Double Generalized Gamma Research Articles

Effects of Eavesdropper on the Performance of Mixed $\eta$–$\mu$ and DGG Cooperative Relaying System

Free-space optical (FSO) channels offer line-of-sight wireless communication with high data rates utilizing unlicensed optical spectrum. The hybrid radio frequency (RF)–FSO system is currently receiving a great deal of research interest because atmospheric turbulence prevents enhanced secrecy performance. Except for the double generalized gamma (DGG) model, traditional FSO models typically are unable to show secrecy performance across all turbulence severity ranges. Due to this, we propose a dual-hop <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\eta$</tex-math></inline-formula> – <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> and unified DGG mixed RF–FSO network while taking into account the following three different eavesdropping scenarios: 1) the eavesdropper is at the RF link; 2) the eavesdropper is at the FSO link; and 3) both eavesdroppers remains active simultaneously. These proposed scenarios' security is examined in terms of the probability, of strictly positive secrecy capacity, secure outage probability and effective secrecy throughput, and further investigation is done into the implications of various system settings on the secrecy performance. The analysis shows that, when compared to the other two scenarios, the third scenario exhibits the worst secrecy condition. Intensity modulation/direct detection (IM/DD) and heterodyne detection (HD) approaches are compared, with HD outperforming IM/DD in terms of secrecy performance. Finally, Monte Carlo simulations are used to confirm all analytical findings.

ABER of M-QAM and K-PSK modulations over double-GG fading channel

ABSTRACT OFDM-based Radio on Free space optical (RoFSO) system gained attention of technocrats and researchers due to high data rates, license-free spectrum and ease of installation among the others. However, it is noteworthy to mention that turbulence-induced fading and pointing error are the major challenges of RoFSO system. Although various literatures include pointing error and/or turbulence induced fading to present different performance measures of RoFSO system, none of them includes all the turbulence condition from weak to strong. In contrary, Double Generalized Gamma (DGG) distribution shows perfect fit over the entire range of turbulence conditions from weak to strong. This research work presents various closed form expressions of BER for M-QAM and K-PSK schemes over DGG distribution under weak, moderate and strong turbulence conditions for the system with and without pointing error. Furthermore, as DGG distribution includes different fading channels such as Double Weibull and Gamma-gamma distribution as its special case. Therefore, we reproduce BER of M-QAM and K-PSK modulation schemes with and without pointing error over Double Weibull and Gamma-gamma fading channels. Simulation shows that irrespective of severity of turbulence, pointing error and/or increase in the order of modulation scheme deteriorate the system performance.

Performance of Dual-Hop Relaying for OWC System Over Foggy Channel With Pointing Errors and Atmospheric Turbulence

Optical wireless communication (OWC) over atmospheric turbulence and pointing errors is a well-studied topic. Still, there is limited research on signal fading due to random fog in an outdoor environment for terrestrial wireless communications. In this paper, we analyze the performance of a decode-and-forward (DF) relaying under the combined effect of random fog, pointing errors, and atmospheric turbulence with a negligible line-of-sight (LOS) direct link. We consider a generalized model for the end-to-end channel with independent and not identically distributed (i.ni.d.) pointing errors, random fog with Gamma distributed attenuation coefficient, double generalized gamma (DGG) atmospheric turbulence, and asymmetrical distance between the source and destination. We develop density and distribution functions of signal-to-noise ratio (SNR) under the combined effect of random fog, pointing errors, and atmospheric turbulence (FPT) channel and distribution function for the combined channel with random fog and pointing errors (FP). Using the derived statistical results, we present analytical expressions of the outage probability, average SNR, ergodic rate, and average bit error rate (BER) for both FP and FPT channels in terms of OWC system parameters. We also develop simplified and asymptotic performance analysis to provide insight on the system behavior analytically under various practically relevant scenarios. We demonstrate the mutual effects of channel impairments and pointing errors on the OWC performance, and show that the relaying system provides significant performance improvement compared with the direct transmissions, especially when pointing errors and fog becomes more pronounced.

