Free space optics (FSO) has emerged as a key technology for high-data-rate wireless communication, thanks to the availability of mature transceiver designs and unlicensed spectrum. Although FSO links are highly directive, atmospheric turbulence introduces random scintillation effects analogous to RF multipath fading, degrading system performance. Traditional models often treat turbulence as an intensity-based stochastic process, providing limited insight into phase distortions and wavefront aberrations such as beam wander. While split-step propagation methods can capture these effects accurately, their computational cost is prohibitive for large-scale simulations. In this paper, we propose a single-phase screen channel model using Zernike polynomials, effectively representing the turbulence-induced phase aberrations without resorting to full multi-screen wave propagation. Because it preserves the full complex wavefront, the proposed method captures both phase and intensity distortions, enabling evaluation of beam-shaping and adaptive optics design and providing an accurate performance baseline for coherent FSO links. Simulation results prove the value of the proposed model, as interesting insights can be derived regarding the intensity distribution at the receiver and the impact of the receiver lens.

The line-of-sight (LOS) requirement of free-space optical (FSO) systems can be relaxed by employing optical relays or optical intelligent reflecting surfaces (IRSs). In this paper, we show that the power reflected from FSO IRSs and collected at the receiver (Rx) lens may scale quadratically or linearly with the IRS size or may saturate at a constant value. We analyze the power scaling law for optical IRSs and unveil its dependence on the wavelength, transmitter (Tx)-to-IRS and IRS-to-Rx distances, beam waist, and Rx lens size. We also consider the impact of linear, quadratic, and focusing phase shift profiles across the IRS on the power collected at the Rx lens for different IRS sizes. Our results reveal that surprisingly the powers received for the different phase shift profiles are identical, unless the IRS operates in the saturation regime. Moreover, IRSs employing the focusing (linear) phase shift profile require the largest (smallest) size to reach the saturation regime. We also compare optical IRSs in different power scaling regimes with optical relays in terms of the outage probability, diversity and coding gains, and optimal placement. Our results show that, at the expense of a higher hardware complexity, relay-assisted FSO links yield a better outage performance at high signal-to-noise-ratios (SNRs), but optical IRSs can achieve a higher performance at low SNRs. Moreover, while it is optimal to place relays equidistant from Tx and Rx, the optimal location of optical IRSs depends on the phase shift profile and the power scaling regime they operate in.

The line-of-sight (LOS) requirement of free-space optical (FSO) systems can be relaxed by employing optical relays and optical intelligent reflecting surfaces (IRSs). Unlike radio frequency (RF) IRSs, which typically exhibit a quadratic power scaling law, the power reflected from FSO IRSs and collected at the receiver lens may scale quadratically or linearly with the IRS size or may even saturate at a constant value. We analyze the power scaling law for optical IRSs and unveil its dependence on the wavelength, transmitter (Tx)-to-IRS and IRS-to-receiver (Rx) distances, beam waist, and lens size. We compare optical IRSs in different power scaling regimes with optical relays in terms of the outage probability, diversity and coding gains, and optimal placement. Our results show that, at the expense of a higher hardware complexity, relay-assisted FSO links yield a better outage performance at high signal-to-noise-ratios (SNRs), but optical IRSs can achieve a higher performance at low SNRs. Moreover, while it is optimal to place relays equidistant from Tx and Rx, the optimal location of IRSs depends on the power scaling regime they operate in.

In this paper, we investigate the modeling and design of intelligent reflecting surface (IRS)-assisted optical communication systems, which can circumvent the line-of-sight (LOS) requirement in multi-link free space optical (FSO) systems. The FSO laser beams incident on the optical IRSs have a Gaussian power intensity profile and a nonlinear phase profile, whereas the plane waves in radio frequency (RF) systems have a uniform power intensity profile and a linear phase profile. Given these substantial differences, the results available for IRS-assisted RF systems are not applicable to IRS-assisted FSO systems. Therefore, we develop a new analytical channel model for point-to-point IRS-assisted FSO systems based on the Huygens-Fresnel principle. Our analytical model captures the impact of the size, position, and orientation of the IRS as well as its phase shift profile on the end-to-end channel. To allow the sharing of the optical IRS by multiple FSO links, we propose three different protocols, namely the time division (TD), IRS-division (IRSD), and IRS homogenization (IRSH) protocols. The proposed protocols address the specific characteristics of FSO systems including the non-uniformity and possible misalignment of the laser beams. Furthermore, to compare the proposed IRS sharing protocols, we analyze the bit error rate (BER) and the outage probability of IRS-assisted multi-link FSO systems in the presence of inter-link interference. Our simulation results validate the accuracy of the proposed analytical channel model for IRS-assisted FSO systems and confirm that this model is applicable for both large and intermediate IRS-receiver lens distances. Furthermore, we show that for the proposed IRSD and IRSH protocols, inter-link interference becomes negligible if the laser beams are properly centered on the IRS and the transceivers are carefully positioned, respectively. Moreover, in the absence of misalignment errors, the IRSD protocol outperforms the other protocols, whereas in the presence of misalignment errors, the IRSH protocol performs significantly better than the IRSD protocol.

