Multi-hop Free Space Optical Research Articles

Multihop radio and optical wireless relaying systems over EGK, DGG, and CU fading channels

Optical wireless communications (OWC) systems provide higher data rates in the unlicensed spectrum bands compared to traditional radio frequency (RF) wireless communications systems. OWC systems are categorized as free space optical (FSO) communications and visible light communications (VLC) for outdoor and indoor environments, respectively. In this paper, we propose a multihop serial RF, FSO, and VLC system and investigate the link performance for five different scenarios with amplify-and-forward and decode-and-forward relaying protocols under different channel conditions. Based on the SNR statistics, we show closed-form expressions for the outage probability for all scenarios and derive their diversity orders. In addition, we examine the accuracy and correctness of the derived expressions by means of Monte Carlo simulations. We further prove that the diversity order is a function of the severity of the RF links and the shaping parameters, the atmospheric turbulence, the pointing error in FSO links, the detection method, and number of links. Finally, the presented results complement and extend several results previously reported in the literature.

Performance analysis of multi-hop parallel FSO system over double generalized gamma distribution considering two transmission beams

The performances of multi-hop parallel free space optical (FSO) communication system are investigated over double generalized gamma (double GG) distribution for plane and spherical waves considering path loss and pointing errors (PE). Specifically, the closed-form expressions of outage probability and average bit error rate (ABER) are derived with Meijer-G function and further confirmed by Monte Carlo (MC) simulation. Subsequently, the outage performances of this system are analyzed in detail with the influence of PE, turbulence strengths, structure parameters and weather conditions for plane and spherical waves. Moreover, cyclic coding is used in this work to further optimize system performance.

Applications of Meijer’s Factorization Theorems in Performance Analyses of All-Optical Multi-Hop FSO Systems

The use of bivariate Fox H-functions (BFHFs) in performance analyses of wireless communication systems has gained considerable attention in past few decades. However, the non-existence of robust built-in routines for evaluating such functions in standard computing systems poses numerous challenges in numerical experiments and simulations. Motivated by the apparent need to circumvent these difficulties in performance analyses of cooperative wireless communications, this work presents an alternative method for obtaining the exact, approximate and asymptotic BFHF-free cumulative distribution function (CDF) of the end-to-end (e2e) signal-to-noise ratio (SNR) of multi-hop amplify-and-forward (AF) relaying wireless communication systems. As an illustration, the e2e performance analysis of an all-optical dual-hop free-space optical (FSO) transmission system over Gamma-Gamma turbulence in the presence of pointing errors is revisited. Specifically, new mathematical formulae for the statistical characteristics of the e2e SNR for systems with AF fixed-gain relaying as well as channel-state-information(CSI)-assisted using heterodyne detection (HD) or intensity modulation with direct detection (IM/DD) are derived in terms of mathematically malleable and uniformly convergent infinite series of weighted Meijer G-functions. The usefulness of the derived CDFs is illustrated through derivation of traditional system performance metrics. The accuracy of the derived analytical formulae is verified via Monte Carlo simulations in MATLAB®. Finally, based on results observed in this paper, useful expansions of common BFHFs in terms of easily computable univariate hypergeometric functions are proposed.

On the performance of a novel multi-hop relay-assisted hybrid FSO / RF communication system with receive diversity