Average bit error rate performance of free-space optical systems over double generalized gamma fading channels based on avalanche photodiode detector

The performance of free-space optical (FSO) communication systems based on avalanche photodiodes (APDs) is investigated over the aggregated double generalized gamma (double GG) fading channels. The approximate average bit error rate (ABER) expression is theoretically derived in terms of the double GG distributions under moderate and strong turbulent atmospheric conditions considering thermal noise and shot noise. The union bound and Hermite polynomials are then used to estimate the ABER performance of M-ary pulse-position modulation (PPM)-based systems and orthogonal frequency division multiplexing scheme (OFDM)-based systems. The ABER performance is studied with different receiver noise temperatures, modulation orders, turbulence strengths, and average photon counts assuming plane wave and spherical wave propagations. The results show that adopting an optimal average APD gain affected by the receiver temperature minimizes the ABER value for both wave propagations. In addition, the present APD-based system offers better ABER performance than that of a PIN-based FSO system over the double GG fading channels at two receiver noise temperatures of 200 and 400 K for both the PPM and OFDM schemes. We provide a reference for FSO system design.

Impact of RF I/Q Imbalance on Interference-Limited Mixed RF/FSO TWR Systems With Non-Zero Boresight Error

In this letter, we investigate a generic model assessing the effect of in-phase/quadrature-phase imbalance (IQI) on an asymmetric dual hop radio frequency/free space optical (RF/FSO) two-way relay (TWR) system in the presence of multiple co-channel interferers (CCIs) at the relay. The fading on the RF and FSO links have been modeled using K-distribution and double generalized Gamma (D-GG) turbulence model, respectively. The impact of non-zero boresight pointing error and type of optical demodulation schemes have been considered on the FSO link. To this end, a closed-form probability density function (PDF) has been derived for the FSO link undergoing D-GG irradiance with non-zero boresight pointing error. Furthermore, the exact and high signal-to-noise (SNR) asymptotic expression for outage probability have been presented. To gain insights into the throughput of the system, approximate and asymptotic expressions for the achievable sum rate (ASR) have been derived. The results show dependency of reliability and throughput offered on IQI at the RF front-end and strength of interference for the considered TWR system.

Unified Performance Analysis of Multi-Hop FSO Systems Over Double Generalized Gamma Turbulence Channels With Pointing Errors

Free space optical (FSO) communication systems provide high bandwidth in unregulated spectrum and act as a powerful line-of-sight wireless connectivity solution. The performance of FSO systems can be seriously impaired by fading as a result of atmospheric turbulence and/or pointing errors due to misalignment. In the context of FSO systems, relaying was proposed as an effective fading mitigation technique due to the fact that the variance is distance-dependent in turbulence channels. In this article, we present a unified performance analysis of multi-hop FSO systems over Double Generalized Gamma (DGG) turbulence channels with pointing error impairments. We assume amplify-and-forward relaying and consider both heterodyne detection and intensity modulation with direct detection. We derive tight closed-form expressions for the outage probability and bit error probability of both fixed-gain and channel state information (CSI)-assisted relaying in terms of the bivariate Fox-H functions and Fox-H functions, respectively. We further analyze asymptotic behavior of the outage probability in terms of simple elementary functions and obtain the achievable diversity orders. Diversity gain is found to be a function of atmospheric turbulence parameters, pointing error, detection type and the number of hops. Monte Carlo simulation results are further provided to verify the accuracy of the derived expressions.