In this paper, we develop an analytical channel model for intelligent reflecting surface (IRS)-assisted free space optical (FSO) systems. Unlike IRS-assisted radio frequency systems, where it is typically assumed that a plane wave is incident on the IRS, in FSO systems, the incident wave is a Gaussian beam with non-uniform power distribution across the IRS. Taking this property into account, we develop an analytical end-to-end channel model for IRS-assisted FSO systems based on the Huygens-Fresnel principle. Our analytical model reveals the impact of the size, position, orientation, and phase-shift configuration of the IRS on the end-to-end channel. Furthermore, we show that results obtained based on geometric optics under the far-field approximation are only valid for a specific range of IRSreceiver lens distances depending on the IRS size, incident beam width, and wavelength. Simulation results validate the accuracy of the proposed analytical results for the FSO beam reflected from the IRS and compare the bit error rate performance obtained for the proposed analytical channel model with that obtained for geometric optics under the far-field approximation.

Intelligent reflecting surfaces (IRSs) have the potential to transform wireless communication channels into smart reconfigurable propagation environments. To realize this new paradigm, the passive IRSs have to be large, especially for communication in far-field scenarios, so that they can compensate for the large end-to-end path-loss, which is caused by the multiplication of the individual path-losses of the transmitter-to-IRS and IRS-to-receiver channels. However, optimizing a large number of sub-wavelength IRS elements imposes a significant challenge for online transmission. To address this issue, in this article, we develop a physics-based model and a scalable optimization framework for large IRSs. The basic idea is to partition the IRS unit cells into several subsets, referred to as tiles, model the impact of each tile on the wireless channel, and then optimize each tile in two stages, namely an offline design stage and an online optimization stage. For physics-based modeling, we borrow concepts from the radar literature, model each tile as an anomalous reflector, and derive its impact on the wireless channel for a given phase shift by solving the corresponding integral equations for the electric and magnetic vector fields. In the offline design stage, the IRS unit cells of each tile are jointly designed for the support of different transmission modes, where each transmission mode effectively corresponds to a given configuration of the phase shifts that the unit cells of the tile apply to an impinging electromagnetic wave. In the online optimization stage, the best transmission mode of each tile is selected such that a desired quality-of-service (QoS) criterion is maximized. We consider an exemplary downlink system and study the minimization of the base station (BS) transmit power subject to QoS constraints for the users. Since the resulting mixed-integer programming problem for joint optimization of the BS beamforming vectors and the tile transmission modes is non-convex, we derive two efficient suboptimal solutions, which are based on alternating optimization and a greedy approach, respectively. We show that the proposed modeling and optimization framework can be used to efficiently optimize large IRSs comprising thousands of unit cells.

In this paper, we investigate the use of intelligent reflecting surfaces (IRSs) to relax the line-of-sight requirement of free space optical (FSO) systems. Considering a Gaussian laser beam, we first design a phase-shift distribution across the IRS that enables the reflection of the incident beam in any desired direction, i.e., realizing the generalized law of reflection. Moreover, for the designed phase-shift profile, we show that there exists an equivalent mirror-assisted FSO system that generates a reflected electric field on a mirror that is identical to that on the IRS in the original system. However, the location of the laser source and the properties of the emitted Gaussian laser beam are different in the original and the equivalent systems. This equivalence allows us to study the mirror-assisted system, employing the image method from geometric optics, instead of directly analyzing the original IRS-assisted system. Based on this analysis, we model the geometric and misalignment losses (GML) and characterize the impact of the physical parameters of the IRS, such as its size, position, and orientation, on the end-to-end FSO channel. Moreover, we develop a statistical model for the GML which accounts for the random movements of IRS, transmitter (Tx), and receiver (Rx) due to building sway. Furthermore, we analyze the outage probability of an IRS-assisted FSO link based on the derived channel model. Our simulation results validate the accuracy of the developed channel model and offer various insights for system design. For instance, both our simulations and theoretical analysis reveal that even if the variances of the fluctuations of the Tx, IRS, and Rx positions caused by building sway are identical, their impact on the end-to-end channel is not necessarily the same and depends on the relative positioning of these three nodes.

