Gamma-gamma Distribution Research Articles

A Mixed FSO/RF Integrated Satellite-High Altitude Platform Relaying Networks for Multiple Terrestrial Users with Presence of Eavesdropper: A Secrecy Performance

In this paper, the secrecy performance of a mixed free space optical (FSO)/radio frequency (RF) integrated satellite-high altitude platform (HAP) relaying networks for terrestrial multiusers with the existence of an eavesdropper is investigated. In this network, FSO is adopted to establish the link between the satellite and HAP for which it experiences Gamma-Gamma distributions under different detection schemes (i.e., heterodyne and intensity modulation direct detection). The transmission between the amplify-and-forward (AF) relaying HAP and terrestrial multiusers is through the RF and is modeled as shadowed-Rician fading distribution. Owning to broadcasting nature of RF link, it is assumed that an eavesdropper attempts to intercept the users’ confidential message, and the eavesdropper link is subjected to Rician distributions. Specifically, the closed-form expression for the system equivalent end-to-end cumulative distribution function is derived by exploiting the Meijer’s G and Fox’s H functions. Based on this expression, the exact closed-form expressions of the system connection outage probability, secrecy outage probability, and strictly positive secrecy capacity are obtained under the different detection schemes at HAP. Moreover, the asymptotic analyze of the system secrecy outage probability is provided to obtain more physical insights. Furthermore, the accuracy of all the derived analytical closed-form expressions is verified through the Monte-Carlo simulations. In addition, the impact of atmospheric turbulence, pointing errors, shadowing severity parameters, and Rician factor are thoroughly evaluated. Under the same system conditions, the results depict that heterodyne detection outperforms the intensity modulation direct detection.

Performance Investigation of MIMO Based CO-OFDM FSO Communication Link for BPSK, QPSK and 16-QAM under the Influence of Reed Solomon Codes

The MIMO based CO-OFDM FSO communication system is emerging as a promising approach to meet the future bandwidth requirements for seamless communication. The atmosphere being the propagation medium is a major hindrance in wide-scale acceptability of FSO technology. For seamless and error-free transmission and reception of data, a novel concept of MIMO integrated with RS code is proposed in this paper. The system performance of an RS 64 (RS (255,127)) coded MIMO-based CO-OFDM FSO communication link was investigated using BPSK, QPSK and 16-QAM under the combined effects of geometric losses, path losses and atmospheric attenuations at a hitherto un-investigated data rate of 40 Gbps and a link distance of 5 km. The modified gamma-gamma distribution was used for modeling a moderately turbulent channel. With link length varying over a range of 1 to 5 km, error correction was maximum in 16-QAM as compared to BPSK and QPSK, with 150 to 167 corrected errors. In terms of PAPR, PSK was more apt than QAM, but with a compromise in BER. The geometric losses were reduced with link length due to an increase in error correction capability for all three modulation cases, with the least losses occurring in 16-QAM. At the target bit error rate (BER), the signal to noise ratio (SNR) required for BPSK and QPSK was higher by 3.98 dB and 6.14 dB compared to 16-QAM.

Analysis of RIS-Based Terrestrial-FSO Link Over G-G Turbulence With Distance and Jitter Ratios

One of the main problems faced by communication systems is the presence of skip-zones in the targeted areas. With the deployment of the fifth-generation mobile network, solutions are proposed to solve the signal loss due to obstruction by buildings, mountains, and atmospheric or weather conditions. Among these solutions, reconfigurable intelligent surfaces (RIS), which are newly proposed modules, may be exploited to reflect the incident signal in the direction of dead zones, increase communication coverage, and make the channel smarter and controllable. This paper tackles the skip-zone problem in terrestrial free-space optical (T-FSO) systems using a single-element RIS. Considering link distances and jitter ratios at the RIS position, we carry out a performance analysis of RIS-aided T-FSO links affected by turbulence and pointing errors, for both heterodyne detection and intensity modulation-direct detection techniques. Turbulence is modeled using the Gamma-Gamma distribution. We analyze the model and provide exact closed-form expressions of the probability density function, cumulative distribution function, and moment generating function of the end-to-end signal-to-noise ratio. Capitalizing on these statistics, we evaluate the system performance through the outage probability, ergodic channel capacity, and average bit error rate for selected binary modulation schemes. Numerical results, validated through simulations, obtained for different RIS positions and link distances ratio values, reveal that RIS-based T-FSO performs better when the RIS module is located near the transmitter.