Outage Performance of Mixed RF-FSO Systems Over DGG and Nakagami-m Channels

In mixed RF (radio frequency)-FSO (free space optical) systems, the FSO link is used for backhauling while RF is used for wireless access. In many practical deployment scenarios especially in urban environments, more than one FSO hop is required to avoid blockage and facilitate the line-of-sight connectivity. In this letter, we study the performance of a triple-hop RF-FSO-FSO link. We assume that the RF link is subject to Nakagami- ${m}$ fading while FSO links are subject to double generalized Gamma (DGG) turbulence in addition to pointing errors. We first derive an exact closed-form expression for outage probability (OP) in terms of bivariate Fox-H function. Then, we carry out an asymptotical analysis to derive achievable diversity gains. We further present simulations to verify the accuracy of the derived expressions and investigate the effect of several system and channel parameters on the performance.

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.

Mixed MUD-RF/FSO Two Way Dcode and Forward Relaying Networks in the Presence of Co-Channel Interference

In this research work, mixed radio frequency (RF)/free-space optical (FSO) decode-and-forward (DF) two-way relaying (TWR) system is investigated in the presence of interference. In order to improve the performance of the RF link, multiuser diversity (MUD) scheme has been implemented. The multiple RF users undergo Nakagami-m distributed fading. The atmospheric turbulence on the FSO link is assumed to follow the double generalized Gamma (D-GG) scintillation model. The model on the FSO link considers two kinds of optical detection schemes, i.e., intensity modulation/direct detection (IM/DD) and coherent demodulation scheme, and also includes the effect of pointing errors. Furthermore, multiple co-channel interferers (CCIs) at the relay node are assumed to undergo Nakagami-m fading. For the considered TWR system, exact closed-loop expressions for the outage probability and bit error rate (BER) have been derived. These exact closed-form expressions have been further simplified for the case of high signal-to-noise (SNR) to derive the asymptotic expressions for the outage probability and BER of the considered system. Finally, the analytical framework developed in the research work has been validated using numerical examples.

Interference-Limited Mixed MUD-RF/FSO Two-Way Cooperative Networks Over Double Generalized Gamma Turbulence Channels

In this letter, the performance of multiuser-radio frequency/free space optics (RF/FSO) two-way relay network in the presence of interference is investigated. The FSO link accounts for pointing errors and both types of detection techniques, i.e., intensity modulation/direct detection as well as coherent demodulation, which is modeled as double generalized gamma (D-GG) turbulence channel. On the other hand, the multiple users on the RF link are assumed to undergo Nakagami-m fading. Multiple co-channel interferers (CCIs) which corrupt the signal at relay node are modeled using Nakagami-m distribution. Specifically, the exact closed-form expressions for the outage probability (OP) of the overall system are derived. Moreover, the closed form expression for the achievable sum-rate (ASR) of the considered system is presented. In order to simplify the results, the asymptotic approximations of the OP and ASR are derived in terms of elementary functions. The results presented in the letter are validated by the Monte Carlo simulations.

Cascaded Rf-Fso-Vlc System using Df Relays

This paper presents performance analysis of cascaded radio frequency-free space optical communication-visible light communication (RF-FSO-VLC) system. The proposed model comprises of the RF link as the core network, a terrestrial optical link for providing last mile connectivity with the indoor cell users communicating through VLC environment. The RF link undergoes Nakagami-m distributed fading, while the terrestrial optical link is modeled by Double Generalized Gamma (DGG) distributed turbulence and Rayleigh-distributed misalignment losses. VLC links are characterized by the randomness in users’ position. Using statistical properties of system signal-to-noise ratio (SNR), outage and error performance of the proposed system is evaluated depending on whether the relays and the destination decode either perfectly or erroneously. The numerical results show that the system performance varies depending on field-of view (FOV) of the detector and user’s position. This is because as FOV increases along with the height of the LED, the outage probability of the system increases. Error probability depends on the type of detection techniques, where a heterodyne detection system performs better than a direct detection system. Moreover, through results it is inferred that severe fading and misalignment losses result in poor error performance of the considered system errors on the performance of the considered cooperative system.

