Gamma-Gamma Fading Research Articles

Outage Probability Analysis and Altitude Optimization of a UAV-Enabled Triple-Hop Mixed RF-FSO-Based Wireless Communication System

In this paper, we present the evaluation of network parameters for the unmanned aerial vehicle (UAV)-enabled triple-hop mixed RF/FSO-based wireless communication system, where one relay is a fixed relay and the second relay is a UAV which acts as decode-and-forward relay for communication from the base station (B) to the multiple mobile users (Mi), i∈{1,2⋯N}. The first hop from B to fixed relay (R1) is the radio frequency (RF) link modeled using α−κ−μ fading distribution, the second hop from the relay R1 to the UAV relay (R2) is a free space optics (FSO) link modeled using Gamma-Gamma fading, and the third hop from R2 to the Mi is, again, an RF link modeled using the Rayleigh fading model. The direct communication between the B and the Mi is not feasible due to the very large distance. We derive the closed form analytical expression for the outage probability of the proposed system and find the effect of the base system parameters on the performance of the system. We also analyze the outage probability of the system at high SNR values to get further insights of the system performance. In addition, altitude optimization of UAV is carried out to know the optimal elevation angle in correspondence with UAV’s optimal altitude in order to maximize performance of the system.

Performance analysis of SAC-OCDMA based Multiplexed-FSO System over Gamma-Gamma Fading using ZCC Optical Code

Performance analysis of SAC-OCDMA based Multiplexed-FSO System over Gamma-Gamma Fading using ZCC Optical Code

Unified performance parameters for IM/DD techniques over gamma-gamma fading channel with pointing errors

In this paper, we discuss the performance of different intensity modulation direct detection techniques (IM-DD) used in free space optical systems (FSO) under different channel impairments such as path loss, atmospheric turbulence, and pointing errors. We derived unified formulas for each of the average symbol error rate (SER) bounds and outage probability for different modulation techniques: OOK, MPPM, and LMPPM. The accuracy of the obtained formulas is validated through comparison with MC-simulation results. Finally, we investigate the effect of system parameters on FSO link performance.

An Insight to the Outage Performance of Multi-Hop Mixed RF/FSO/UWOC System

In this paper, we investigate the outage performance of the three-hop mixed system integrating radio frequency (RF), free space optics (FSO), and under water optical communication (UWOC) system. The closed-form analytical expressions for the outage probability of the system are derived. In the considered system, the RF channel follows the Nakagami-m distribution, the FSO channel observes the Gamma-Gamma fading statistics, and the UWOC link experiences a mixture Exponential Generalized Gamma (EGG) fading distribution. To verify the derived analytical expressions, numerical simulations are also carried out, and we present the influence of the various link parameters such as path loss, atmospheric turbulence, pointing errors, angle-of-arrival fluctuations, water salinity, and scintillation on the performance of the decode and forward (DF) relayed multi-hop communication system.

Performance analysis of a dual-hop parallel relayed mixed FSO-UWOC system

Abstract In this paper, we propose a dual-hop parallel relayed mixed free space optical-underwater optical communication (FSO-UWOC) system model to setup a high-speed communication link connecting a distant sender located at the lighthouse tower and the receiver inside the deep ocean to transmit and receive the data for the applications such as deep sea exploration, marine life study etc. The proposed model is the setup of multiple parallel cooperative dual hop communication link for the betterment of the overall system performance under the worst case scenarios. The receiver examines the end-to-end signal to noise ratio and a relay is selected which has the maximum SNR. The selected relay then decodes the incoming optical signal through FSO link into its corresponding visible light signal and further transmits it to the underwater exploration devices such as underwater drone via VLC link. The FSO link is modelled by the Gamma-Gamma fading distribution and the VLC link is modelled by Exponential Generalized Gamma distribution. The end-to-end SNR of the system is utilized to derived the outage probability of the FSO-UWOC system and the impact of the individual link parameters is studied and presented for the proposed system model.

On the Optimal Moment-Based Estimation of Gamma-Gamma Fading Channel Parameters

In this article, we derive closed-form expressions of fractional moment-based estimators for the Gamma-Gamma fading channel parameters. Most notably, as a special case of the closed-form expressions, the optimal moment-based estimators are derived by using not only the moments of the signal power but also the moments of its logarithm and their joint moments. The performance of the derived optimal moment-based estimators is analyzed in terms of the normalized mean square error via Monte Carlo simulations, along with that of conventional moment-based estimators, maximum-likelihood estimators, and Cramér-Rao lower bounds. From the numerical results, we show that the optimal moment-based estimators are superior to the conventional moment-based estimators and achieve near maximum-likelihood estimators and Cramér-Rao lower bounds performance under various channel conditions.

