such as optimum values for beam divergence angle, photodetector size, receiver lens radius, and transmit power, among many others) is much more needful and challenging relative to the ground-based counterpart. Moreover, to avoid the time consumed in Monte-Carlo simulations, existence of a simple and tractable channel model is very important and necessary. To address this need, in this paper, for the weak turbulence conditions, we construct a novel channel model for the considered system model under the effect of log-normal atmospheric turbulence channel. Then, for moderate to strong turbulence conditions, a novel closed-form statistical channel model is derived for Gamma-Gamma turbulence channel. The provided channel models, despite being simple and tractable, include the combined effects of atmospheric turbulence as well as the pointing errors. These also include the effects of receiver field-of-view limitation and inherent position, and orientation deviations of UAVs. Subsequently, for better performance analysis, the closed-form expressions for the outage probability and bit error rate (BER) are derived. Finally, the validity of the proposed novel channel models as well as the closed-form expressions for the outage probability and BER are confirmed by employing Monte-Carlo simulations. The developed results can therefore be applied as a benchmark for finding the optimal tunable parameters of UAV-based FSO links under different channel conditions and different levels of UAV instability without resorting to time-consuming Monte-Carlo simulations.

Performance of OFDM-FSO Communication System with Different Modulation Schemes over Gamma-Gamma Turbulence Channel

Performance of OFDM-FSO Communication System with Different Modulation Schemes over Gamma-Gamma Turbulence Channel

Bit error rate of pulse position modulation wireless optical communication in gamma-gamma oceanic anisotropic turbulence

Pulse position modulation (PPM) technology combined with the system of wireless optical communication received by the photon detector has the advantages of high energy efficiency and strong anti-interference capability. This technology has received extensive attention in the field of underwater wireless optical communication (UWOC) system. Affected by ocean turbulence, the UWOC system will produce the intensity fluctuations, leading the system performance to degrade. The Gamma-gamma intensity fluctuation probability model, which is a two-parameter model, possesses a wide range of applications. It can describe weak, medium and strong fluctuation in light intensity statistics. In this paper, firstly, based on the relationship between the weak atmospheric turbulent spherical wave scintillation index and the weak ocean anisotropic turbulent spherical wave scintillation index, the equivalent structural parameter expressed by both ocean turbulence parameters and anisotropy factor is derived. Then, using the structural parameter combined with the gamma-gamma turbulence channel and the asymptotic Rytov theory, the bit error rate (BER) under anisotropic ocean turbulence is calculated based on the BER formula of the PPM communication system. Finally, numerical simulations are carried out to analyze the ocean turbulence parameters, the average avalanche photodiode (APD) gain, the PPM modulation order, the data bit rate, and the influences of transmission distance on the BER under different anisotropic ocean turbulences. The results indicate that the negative effect of turbulence becomes stronger with increasing the ratio between the contributions of temperature and salinity to the refractive index spectrum, the dissipation rate of mean-squared temperature, data bit rate, and propagation distance. As the viscosity coefficient increases, the BER decreases. When the isotropic ocean turbulence and the anisotropy factors are very small, the increase of the rate of dissipation of kinetic energy per unit mass of fluid will result in a decrease in BER. When the turbulent environment anisotropy is further strengthened, the BER first increases and then decreases as the rate of dissipation of kinetic energy per unit mass of fluid increases. As the average APD gain increases, the BER first decreases and then increases. This trend is especially noticeable as the anisotropy factor increases. The choice of the average APD gain is important for finding the minimum value of the BER. In general, the system is more affected by salinity fluctuation than by temperature fluctuation. As the rate of dissipation of mean-squared temperature increases and the viscosity coefficient decreases, the negative effects of turbulence becomes more and more serious. When the system propagates longer distances or works at a higher data bit rate, the system is severely affected by turbulence, which limits the system operating distance and data transmission rate. However, using a smaller modulation order and choosing the right APD can conduce to improving the system performance. In addition, the PPM UWOC system can perform better when the system operates within acceptable bit error rate as the ocean turbulence environment becomes more anisotropic. This study will provide reference for the construction and performance estimation of UWOC system platform.