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.

Analytical performance evaluation of a 2 × 2 Alamouti STBC OFDM FSO- communication system over turbulent atmospheric channel

An expository methodology is introduced to assess the CNR and BER performance of a STBC OFDM FSO framework over turbulent channel. Expressions are developed for conditional CNR and BER for a given turbulence induced fading. Average BER is then found considering the pdf of turbulence induced fading of gamma-gamma distribution. Results are evaluated for 2 × 2 Alamouti STBC OFDM FSO communication system over turbulent atmospheric channel for several values of system parameters viz. number of OFDM subcarriers, turbulence variance, link distance, data rate and power penalty suffered by the system due to atmospheric turbulence. The results show that the BER performance is strongly degraded due to the effect of atmospheric turbulence. Systems suffers significant amount of power penalty in receiver sensitivity at a given BER. However, the power penalty can be reduced by increasing the number of OFDM subcarriers. For example, power penalty at a BER of10−9 for 2 × 2 STBC with N = 16 OFDM subcarriers is found to be 5.5 dB and the power penalty reduces to 0.35 dB when N is increased to 64.

Performance analysis of OFDM based FSO communication system with TCM codes

Various channel coding schemes have been used over free space optical (FSO) links to alleviate the effects of turbulence induced fading. In this paper, performance analysis for TCM coded orthogonal frequency division multiplexing (OFDM) based FSO communication systems, operating over atmospheric turbulence channels. Analysis have been done in terms of bit error rate (BER) as a function of signal to noise ratio (SNR), considering the log-normal distribution model during weak turbulence and gamma-gamma distribution model for moderate and strong turbulence conditions. The integration of TCM with OFDM can solve bandwidth issue and bit rate degradation during wireless communication. Various modulation schemes have been studied for the said system keeping in mind different requirements such as band width and data rate etc. The simulation results and analysis have shown that the TCM coder with 16-QAM provides considerable coding gain as compared to uncoded system during all turbulence conditions. This system acts as high-performance wireless communication system (HPWCS) by providing BER of 10−9 which is necessary for stable operation on communication system.

Scintillation and bit error rate in bidirectional laser communications between an aerial vehicle and a satellite using annular optical beams in strong turbulent atmosphere

Scintillation index is examined for annular optical beams in a strong atmospheric medium of a slant path. On-axis scintillations have small- and large-scale components and are formulated for the uplink/downlink of aerial vehicle-satellite laser communications. For this purpose, the unified Rytov method and the amplitude spatial filtering of the atmospheric spectrum are utilized. Performances given by the average bit error rate (BER) are investigated by employing the corresponding scintillation index, which is found by using intensity having gamma-gamma distribution. Strong atmospheric turbulence effects on the scintillation index and BER of the collimated annular optical beam having various thicknesses are reported for the up/down vertical links, and these are compared with the scintillations of the collimated Gaussian optical beams against propagation length, source size, and the zenith angle with the selected thickness. Utilizing the scintillations found, BER changes against average signal-to-noise ratio (SNR)are plotted for up/down vertical links. The scintillation index and BER in the downlink are found to be different than the scintillation index and BER in the uplink for strong atmospheric turbulence, mainly because the structure constant is a function of the altitude. Considering the location where the aerial vehicle and satellite are deployed as the reference points, annular beams are more advantageous than the Gaussian beams at up/down slant link lengths. The effect of the thickness of the annular beam is apparent for the uplink, where thin annular beams are more advantageous at small link lengths and thick annular beams are more advantageous at large link lengths. In the downlink, thin annular beams are more advantageous at all link lengths.

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.