In this paper, we investigate the statistics of the free space optics (FSO) communication channel between a hovering unmanned aerial vehicle (UAV) and a central unit. Two unique characteristics make UAV-based FSO systems significantly different from conventional FSO systems with static transceivers. First, for UAV-based FSO systems, the incident laser beam is not always orthogonal to the receiver lens plane. Second, both position and orientation of the UAV fluctuate over time due to dynamic wind load, inherent random air fluctuations in the atmosphere around the UAV, and internal vibrations of the UAV. On the contrary, for conventional FSO systems, the laser beam is always perpendicular to the receiver lens plane and the relative movement of the transceivers is limited. In this paper, we develop a novel channel model for UAV-based FSO systems by quantifying the corresponding geometric and misalignment losses (GML), while taking into account the non-orthogonality of the laser beam and the random fluctuations of the position and orientation of the UAV. In particular, for diverse weather conditions, we propose different fluctuation models for the position and orientation of the UAV and derive corresponding statistical models for the GML. We further analyze the performance of a UAV-based FSO link in terms of outage probability and ergodic rate and simplify the resulting analytical expressions for the high signal-to-noise ratio (SNR) regime. Finally, simulations validate the accuracy of the presented analysis and provide important insights for system design. For instance, we show that for a given variance of the fluctuations, the beam width should be properly adjusted to minimize the outage probability.

In this paper, we investigate the use of intelligent reflecting surfaces (IRSs) (i.e., smart mirrors) to relax the line-of-sight requirement of free space optical (FSO) systems. We characterize the impact of the physical parameters of the IRS, such as its size, position, and orientation, on the quality of the end-to-end FSO channel. In addition, we develop a statistical channel model for the geometric and the misalignment losses which accounts for the random movements of the IRS, transmitter, and receiver due to building sway. This model can be used for performance analysis of IRS-based FSO systems. Our analytical results shows that depending on the angle between the beam direction and the IRS plane, building sway for the IRS has either a smaller or larger impact on the quality of the end-to-end FSO channel than building sway for the transmitter and receiver. Furthermore, our simulation results validate the accuracy of the developed channel model and offer insight for system design.

This paper considers the uplink of a cloud radio access network (C-RAN) comprised of several multi-antenna remote radio units (RUs) which compress the signals that they receive from multiple mobile users (MUs) and forward them to a CU via wireless fronthaul links. To enable reliable high rate fronthaul links, we employ a hybrid radio frequency (RF)/free space optical (FSO) system for fronthauling. Moreover, to strike a balance between complexity and performance, we consider three different quantization schemes at the RUs, namely per-antenna vector quantization (AVQ), per-RU vector quantization (RVQ), and distributed source coding (DSC), two different RF fronthaul transmission modes, namely orthogonal transmission and non-orthogonal transmission, and two different detectors at the CU, namely the linear minimum mean square error detector and the optimal successive interference cancellation detector. For this network architecture, we investigate the joint optimization of the quantization noise covariance matrices at the RUs and the RF time allocation to the multiple-access and fronthaul links for rate region maximization. To this end, we formulate a unified weighted sum rate maximization problem valid for each possible combination of the considered quantization, RF fronthaul transmission, and detection schemes. To handle the non-convexity of the unified problem, we transform it into a bi-convex problem which facilitates the derivation of an efficient suboptimal solution using alternating convex optimization and golden section search. Moreover, by introducing a backoff parameter to reduce the probability of infeasibility, we generalize the proposed optimization framework to account for imperfect channel estimation. Our simulation results show that for each combination of the considered quantization, RF fronthaul transmission, and detection schemes, C-RAN with hybrid RF/FSO fronthauling can achieve a considerable sum rate gain compared to conventional systems employing pure FSO fronthauling, especially under unfavorable atmospheric conditions. In addition, employing a more sophisticated quantization scheme can significantly improve the system performance under adverse atmospheric conditions. In contrast, in clear weather conditions, when the FSO link capacity is high, the simple AVQ scheme performs close to the optimal DSC scheme. Furthermore, our simulation results suggest that the proposed algorithm can be adapted to the quality of the channel estimates by tuning the backoff parameter.

We consider a drone-based communication network, where several drones hover above an area and serve as mobile remote radio heads for a large number of mobile users. We assume that the drones employ free space optical (FSO) links for fronthauling of the users' data to a central unit. The main focus of this paper is to quantify the geometric loss of the FSO channel arising from random fluctuation of the position and orientation of the drones. In particular, we derive upper and lower bounds, corresponding approximate expressions, and a closed-form statistical model for the geometric loss. Simulation results validate our derivations and quantify the FSO channel quality as a function of the drone's instability, i.e., the variation of its position and orientation.

We consider a free space optical (FSO) backhauling system which consists of two base stations (BSs) and one central unit (CU). We propose to employ non-orthogonal multiple access (NOMA) for FSO backhauling where both BSs transmit at the same time and in the same frequency band to the same photodetector at the CU. We develop a dynamic NOMA scheme which determines the optimal decoding order as a function of the channel state information at the CU and the quality of service requirements of the BSs, such that the outage probabilities of both BSs are jointly minimized. Moreover, we analyze the performance of the proposed NOMA scheme in terms of the outage probability over Gamma-Gamma FSO turbulence channels. We further derive closed-form expressions for the outage probability for the high signal-to-noise ratio regime. Our simulation results confirm the analytical derivations and reveal that the proposed dynamic NOMA scheme significantly outperforms orthogonal transmission and existing NOMA schemes.