Influence of detection noise on the maximum likelihood estimation of atmospheric turbulence fading parameters.

Free space optical system design and performance analysis are highly related to channel statistics obtained by the channel parameter estimation. The accurate estimation of the channel parameters and scintillation index needs to consider the photoelectric detection noise at the receiving end. We propose a maximum likelihood (ML) method for estimating the parameters of a gamma-gamma fading channel affected by photoelectric detection noise. The Newton-Raphson method and expectation maximization (EM) algorithm are developed to compute the ML estimates of atmospheric turbulence fading parameters and variance of the detection noise. We also derive the Cramer-Rao bound for the unknown parameters. By way of the mean square estimation errors, our estimation technique performance is compared with existing methods of the estimation which ignore detection noise. Based on the measured channel and detection noise data under three weather conditions, it is verified that the proposed EM algorithm, considering the influence of detection noise, can significantly improve the estimation accuracy of atmospheric turbulence fading parameters.

Mixed FSO/RF Based Multiple HAPs Assisted Multiuser Multiantenna Terrestrial Communication

In this work, a mixed free-space optics (FSO)/radio-frequency (RF) based multiple serial high altitude platforms (HAPs) assisted multiuser multiantenna terrestrial communication system is considered. For the considered multi-hop system, earth station to HAP and HAP to HAP links are assumed as FSO links, and HAP to terrestrial mobile users (MUs) link is assumed as RF link. At the FSO detector both the heterodyne detection and intensity modulation direct detection techniques are considered. Atmospheric turbulence of the ES to HAP FSO link is modeled with Gamma-Gamma fading along with the pointing error impairments. As HAP situates in the stratosphere, negligible atmospheric turbulence exists at HAP altitude (20 km), hence, only pointing error is considered for the inter HAP links. Further, the HAP consists of multiantenna array to provide high data-rates to the terrestrial users via RF links, considered to be Nakagami-m distributed. The intermediate HAPs perform selective decode-and-forward relaying and opportunistic user scheduling is performed for the best user selection. For the performance analysis, analytical expression of overall outage probability is obtained and the impact of various selection parameters like pointing error, FSO detection type, MU selection, number of antennas, and RF fading severity are observed on the outage performance. Asymptotic outage probability is also derived to obtain the diversity order of the considered communication system. Further, considering various modulation schemes, a generalized average bit-error-rate expression is derived and the impact of pointing error, FSO detection type, MU selection, number of antennas, and RF fading severity are observed on its performance. Finally, derived results are validated through Monte-Carlo simulations.

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.

On the Performance of Mixed FSO-UWOC Dual-Hop Transmission Systems

In this letter, a performance study of a mixed dual-hop communication system consisting of free-space optical/underwater wireless optical communication (FSO-UWOC) links is presented. In particular, considering both heterodyne detection and intensity modulation with direct detection (IM/DD), we assume that the FSO channel suffers a Gamma-Gamma fading in the presence of pointing error impairments, while the UWOC channel experiences a mixture Exponential-Generalized Gamma (EGG) fading with pointing errors. Assuming a fixed-gain amplify-and-forward (AF) protocol, closed-form expressions for the outage probability, average bit-error-rate, and average capacity in terms of the bivariate Fox’s H-function are derived. To verify the derived analytical expressions, numerical results are provided to verify the accuracy of our results.

Performance Analysis of Dual-Hop Mixed Power Line Communication/Free-Space Optical Cooperative Systems

In this paper, we study a mixed cooperative communication system consisting of power line communication (PLC) and free-space optical communication (FSO) links, where the PLC link suffers from log-normal fading and is affected by both impulsive and background noises. Meanwhile, the FSO link undergoes Gamma-Gamma fading with both atmospheric turbulence and pointing errors. More specifically, we present closed-form expressions for the probability density function and the cumulative distribution function of the end-to-end signal-to-noise ratio of the proposed model. Consequently, the outage probability and the bit error rate (BER) performance are derived in terms of univariate Fox-H and bivariate Fox-H functions. Finally, the analytical results are verified using Monte Carlo simulations, providing useful insights into the capabilities of the proposed system.