Atmospheric Turbulence-Controlled Cryptosystems

To overcome the limitations of QKD, post-quantum cryptography, and computational security-based cryptography protocols in this paper, an atmospheric turbulence-controlled cryptosystem is proposed. The proposed encryption scheme employs the traditional scheme to utilize the atmospheric turbulence as the common source of randomness only in the initialization stage to determine the common parameters to be used in the proposed encryption scheme. To overcome low secret-key rates of traditional scheme, dictated by the long coherence time Tc of turbulence channel, the proposed encryption scheme updates the parameters of gamma-gamma distribution, used to generate irradiance samples for cumulative distribution function-based determination of the key, every Tc seconds and as such the final key is shaped by the atmospheric turbulence channel. We also describe a scheme that randomly selects one of several available paths in which the simultaneously measured irradiance samples, after interleaving, are used to generate the raw key. The secret-key rates of the proposed schemes are orders of magnitude higher compared to corresponding traditional QKD and source type physical-layer security schemes and are comparable with the state-of-the-art optical communication data rates.

Statistical evaluation of the performance of free-space-optical link affected by optical turbulence with gamma-gamma distribution through time series generated by simulation

In this article, the statistical evaluation of the performance of FSO links subject to dynamic fluctuations of atmospheric optical turbulence that affect the instantaneous value of the received optical power is presented. We reproduce this temporal domain effect with time series generated by simulation considering the optical turbulence as a stochastic process with Gamma-Gamma probability distribution. Also, a phase screen was used in order to observe the impact that optical turbulence has over the optical information field's spatial phase. With our simulations, it is possible to get the two most essential performance parameters required for the practical implementation of FSO links. We obtained the mean signal-to-noise ratio (SNR) and the mean bit error rate (BER) of FSO links affected by optical turbulence with Gamma-Gamma distribution. The methodology presented in this paper may be readily used to design and implement real-world FSO links.

Performance Analysis of Dual-Hop Wireless Systems Over Mixed FSO/RF Fading Channel

This paper investigates the performance of a dual-hop mixed free-space optical (FSO)/radio frequency (RF) system. To this end, the FSO link is subject to the Gamma-Gamma distribution effects that account for pointing error impairments and under both heterodyne detection and intensity modulation with direct detection (IM/DD) methods, while the RF link undergoes the α- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F</i> distribution fading. For amplify-and-forward (AF) and decode-and-forward (DF) relaying, we derived the closed-form expressions of various important performance metrics by using bivariate Fox's H-functions, such as the average bit-error rate (BER), end-to-end outage probability (OP), effective capacity, and ergodic capacity. We unveil the effects of system and channel parameters on performance. Furthermore, we provide an asymptotical analysis to discuss significant diversity gains. Note that our results include previous works as special cases, which provides a framework. Finally, our derived expressions have confirmed the correctness via exactly matching Monte Carlo simulation results.

Performance of Hybrid RF/FSO Cooperative Systems Based on Quasicyclic LDPC Codes and Space-Coupled LDPC Codes

Free space optical (FSO) communication systems provide wireless line of sight connectivity in the unlicensed spectrum, and wireless optical communication achieves higher data rates compared to their radio frequency (RF) counterparts. FSO systems are particularly attractive for last mile access problem by bridging fiber optic backbone connectivity to RF access networks. To cope with this practical deployment scenario, there has been increasing attention to the so-called dual-hop (RF/FSO) systems where RF transmission is used at a hop followed by FSO transmission to another. In this article, we study the performance of cooperative transmission systems using a mixed RF-FSO DF (decode and forward) relay using error-correcting codes including QC-LDPC codes at the relay level. The FSO link is modeled by the gamma-gamma distribution, and the RF link is modeled by the Additive White Gaussian Noise (AWGN) model. Another innovation in this article is the use of cooperative systems using a mixed FSO/RF DF relay using quasicyclic low-density parity check (QC-LDPC) codes at the relay level. We also use the space-coupled low-density parity check (SC-LDPC) codes on the same scheme to show its importance in cooperative optical transmission but also in hybrid RF/FSO transmission. The latter will be compared with QC-LDPC codes. The use of mixed RF/FSO cooperative transmission systems can improve the reliability and transmission of information in networks. The results demonstrate an improvement in the performance of the cooperative RF/FSO DF system based on QC-LDPC and SC-LDPC codes compared to RF/FSO systems without the use of codes, but also to the DF systems proposed in the existing literature.