Polar-Coded MIMO FSO Communication System Over Gamma-Gamma Turbulence Channel With Spatially Correlated Fading

In this paper, for the first time to the best of our knowledge, a polar-coded multiple-input multiple-output (MIMO) free space optical (FSO) communication system is proposed to combat turbulence-induced fading. Here, the spatially correlated fading, which dominates the MIMO FSO system aggravation, is taken into consideration in this polar-coded MIMO FSO system. To evaluate our scheme, the ergodic capacity of the gamma-gamma modeled MIMO FSO turbulence channel with and without spatially correlated fading is studied. The results of ergodic capacity and Monte Carlo simulation show that the polar-coded multiple photodetector scheme can effectively mitigate the fading induced by turbulence, and the polar-coded multiple optical sources scheme is robust to the spatially correlated turbulence. Further, more than 20 dB net coding gain (NCG) is achieved for the polar-coded MIMO FSO scheme in a strong turbulence condition with spatially correlated fading. Compared with low density parity check codes, polar codes achieve a 0.4–1.6 dB NCG improvement under a strong turbulence condition with and without spatially correlated fading, which verifies that our scheme is a promising candidate for combating turbulence-induced fading.

Performance improvement of FSO system using multi‐pulse pulse position modulation and SIMO under atmospheric turbulence conditions and with pointing errors

Free space optics (FSO) communication links are impaired by the fading due to turbulence and misalignment. In this paper, we theoretically analyze the pointing error effects on performance of FSO systems using multi-pulse pulse position modulation (MP-PPM) over the Gamma-Gamma turbulence channel. We consider the moderate and strong atmospheric turbulence regimes with the combined effect of the pointing errors (PEs), and study the link average symbol error rate (ASER) and the outage probability. The numerical results are presented to show the impact of the pointing error on the ASER and the system outage. However, to overcome the channel degradation resulting from the turbulence effects and the PE, the single-input multiple-output (SIMO) system with maximal ratio combining (MRC) diversity is used. Exact close-form expressions for ASER and outage probability are derived and verified by using Monte Carlo simulation. We concluded that the optimal values of the system parameters are, the transmitted power is 20 dBm, jitter variance should be less than 0.5 m and laser beam width equals 0.2 cm. These values are significantly reduced the impacts of misalignment and fading whereas outage probability is less than at maximum jitter variance.

PDM-DPSK-MPPM hybrid modulation for multi-hop free-space optical communication

A hybrid polarization division multiplexed-differential phase shift keying-multipulse pulse position modulation (PDM-DPSK-MPPM) scheme for multi-hop free-space optical (FSO) communication is investigated. The analytical bit error rate (BER) of the proposed system in Gamma-Gamma turbulence channels is derived and verified using computer simulation. The results show that both multi-hop and hybrid modulation schemes are efficient techniques to improve the performance of FSO links. Compared with the traditional binary phase shift keying (BPSK) and MPPM, the hybrid scheme can improve the bandwidth-utilization efficiency and reliability of the system. Compared with the coherent demodulation of PDM-QPSK-MPPM, the system complexity is reduced at the cost of the degradation of BER performance, which can improve the practicality of hybrid modulation technology in FSO system.

Phase Modulation Schemes in Food Free Space Optical Coherent System

In this study, it is the most appropriate modulation format for food free space optical (FFSO) system compared with other modulation schemes. Performance of BER for BPSK, DPSK and QPSK has been detail discussed under Gamma-Gamma turbulent channel with intensity scintillation and phase fluctuations. The closed average BER expression and channel capacity expression have been derived by adopting the method of generalized hypergeometric. From experiments show that BER and transmission power degraded seriously for the three kinds of modulation format owing to intensity scintillation and phase fluctuations. Comparing performance of the three modulation methods under the atmospheric turbulence, the results for the performance of BPSK and QPSK almost unanimously, in the case of an given SNR it is obvious that BPSK with lower BER. Therefore, BPSK modulation has a good BER and effective resist turbulent but the transmission power will not be increased.