On Secrecy Performance of Millimeter-Wave RF-Assisted FSO Communication Systems

In this article, we study the physical-layer security performance of the mixed millimeter-wave (mm-wave) radio frequency (RF) assisted free-space optical (FSO) system as a future candidate transmission technology. The Rician and the Gamma-Gamma fading are investigated for the mm-wave RF and the FSO channels, respectively. More precisely, to analyze the secrecy performance of our considered system, we derive exact closed-form expressions for the average secrecy capacity and lower bound of the secrecy outage probability. Our considered system model involves the fixed-gain and the variable-gain relaying protocols, mm-wave characteristics and pointing errors in the RF and the FSO links and finally the heterodyne detection and the intensity modulation with direct detection techniques. Monte Carlo simulation results are provided to verify our analytical results and also to investigate the effects of mentioned parameters and techniques in the security performance of the proposed mixed system.

Mixed RF/FSO Relay Networks: RIS-Equipped RF Source vs RIS-Aided RF Source

This letter proposes and evaluates the performance of reconfigurable intelligent surface (RIS)-equipped source mixed radio frequency (RF)/free space optical (FSO) relay network with opportunistic RF source scheduling. Closed-form analytical approximations are derived for the outage probability and average symbol error probability (ASEP) assuming Rayleigh and Gamma-Gamma fading models for the RF and FSO channels, respectively. Moreover, the system is studied at the high signal-to-noise ratio (SNR) regime, where the diversity order and coding gain are provided. Results illustrate that at high SNR values, the system performance is dominated by the worst hop and the diversity order is equal to G <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> =min(KN,α,β,ζ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ), where K is the number of RF sources, N is the number of reflecting elements at each source, α and β are the atmospheric turbulence parameters of the FSO link, and ζ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> is a measure for the alignment quality of the FSO source and receiver. In addition, findings show that for the same G <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> , N is more impactful on the performance than K through the coding gain G <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> . Furthermore, the RIS-equipped source scenario where RIS is internally implemented in RF sources is shown to outperform the RIS-aided scenario where RIS is used as relay in terms of both G <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> and G <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> .

Performance of optical space shift keying under jamming.

In this paper, the effect of jamming in a free-space optical (FSO) communication system that employs optical space shift keying (OSSK) is studied. The optical link suffers from saturated atmospheric turbulence (AT). Hence, the channel fading coefficients follow negative exponential probability density function (PDF). Along with additive Gaussian noise, the jammer, under consideration, is an additional source of noise, and jamming signals also suffer from saturated AT. Thus, the jamming channel also follows the negative exponential PDF. A multiple-input single-output (MISO) FSO system is used to mitigate the effects of jammer and channel fading. Explicitly, we employ a 2×1 MISO-OSSK system for analysis and derive a closed-form expression of bit error rate (BER) of the considered system. Moreover, the jammer's effect is also studied numerically under the gamma-gamma (GG) fading channel.

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.

Assessment of the FSO communication system using adaptive and MIMO MPPM with pointing errors and an atmospheric turbulence channel.

The terrestrial free space optical (FSO) communication system is attracting increased attention among the scientific and commercial research community due to its ultra-high data rate capability, licensed free large bandwidth, cost efficiency, fast and easy deployment, and secure wireless data transmission. However, the FSO system is severely affected by atmospheric conditions such as local weather conditions and fading due to turbulence. Moreover, system performance is significantly affected by pointing errors, which are caused by the misalignment between transmitter-receiver sections. Many statistical models have been proposed in the literature in order to address this significant impairment of the FSO system. In this paper, M-ary pulse position modulation (MPPM)-based FSO signal transmission over a Gamma-Gamma (G-G) fading channel is analyzed in the presence of weak to strong atmospheric turbulence and pointing errors. A multiple-input-multiple-output (MIMO) system with an equal gain combining (EGC) diversity scheme is proposed to enhance the performance of the system. The analytical closed-form expressions are obtained in terms of MeijerG-function to approximate the average bit error rate (BER) and outage probability. Furthermore, the adaptive transmission modulation (ATM) scheme is proposed to enhance the bandwidth efficiency of the FSO system link. The analytical results exhibit that the effect of turbulence and misalignment on the performance metrics (BER, outage probability) and the proposed MIMO-FSO communication link with the EGC scheme appreciably improves the system performance, and Monte Carlo simulation confirms the validation of the analytical expressions. It can also observe that bandwidth efficiency significantly improved with the proposed ATM scheme over non-adaptive counterparts.