Analysis of M-QAM Modulated Underwater Wireless Optical Communication System for Reconfigurable UOWSNs Employed in River Meets Ocean Scenario

In this paper, the bit error rate (BER) performance of underwater wireless optical communication system employing with M-ary quadrature amplitude modulation is proposed for underwater optical wireless sensor networks (UOWSN) in river meets ocean scenario. The underwater channel degradation effects such as absorption, scattering and oceanic turbulence is taken into account. The oceanic turbulence is modelled by the Gamma-Gamma distribution. The first time, we proposed re-configurable UOWSN for the real time scenario of the river meets the ocean and derived the novel closed form analytical BER expressions of the proposed system over Gamma-Gamma turbulence with attenuation effects. The impact of oceanic turbulence parameters such as the variations of temperature, kinetic energy, viscosity, salinity, link range and the water type of system performance is investigated for river water, mixed water (river and ocean water) and ocean water. The proposed system and the related analysis will be highly useful in UOWSN and the Internet of underwater thing (IoUT) applications.

Enhancement of reliability and security in spatial diversity FSO-CDMA wiretap channel

Abstract Due to atmospheric turbulence, the reliability and security of free space optical (FSO) communication will be affected seriously. In this paper, we propose a novel scheme of quasisynchronous spatial diversity free-space optical code division multiple access (FSO-CDMA) wiretap channel based on gamma-gamma distribution. Considering multiple access interference, shot noise, thermal noise and background noise, performances of bit error rate (BER) and physical-layer security are analyzed theoretically. The physical-layer security of quasisynchronous spatial diversity FSO-CDMA wiretap channel is evaluated by secrecy capacity and interception probability. Closed-form expression of interception probability is obtained. In order to compare the performances between conventional spatial diversity FSO-CDMA and the proposed scheme, Optisystem simulation is carried out. The results indicate that quasisynchronous spatial diversity FSO-CDMA scheme can improve the reliability and physical-layer security simultaneously.

Performance analysis of mixed MISO RF/SIMO FSO relaying systems

This paper investigates the end-to-end performance of a dual-hop mixed multiple-input single-output (MISO) radio-frequency (RF)/ single-input multiple-output (SIMO) free-space optical (FSO) relaying system. The Rayleigh distribution and the Gamma-Gamma (ΓΓ) distribution are adopted to describe the RF link and the turbulence effects of the FSO link, respectively. We consider Alamouti-type space-time block coding (A-STBC) and transmitter antenna selection (TAS) schemes from the source to the relay. There are amplify-and-forward (AF) with fixed gain and variable gain protocols for the relay. The closed-form expressions of the outage probability, outage capacity, average symbol error rate (SER) and channel capacity are derived in this paper. We discuss the end-to-end performance of different coding and relay schemes under different turbulence conditions.

Vertical Underwater Visible Light Communication Links: Channel Modeling and Performance Analysis

Underwater visible light communication (UVLC) has been introduced to support emerging high data rate applications such as real-time image and video transmission. Initial works on UVLC build upon the assumption of fixed turbulence strength through the transmission range which can be justified only for horizontal links. In vertical underwater links, the gradient of temperature and salinity changes with depth. This effectively results in ocean stratification where water with different values of salinity and temperature form non-mixing layers. In this paper, we first model the vertical underwater link as a cascaded fading channel where fading coefficients associated with different layers are modeled as independent and non-identical distributed. Based on the cascaded lognormal and Gamma-Gamma distributions respectively for weak and moderate/strong turbulence conditions, we first derive closed-form expressions for the bit error rate (BER) performance of UVLC systems. Then, we analyze the asymptotic BER performance and determine the diversity orders. In addition, we derive closed-form expressions for the average ergodic capacity of underwater cascaded fading channels under consideration. We present simulation results to confirm the analytical findings.