This paper considers the uplink of a cloud radio access network (C-RAN) comprised of several multi-antenna remote radio units (RUs) which send the data that they received from multiple mobile users (MUs) to a central unit (CU) via a wireless fronthaul link. One of the fundamental challenges in implementing C-RAN is the huge data rate required for fronthauling. To address this issue, we employ hybrid radio frequency (RF)/free space optical (FSO) systems for the fronthaul links as they benefit from both the large data rates of FSO links and the reliability of RF links. To efficiently exploit the fronthaul capacity, the RUs employ vector quantization to jointly compress the signals received at their antennas. Moreover, due to the limited available RF spectrum, we assume that the RF multiple-access and fronthaul links employ the same RF resources. Thereby, we propose an adaptive protocol which allocates transmission time to the RF multiple-access and fronthaul links in a time division duplex (TDD) manner and optimizes the quantization noise covariance matrix at each RU such that the sum rate is maximized. Our simulation results reveal that a considerable gain in terms of sum rate can be achieved by the proposed protocol in comparison with benchmark schemes from the literature, especially when the FSO links experience unfavorable atmospheric conditions.

In this paper, we investigate the performance of a dual-hop block fading cognitive radio network with underlay spectrum sharing over independent but not necessarily identically distributed (i.n.i.d.) Nakagami-m fading channels. The primary network consists of a source and a destination. Depending on whether the secondary network which consists of two source nodes have a single relay for cooperation or multiple relays thereby employs opportunistic relay selection for cooperation and whether the two source nodes suffer from the primary users' (PU) interference, two cases are considered in this paper, which are referred to as Scenario (a) and Scenario (b), respectively. For the considered underlay spectrum sharing, the transmit power constraint of the proposed system is adjusted by interference limit on the primary network and the interference imposed by primary user (PU). The developed new analysis obtains new analytical results for the outage capacity (OC) and average symbol error probability (ASEP). In particular, for Scenario (a), tight lower bounds on the OC and ASEP of the secondary network are derived in closed-form. In addition, a closed from expression for the end-to-end OC of Scenario (a) is achieved. With regards to Scenario (b), a tight lower bound on the OC of the secondary network is derived in closed-form. All analytical results are corroborated using Monte Carlo simulation method.

Hybrid radio frequency (RF)/free space optical (FSO) systems are among the candidate enabling technologies for the next generation of wireless networks, since they benefit from both the high data rates of the FSO subsystem and the high reliability of the RF subsystem. In this paper, we focus on the problem of throughput maximization in the parallel hybrid RF/FSO relay channel. In the parallel hybrid RF/FSO relay channel, a source node sends its data to a destination node with the help of multiple relay nodes. Thereby, for a given relay, the source-relay and the relay-destination FSO links are orthogonal with respect to each other due to the narrow beam employed for FSO transmission, whereas due to the broadcast nature of the RF channel, half-duplex operation is required for the RF links if self-interference is to be avoided. Moreover, we consider the two cases where the relays are and are not equipped with buffers. For both cases, we derive the optimal relay selection policies for the RF and FSO links and the optimal time allocation policy for transmission and reception for the RF links. The proposed optimal protocols provide important insights for an optimal system design. Since the optimal buffer-aided policy introduces an unbounded delay, we also propose a suboptimal buffer-aided policy, which ensures certain target average delays. Moreover, we present distributed implementations for both the proposed optimal protocols. Simulation results demonstrate that a considerable gain can be achieved by the proposed adaptive protocols in comparison with benchmark schemes from the literature.

Hybrid radio frequency (RF)/free space optical (FSO) systems are among the candidate enabling technologies for the next generation of wireless networks since they benefit from the advantages of both the FSO subsystem, e.g. high data rates, and the RF subsystem, e.g. high reliability in terms of link connectivity. In this paper, we focus on the problem of throughput maximization in the parallel hybrid RF/FSO relay channel. In the parallel hybrid RF/FSO relay channel, a source node sends its data to a destination node with the help of multiple relay nodes. Thereby, the source-relay and the relay-destination FSO links are orthogonal with respect to each other due to the narrow beam employed for FSO transmission whereas the RF links are half duplex with respect to each other due to the broadcast nature of RF signals. We derive the optimal relay selection policies for transmission and reception for the RF and FSO links and the optimal time allocation policy to the RF relay reception and transmission links. Simulation results demonstrate that a considerable gain can be achieved by the proposed adaptive protocol in comparison with benchmark schemes from the literature.