Hybrid RF-FSO System Cascaded with UWOC Link

This work presents outage analysis of a hybrid communication system, where radio frequency (RF) and free space optical (FSO) communication links transmit in parallel to the then cascaded underwater wireless optical communication (UWOC) link forming a RF/FSO-UWOC cooperative system. Optical wireless communication (OWC) is being used as a viable communication technology by researchers due to its advantages such as fast speed, cost effectiveness, and highly secure transmission. The proposed architecture connects the terrestrial and the underwater regions to form an end-to-end cooperative system. This hybrid RF/FSO back-haul link makes the system more reliable as the optical link is highly susceptible to weather conditions. The channel models considered are Nakagami-m distributed fading, Double Generalized Gamma (DGG) distributed atmospheric turbulence along with Rayleigh distributed misalignment losses and mixture of Exponential Generalized Gamma (EGG) distributed oceanic turbulence for RF, FSO, and UWOC links, respectively. Results show that outage performance is severely affected due to RF fading, DGG distributed irradiance, air bubble concentration, temperature gradient, and saltiness of water source.

Outage Analysis of Mixed Dual-Hop RF-FSO Communication System Over Fading Channels with Pointing Errors

In this paper, we consider a mixed dual-hop RF-FSO communication system, where RF link is subjected to Rice fading, while FSO link experience double generalized Gamma (GG) turbulence with pointing errors. The double GG distribution is a newly developed turbulence model, which contains commonly used turbulence models as its special case and matches excellently with the existing experimental data. The Rician fading model represents propagation conditions which include the presence of the line-of-sight component and also, it includes the Rayleigh fading model as its special cases. Here we first derive a novel, analytical closed-form expression for the cumulative distribution function for the end-to-end signal-to-noise ratio of the considered system. We show that our derived result contains the existing results presented in the literature as its special case. Then, relaying on the developed analytical results, we derive a closed-form expression for the outage probability and using it, we analyze the outage performance of the mixed dual-hop RF_FSO system and investigate the impact of the pointing errors. Numerical results are further demonstrated to confirm the analytical results.

A framework on the performance analysis of relay-assisted FSO transmission systems

In this work, we tend to analyze the performance of dual-hop relayed free-space optical (FSO) transmission systems. To do this, the FSO links are modeled as the Double Generalized Gamma (DGG) distribution with generalized pointing error impairment and under both heterodyne detection (HD) and intensity modulation with direct detection (IM/DD) methods. Using amplify-and-forward (AF) fixed-gain relaying as well as channel state information (CSI)-assisted AF relaying along with decode-and-forward (DF) relaying, we derive closed-form expressions for the outage probability (OP), the average bit error rate (BER) and the ergodic capacity (EC) in terms of the bivariate Fox-H function. Additionally, we analyze high signal-to-noise-ratio (SNR) behavior of the OP and formerly we derive the diversity order of the considered system. To asses the accuracy of the obtained results, numerical and Monte-Carlo simulation results are provided. Based on the high SNR analysis, we further provide a diversity gain analysis and discuss the bottlenecks in the dual-hop FSO systems.

Statistical Analysis of FSO Links Employing Multiple Transmitter/Receiver Strategy over Double-Generalized and Gamma–Gamma Fading Channel Using Different Modulation Techniques

AbstractFree space optical (FSO) communication links have recently received lot of attention as high bandwidth and cost-effective access technique. However, the transmission medium, i. e. atmosphere, itself is a major spoilsport factor as atmospheric turbulence may lead to fading. The legacy of spatial diversity techniques which have already proven their worth as effective mechanism to counter channel fading in radio links has also been extended to FSO links in this paper. A mathematical model to evaluate error rate performance of FSO links over strong turbulent conditions using gamma–gamma and double-generalized gamma channel model for different modulation techniques has also been included. It was observed that higher modulation techniques such as binary phase shift keying (BPSK) and differential phase shift keying (DPSK) allow superior error performance as compared to on–off keying (OOK) links, and this performance further enhances with incorporation of spatial diversity techniques. However, across different diversity options, explained in this paper, BPSK–MISO links were the best choice for turbulent conditions.