On the Performance Analysis of Higher Order QAM Schemes Over Mixed RF/FSO Systems

In this work, the performance of a dual-hop variable gain amplify-and-forward (AF) mixed radio frequency (RF)/free space optics (FSO) system is analyzed in details. As variable gain AF relay network is considered, processing delay results in outdated channel state information (CSI) during amplification at the relay. For general applicability, the RF link is modeled with the generalized Nakagami-m fading. The FSO link is modeled with the Gamma-Gamma distribution which is affected with the atmospheric turbulence and pointing error impairments, and both the intensity modulation with direct detection (IM/DD) and heterodyne detection are employed at the FSO receiver. In this context, analytical expressions of outage probability and ergodic capacity are derived in terms of Meijer-G function and extended generalized bivariate Meijer-G function. For diversity order, asymptotic outage probability expression is also derived. Further, cumulative distribution function based generalized average symbol error rate expressions for various quadrature amplitude modulation (QAM) schemes such as hexagonal QAM, rectangular QAM, and cross QAM are derived in terms of Meijer-G function. Furthermore, a detailed comparative study of various modulation schemes is presented and the impact of pointing error, atmospheric turbulence, outdated CSI, and Nakagami-m parameter are highlighted on the system performance. Finally, all the analytical results are verified through Monte-Carlo simulations.

Dual-hop deep space-terrestrial FSO/RF communication under solar scintillation: Performance analysis and challenges

Deep space communication has been a fundamental guarantee for space exploration but encounters solar scintillation during superior solar conjunction. In this paper, a paradigm for deep space-terrestrial free space optical (FSO)/radio frequency (RF) communication is proposed, and the outage probability performance of the dual-hop amplify-and-for-ward (AF) based FSO/RF communication system is investigated. Specifically, the asymmetric dual-hop channel models are considered, where the Gamma-Gamma distribution characterizes the FSO link between the deep space probe and a relay satellite that undergoes coronal turbulence, while the RF link between the satellite and the terrestrial receiver follows the shadowed-Rician fading model due to the shadowing effect. Moreover, the closed-form expressions of the outage probability for both channel state information (CSI)-assisted and fixed gain relay systems are presented with the consideration of multiple antennas equipped on the destination, which provide practical insights to the link performance. Simulation results present the validation of our theoretical expressions and highlight a strategy for the improvement of the outage probability performance for deep space-terrestrial communication. Finally, some open issues and research directions that should be further investigated for the actual deep space communication system during superior solar conjunction are identified.

Performance of Multibeam Very High Throughput Satellite Systems Based on FSO Feeder Links With HPA Nonlinearity

Due to recent advances in laser satellite communications technology, free-space optical (FSO) links are presented as an ideal alternative to the conventional radio frequency (RF) feeder links of the geostationary satellite for next generation very high throughput satellite (VHTS) systems. In this paper, we investigate the performance of multibeam VHTS systems that account for nonlinear high power amplifiers at the transparent fixed gain satellite transponder. Specifically, we consider the forward link of such systems, where the RF user link is assumed to follow the shadowed Rician model and the FSO feeder link is modeled by the Gamma-Gamma distribution in the presence of beam wander and pointing errors where it operates under either the intensity modulation with direct detection or the heterodyne detection. Moreover, zero-forcing precoder is employed to mitigate the effect of inter-beam interference caused by the aggressive frequency reuse in the user link. The performance of the system under study is evaluated in terms of the outage probability, the average bit-error rate (BER), and the ergodic capacity that are derived in exact closed-forms in terms of the bivariate Meijer’s G function. Simple asymptotic results for the outage probability and the average BER are also obtained at high signal-to-noise ratio.

Performance of free space optical communication system based on M-ary PPM modulation over double generalized gamma channel

In this paper, we provide analytical results on average Symbol Error Probability (SEP) of a Free Space Optics (FSO) link employing M-ary Pulse Position Modulation (PPM), subjected to turbulent atmosphere modeled with Double Generalized Gamma (DGG) distribution. FSO link is generally impaired by turbulent atmosphere and pointing errors. As far as we know, results are presented in previous works by considering the atmosphere turbulence modeled with a Gamma-Gamma distribution. In our work, we also give asymptotic results on average SEP in order to approximate its evolution at high Signal-to-Noise-Ratio (SNR). Numerical results showed that FSO link performance is enhanced when PPM-modulation index is increased, for both strong and moderate turbulence regimes, and for both strong and weak pointing error jitter. Monte-Carlo simulations were presented to corroborate our analytical expressions.