One of the main problems in mobile communication systems is long-range links in weather conditions that could disrupt Radio Frequency (RF) connection. This problem could be solved by use of diversity or consuming more power or adding processing complexity. However, a mobile device has limited size and a small battery, and does not afford multiple antennas, or higher power consumption, or more complexity. So it is better to implement these techniques on the receiver, which is the base station. In this paper, a novel multi-hop hybrid Free Space Optical (FSO) / RF system is presented as a solution for the proposed scenario (long-range links in bad weather condition). In the proposed structure, a mobile user is connected to the source Base Station with receive diversity, and the source Base Station is connected to the destination Base Station via a multi-hop hybrid parallel FSO / RF link. In order to have a favorable performance with the lowest possible complexity, selection combining as well as demodulate and forward relaying are used at all hops of the proposed structure. The proposed structure has advantages of FSO, RF, and relay-assisted systems at the same time. The innovations and contributions of this paper, which are first introduced in the multi-hop hybrid FSO/ RF hybrid structure, include the novelty of the proposed structure, the presentation of new exact and asymptotic mathematical solutions, use of demodulate and forward protocol, taking into account a wide range of atmospheric turbulence with the effect of pointing error, use of selection combining at each relay. In order to show the efficiency of the proposed structure, Bit Error Rate and Outage Probability of the proposed structure are investigated in a wide range of atmospheric turbulence from moderate to saturate. Considering these criteria, closed-form exact and asymptotic expressions are derived and verified by MATLAB simulations. Results indicate that the proposed structure shows independent performance at moderate to strong atmospheric turbulence regimes. Hence, it is not required to adaptively adjust system parameters in order to have a constant performance. Accordingly, this structure is economically affordable and particularly suitable for mobile communications that should deal with frequent changes in atmospheric turbulence in urban by a limited complexity and power consumption.

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.

Multi-Hop Relay Based Free Space Optical Communication Link for Delivering Medical Services in Remote Areas

Free Space Optical (FSO) communication links are although extremely vulnerable to atmospheric adversities, multi-hop relay transmission can however, significantly improve the link performance and reliability. This paper proposes 120 Gbps DP-16 QAM modulated multi-hop serial FSO link with coherent reception for delivering medical consultation services in remote and isolated locations. Considering the current situation wherein pandemic of highly infectious nature, COVID-19 has affected millions of people globally; doctors can use the proposed high-speed architecture for “contact-less” supervision of quarantined patients and suspects through video conferencing. Each relay terminal uses an all-optical amplify-and-forward technique with Erbium-doped fiber amplifier (EDFA) and gain optimization as its core elements. As a possible last-mile application for delivering medical/health care services, the proposed link has been evaluated for reliability by exposing the link to varied atmospheric conditions. Our results reveal that at target BER of $10^{-5}$ , the useful communication link range of proposed multi-hop link increments by 1.8 kms as compared to direct link that operates under similar channel conditions. Furthermore, compared to results from recent literature on high-speed FSO [30], the proposed link shows enhancement in link range by approximately 0.7 km. The analysis also reveals that as the number of relay nodes increases, the error performance of the link for different atmospheric conditions approaches a state of convergence.

Performance analysis for a mixed RF and multihop FSO communication system in 5G C-RAN

In this paper, we investigate the performance of a mixed radio frequency (RF) and multihop free space optical (FSO) system in a fifth-generation cloud radio access network (C-RAN) architecture. To cope with the practical channel characteristics, the RF link is assumed to experience the $ \kappa - \mu $ shadowed fading that has recently been proposed to model the small-scale multipath fading as well as line-of-sight shadowing. For FSO links, we adopt the exponentiated Weibull distribution, which can represent irradiance fluctuations at the finite receiving aperture over a wide range of turbulence conditions. Furthermore, we consider the pointing error between the FSO end devices. We first derive a novel probability density function (PDF) expression for the $ \kappa - \mu $ shadowed fading so that the $ \kappa $, $ m $, and $ \mu $ can be equal to the arbitrary positive real value. Then, we study the outage probability and the average symbol error rate (ASER) of the considered system. Our analysis is based on a decode-and-forward (DF) relaying scheme. We choose M-ary quadrature amplitude modulation (M-QAM) for the RF link and binary pulse position modulation (BPPM) for the FSO links. Finally, to provide more insights, we present the asymptotic approximate expressions in high signal-to-noise ratio regimes. Our research shows that the performance of the mixed RF and multihop FSO system can be improved by the large receiving aperture and the increasing number of hops.