Performance of orthogonal frequency division multiplexing based 60-GHz transmission over turbulent free-space optical link

Abstract In this paper, radio-over-free-space optic (RoFSO) transmission is investigated for the next-generation wireless networks. Here, the 60 GHz based radio frequency (RF) system is demonstrated using 16-quadrature amplitude modulation with orthogonal frequency division multiplexing scheme. System performance for FSO link is evaluated by modeling the channel with the gamma-gamma fading. The optical spectrum and constellation diagram of the received signals are analyzed. The improvement reported for error vector magnitude is 3.8–0.6% and symbol error rate of 0.03–0.005 for free-space range of 0.2–1 km. Proposed work claims that orthogonal frequency division multiplexing can be helpful for the FSO systems by providing robustness to adverse atmospheric turbulence.

Parameter Estimation of Gamma‐Gamma Fading with Generalized Pointing Errors in FSO Systems

In this paper, the challenges of parameter estimation for the Gamma‐Gamma turbulence channels with generalized pointing errors are addressed. The Kolmogorov‐Smirnov goodness‐of‐fit statistical test results indicate that the approximate probability density function obtained by the saddlepoint approximation (SAP) method provides a better approximation for a larger value wz, and this means that the proposed method is more efficient for the FSO links over long distances when the transmit divergence angle at the transmitter side is fixed. Also, an additional parameter k needs to be estimated in addition to the shaping parameters α and β under the SAP method. An estimation scheme for the shaping parameters is proposed based on the SAP method. The performance of the proposed estimation is investigated by using the mean square error (MSE) and normalized mean square error (NMSE). The results indicate the proposed estimator exhibits satisfactory performance in both noiseless and noisy environments. The effects of the receiver aperture on the estimation performance are also discussed.

Modulated Retro-Reflector-Based Physical-Layer Network Coding for Space Optical Communications

We propose a Modulated Retro-Reflector (MRR) based Physical-Layer Network Coding (PNC) framework for space two-way relay (TWR) optical communications. MRR PNC simplifies the end node's design by replacing pointing, acquisition and tracking mechanisms which require large size, weight, and power (SWaP) consumption. Each end node modulates its data on top of the interrogating beam from the relay node so that the two end nodes' frequencies are synchronized and there is no carrier frequency offset between the two end nodes and the relay. However, the transmitted signal based on the interrogating beam and twice the channel fading leads to noise aggregation. We analyze the impact of this noise aggregation by deriving the bit error rate (BER) for MRR PNC and performing simulations in Gamma-Gamma fading channels. The simulation results show that MRR PNC has a 3 dB optical signal noise ratio penalty compared with MRR “point-to-point” systems. The overall system throughput of MRR PNC is 99% higher than the traditional non-network-coded scheme in the ≥6 dB (for BPSK, ≥9 dB for QPSK) signal noise ratio regime. We propose using low-density parity-check (LDPC) codes to mitigate the problem of the degradation of the BER caused by the noise aggregation in MRR PNC. Our simulation results show that a rate 1/2 LDPC code can achieve 2 dB coding gain on BER 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> . We show that the asynchrony penalty is 3 dB on BER 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> compared with a synchronous system. The implication is that when channel coding is used, the system can still work. Our findings show that MRR PNC can double the system throughput while keeping low values of SWaP, is feasible for space TWR optical communications.

Performance improvement of hybrid OFDM-FSO system using modified OFDM receiver

Recently, free-space optical (FSO) communication systems have enlarged research and gained popularity because of its inherent advantages. The orthogonal frequency division multiplexing (OFDM) technique helps to improve the performance of the FSO communication system by using a simultaneous multi-carrier transmission scheme. The performance of the hybrid FSO-OFDM system is dependent on different parameters such as the number of sub-carriers, the nature of the laser beam, applied base band modulation, and atmospheric turbulence conditions etc. In this work, a modified OFDM receiver is proposed that improves the bit error rate (BER) significantly. This paper analyses the performance of the FSO communication system by using the proposed modified OFDM receiver over Gamma-Gamma fading channel under different weather and atmospheric turbulence conditions. Simulation results exhibit a significant improvement in the BER performance compared to the existing OFDM receivers for the FSO communication system.