Analysis of Device-to-Device Communication over Double-Generalized Gamma Channels

Analysis of Device-to-Device Communication over Double-Generalized Gamma Channels

Analysis of Device-to-Device Communication over Double-Generalized Gamma Channels

In this paper, performance of a device-to-device (D2D) communication system is analyzed over double-generalized Gamma (dGG) fading channels. The dGG is a generic distribution for modeling double-scattering fading conditions. Co-channel interference (CCI) caused by various wireless devices in the system is also considered. The CCI fading channel is assumed to be Nakagami distributed. Analytical expressions for important statistical metrics, i.e. probability density function (PDF) and cumulative distribution function (CDF) of signal-to-interference ratio (SIR), are presented. Based on these statistical parameters, expressions for the outage probability, channel capacity and symbol error rate (SER) of the D2D communication system are presented. The performance of D2D system is then discussed and analyzed with the help of numerical results with arbitrary channel fading, path-loss and interference conditions.

ABERs of LDPC-Coded Multi-Hop FSO Over Double GG Fading Channels With Pointing Error and Path Loss

The average bit error rate (ABER) performances of low-density parity-check (LDPC)-coded multi-hop free-space optical (FSO) communication system with decode-and-forward strategy over the aggregated double generalized gamma (double GG) fading channels for plane and spherical waves are investigated. In particular, on the basis of the unified closed-from expressions of the composite probability density function and cumulative distribution function in terms of the Meijer’s G function, the analytical expression of the ABER for this multi-hop FSO system is derived by generalized Gauss-Laguerre quadrature rule and verified by Monte Carlo simulation. Furthermore, LDPC codes are adopted to improve the system performance. The results show that the ABER performance over double GG distribution is mainly limited by both pointing error and path loss for these two transmission beams, whereas the fading can be significantly improved by LDPC codes, and the coding gain improvement becomes more apparent by decreasing the normalized beam-width, increasing the normalized jitter and hop numbers. This work is beneficial for the FSO system design.

Asymptotic Performance Analysis of Two-Way Relaying FSO Networks With Nonzero Boresight Pointing Errors Over Double-Generalized Gamma Fading Channels

In this correspondence, an asymptotic performance analysis for two-way relaying free-space optical (FSO) communication systems with nonzero boresight pointing errors over double-generalized Gamma fading channels is presented. Assuming amplify-and-forward relaying, two nodes having the FSO ability can communicate with each other through the optical links. With this setup, we derive some asymptotic analytical results for the outage probability and average bit error rate. Furthermore, we provide an asymptotic average capacity analysis for high signal-to-noise ratio by using the moments-based method.

On the Double-Generalized Gamma Statistics and Their Application to the Performance Analysis of V2V Communications

Important statistical properties of the double-generalized Gamma (dGG) distribution are studied in this paper. The dGG distribution is suitable for modeling non-homogeneous double-scattering radio propagation fading conditions, which can be frequently observed in vehicle-to-vehicle (V2V) communications. In this context, important statistical metrics for the bivariate dGG distribution, such as the joint probability density function, cumulative distribution function, and the moments, are derived for the first time, while simplified expressions for the corresponding marginal statistical metrics are presented. Moreover, the second-order statistics of this distribution are also analytically studied. The derived analytical framework has been employed to analyze the performance of a transmit antenna selection system operating in V2V communication channels modeled by the dGG distribution. In this scenario, the impact of outdated channel state information (CSI) to the system’s performance is investigated in terms of various metrics, including the level crossing rate and the average fade duration. Furthermore, simplified asymptotic closed-form expressions for the outage probability have been derived to examine the achievable diversity and coding gains. Based on our analysis, insightful discussions are provided. It is shown that the diversity gain is independent from the number of transmit antennas when the available CSI becomes outdated.