On the performance of a multi-user multi-hop hybrid FSO/RF communication system

One of the main problems in mobile communication systems is long-range impassable links or some specific atmospheric conditions under which Radio Frequency (RF) connection becomes easily disrupted. One way to solve this problem is by consuming more power or adding processing complexity, but a small user mobile phone cannot deserve more complexity or power supply. Another way is to use an access point that amplifies received signal via short-range RF link and forwards it to via long-range Free Space Optical (FSO) link. In this paper, a novel multi-user multi-hop hybrid FSO / RF communication system is presented. This structure consists of two main parts. The first part establishes the connection between the mobile users and the source base station, and the second part establishes the connection between the source and the destination base stations. In the first part, mobile users want to connect to the source base station via a long-range link; therefore, an amplify and forward relay is used for communication establishment. In the second part, the source and the destination base stations are connected via a multi-hop hybrid parallel FSO / RF link with demodulating and forward relaying. The FSO link in moderate to strong and in saturated regimes is assumed at Gamma–Gamma and Negative Exponential atmospheric turbulence, respectively, also the effect of pointing error is considered, and RF link has Rayleigh fading. New closed-form exact and asymptotic expressions are derived for the Outage Probability and Bit Error Rate (BER) of the proposed structure. Derived expressions are verified with MATLAB simulations. The proposed structure has advantages of FSO, RF, relay-assisted, and multi-user systems at the same time. Results indicate that it has low dependence on the number of users and the number of relays. Therefore, it is suitable for areas with varying population and long-range links. This structure offers independent performance without additional power consumption, processing latency, and complexity. The innovations and contributions of this paper, which are first introduced in the multi-hop hybrid FSO / RF hybrid structure, include the novelty of the proposed structure, the presentation of new exact and asymptotic mathematical solutions, use of multi-user scheme in a multi-hop FSO / RF structure, BER analysis, using amplify and forward as well as decode and forward protocols, taking into account a wide range of atmospheric turbulence with the effect of pointing error, using opportunistic selection schemes at each relay.

Unified Error Performance of a Multihop DF-FSO Network With Aperture Averaging

In this paper, the performance of a multihop decode-and-forward (DF) based freespace optical (FSO) network is investigated over a unified exponentiated Weibull distributed atmospheric turbulence channel with pointing error and both types of detection techniques, i.e., heterodyne detection and intensity modulation/direct detection (IM/DD). We consider the aperture averaging receivers at both the intermediate relays and the destination to diminish the disadvantageous impact of atmospheric turbulence. First, we derive the new unified expression of the probability density function of the instantaneous signal-to-noise ratio (SNR). Based on the derived statistics, the unified closed-form expression of the average symbol error rate (SER) for the considered multihop network employing differentially modulated M-ary phase shift keying data, is obtained by utilizing a transition probability matrix. It is shown that increasing the hop count by 1 provides similar performance gain under both detection schemes. Further, a small increase in aperture size results in greater improvement under moderate turbulence rather than strong turbulence. The mutual information of the considered network is obtained with binary differential data, and it is demonstrated through results that, in the low-SNR region, the heterodyne receiver provides less mutual information as compared with the IM/DD receiver. However, beyond a particular SNR value (which depends on the hop count, aperture size, and turbulence strength), the heterodyne receiver attains more mutual information in comparison with the IM/DD receiver. The unified expression of outage probability for the DF-based multihop FSO network is also derived in terms of Meijer's G function. In addition, the asymptotic SER performance is examined in order to get impactful insight of network performance at high SNRs. All analytical results derived are verified through simulations.

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.

Free-Space Optical Systems over Correlated Atmospheric Fading Channels: Spatial Diversity or Multihop Relaying?

Both spatial diversity and multihop relaying are considered to be effective methods for mitigating the impact of atmospheric turbulence-induced fading on the performance of free-space optical (FSO) systems. Multihop relaying can significantly reduce the impact of fading by relaying the information over a number of shorter hops. However, it is not feasible or economical to deploy relays in many practical scenarios. Spatial diversity could substantially reduce the fading variance by introducing additional degrees of freedom in the spatial domain. Nevertheless, its superiority is diminished when the fading sub-channels are correlated. In this paper, our aim is to study the fundamental performance limits of spatial diversity suffering from correlated Gamma-Gamma (G-G) fading channels in multihop coherent FSO systems. For the performance analysis, we propose to approximate the sum of correlated G-G random variables (RVs) as a G-G RV, which is then verified by the Kolmogorov-Smirnov (KS) goodness-of-fit statistical test. Performance metrics, including the outage probability and the ergodic capacity, are newly derived in closed-form expressions and thoroughly investigated. Monte-Carlo (M-C) simulations are also performed to validate the analytical results.

A Generic Simulation Approach for the Fast and Accurate Estimation of the Outage Probability of Single Hop and Multihop FSO Links Subject to Generalized Pointing Errors

When assessing the performance of the free space optical (FSO) communication systems, the outage probability encountered is generally very small, and thereby the use of nave Monte Carlo simulations becomes prohibitively expensive. To estimate these rare event probabilities, we propose in this paper an importance sampling approach which is based on the exponential twisting technique to offer fast and accurate results. In fact, we consider a variety of turbulence regimes, and we investigate the outage probability of FSO communication systems, under a generalized pointing error model based on the Beckmann distribution, for both single and multihop scenarios. Selected numerical simulations are presented to show the accuracy and the efficiency of our approach compared with naive Monte Carlo.

Performance analysis of MISO multi-hop FSO links over log-normal channels with fog and beam divergence attenuations

The performance analysis of a multi-hop decode and forward relaying free-space optical (FSO) communication system is presented in this paper. The considered FSO system uses intensity modulation and direct detection as means of transmission and reception. Atmospheric turbulence impacts are modeled as a log-normal channel, and different weather attenuation effects and geometric losses are taken into account. It is shown that multi-hop is an efficient technique to mitigate such effects in FSO communication systems. A comparison with direct link and multiple-input single-output (MISO) systems considering correlation effects at the transmitter is provided. Results show that MISO multi-hop FSO systems are superior than their counterparts over links exhibiting high attenuation. Monte Carlo simulation results are provided to validate the bit error rate (BER) analyses and conclusions.

Multihop Free-Space Optical Communications Over Turbulence Channels with Pointing Errors using Heterodyne Detection

This paper proposes and analyzes the performance of the multihop free-space optical (FSO) communication links using a heterodyne differential phase-shift keying modulation scheme operating over a turbulence induced fading channel. A novel statistical fading channel model for multihop FSO systems using channel-state-information-assisted and fixed-gain relays is developed incorporating the atmospheric turbulence, pointing errors, and path-loss effects. The closed-form expressions for the moment generating function, probability density function, and cumulative distribution function of the multihop FSO channel are derived using Meijer's G-function. They are then used to derive the fundamental limits of the outage probability and average symbol error rate. Results confirm the performance loss as a function of the number of hops. Effects of the turbulence strength varying from weak-to-moderate and moderate-to-strong turbulence, geometric loss, and pointing errors are studied. The pointing errors can be mitigated by widening the beam at the expense of the received power level, whereas narrowing the beam can reduce the geometric loss at the cost of increased misalignment effects.

Power Allocation for Quantum-Limited Multihop Free-Space Optical Communication Systems

In this paper, we propose two novel power allocation strategies for multihop Free-Space Optical (FSO) networks with any number of hops. These strategies correspond to the analytical solutions obtained from minimizing two different upper-bounds on the conditional error probability under the quantum-limit scenario. The performance of the first strategy is evaluated numerically and closed-form expressions of the average probability of error are derived for the second strategy. We also quantify the reduction in the fading variance and scintillation index provided by multihop FSO systems associated with the second power allocation scheme that compromises performance for simplicity. Results show the superiority of the proposed schemes compared to the equal power distribution strategy.

Outage probability of relayed free space optical communication systems

Free space optical (FSO) communication is highly sensitive to atmospheric turbulence. The use of relays where the distance between the transmitter and the receiver is scaling down via multi-hop routing can improve the performance of an FSO link. In this reported work, the outage probability of a multi-hop FSO communication system with amplify-and-forward relays, assuming strong turbulence fading channels, is analytically derived. The turbulence-induced fading is modelled as a multiplicative random process which follows the K or the negative exponential distribution.