Physical layer security (PLS) is an attractive paradigm for protecting information confidentiality without the use of traditional key-based cryptography. This paper proposes a design of probabilistic constellation shaping to improve the PLS performance of optical wireless channels using$M$-ary pulse amplitude modulation ($M$-PAM) with the signal-dependent noise model. Specifically, the proposed design aims to maximize the reliability (i.e., minimization of the bit error rate - BER) of the legitimate user's channel while guaranteeing that the modulationconstrained secrecy capacity is at least equal to that achieved by the uniform signaling. For this purpose, a novel upper bound for the BER of$M$-PAM constellation with signal-dependent noise channels with arbitrary input distribution is derived. Simulation results reveal that the proposed PCS design achieves a considerably lower BER of the legitimate user's channel while attaining the same secrecy capacity as the uniform signaling.

This paper proposes a joint design of probabilistic constellation shaping (PCS) and precoding to enhance the sum-rate performance of multi-user visible light communications (VLC) broadcast channels subject to signal amplitude constraint. In the proposed design, the transmission probabilities of bipolarM-pulse amplitude modulation (M-PAM) symbols for each user and the transmit precoding matrix are jointly optimized to improve the sum-rate performance. The joint design problem is shown to be a complex multivariate non-convex problem due to the non-convexity of the objective function. To tackle the original non-convex optimization problem, the firefly algorithm (FA), a nature-inspired heuristic optimization approach, is employed to solve a local optima. The FA-based approach, however, suffers from high computational complexity. Thus, using zero-forcing (ZF) precoding, we propose a low-complexity design, which is solved using an alternating optimization approach. Additionally, considering the channel uncertainty, a robust design based on the concept of end-to-end learning with autoencoder (AE) is also presented. Simulation results reveal that the proposed joint design with PCS significantly improves the sum-rate performance compared to the conventional design with uniform signaling. For instance, the joint design achieves$\mathbf {17.5\%}$and$\mathbf {19.2\%}$higher sum-rate for 8-PAM and 16-PAM, respectively, at 60 dB peak amplitude-to-noise ratio. Some insights into the optimal symbol distributions of the two joint design approaches are also provided. Furthermore, our results show the advantage of the proposed robust design over the non-robust one under uncertain channel conditions.

This paper studies a practical design of probabilistic constellation shaping (PCS) for enhancing the performance of physical layer security in visible light communications (VLC). In particular, we consider a wiretap VLC channel employing a probabilistically shapedM-ary pulse amplitude modulation (PAM) constellation. Considering the requirements for reliability of the legitimate user’s channel, flickering-free transmission, and symmetric constellation distribution, the optimal constellation distributions to maximize modulation-constrained secrecy capacity or the bit error rate (BER) of eavesdropper’s channel are investigated for both scenarios of known and unknown eavesdropper’s channel state information (CSI). To formulate the constraint on the channel reliability, tractable closed-form expressions for the upper bound and approximate BER ofM-ary PAM under an arbitrary symbol probability are derived. The design problem is shown to be non-convex due to the non-convex BER constraint. By proving that the upper bound BER is a concave function of the constellation distribution, a suboptimal solution based on the convex-concave procedure (CCCP) is presented. Our findings reveal that while the uniform signaling can only satisfy the BER constraint when the optical power is beyond a certain value, the proposed PCS design works in the entire region of the optical power. Some insights into the optimal constellation distribution with respect to the emitted optical power are also discussed.

This paper proposes a joint design of probabilistic constellation shaping (PCS) and precoding to enhance the sum-rate performance of multi-user visible light communications (VLC) broadcast channels subject to signal amplitude constraint. In the proposed design, the transmission probabilities of bipolar M-pulse amplitude modulation (M-PAM) symbols for each user and the transmit precoding matrix are jointly optimized to improve the sum-rate performance. The joint design problem is shown to be a complex non-convex problem due to the non-convexity of the objective function. To tackle the problem, the firefly algorithm (FA), a nature-inspired heuristic optimization approach, is employed to solve a local optima to the original non-convex optimization problem. The FA-based approach, however, suffers from high computational complexity. Therefore, we propose a low-complexity design based on zero-forcing (ZF) precoding, which is solved using an alternating optimization (AO) approach. Simulation results reveal that the proposed joint design with PCS significantly improves the sum-rate performance compared to the conventional design with uniform signaling. Some insights into the optimal symbol distributions of the two joint design approaches are also provided.

This paper investigates the energy efficiency (EE) of rate-splitting multiple access (RSMA)-based visible light communications (VLC) with confidential private messages. We first formulate an EE maximization problem that takes into account the achievable rate of the common message and the sum secrecy rate of private messages. Due to the fractional non-convex nature of the design problem, an algorithm that leverages the Dinkelbach algorithm and convex-concave procedure (CCP) is proposed to solve local optima. In this study, the channel similarity$S_{C}$and the rate-splitting power allocation ratio$\rho$are jointly considered to evaluate EE performance and trade-offs between the achievable common rate and the sum secrecy rate. Numerical results reveal that when$S_{C}$is below 0.7, the EE saturates at its optimum as$\rho$increases, while when$S_{C}$exceeds 0.7, an optimal$\rho$exists beyond which the EE starts declining. Moreover, it is observed that while the relationship between the sum secrecy rate and$S_{C}$is inversely proportional, it is directly proportional in the case of the common rate.

This paper proposes a practical design of proba-bilistic constellation shaping (PCS) for physical layer security in visible light communications. In particular, the$M$-ary PAM symbol distribution is optimized to maximize the secrecy capacity given constraints on the legitimate user's bit error rate (BER) and flickering mitigation. For this purpose, an approximate closed-form expression for the BER of M-ary PAM under an arbitrary symbol probability is derived and the issue of flickering caused by the channel-dependent solution is described. The design problem is shown to be non-convex due to the non-convex BER constraint. Thus, a suboptimal solution based on successive convex approximation (SCA) is presented. Our findings reveal that while the uniform signaling and PCS design without BER constraint can only satisfy the BER constraint when the optical power is beyond a certain value, the proposed PCS design works in all regions of the optical power. Some insights into the optimal symbol distribution with respect to the optical power are also discussed.

Though visible light communication (VLC) systems are contained to a given room, improving their security is an important criterion in any practical deployment. This paper studies the design of artificial noise (AN) to enhance physical layer security in VLC systems in the context of input signals with no explicit amplitude constraint (e.g., multicarrier systems). In such systems, clipping is needed to constrain the input signals within the limited linear ranges of the LEDs. However, this clipping process gives rise to non-linear clipping distortion, which must be incorporated into the AN design. To solve the design problem, a sub-optimal approach is presented using the Charnes-Cooper transformation and the convex-concave procedure (CCP). Then, a novel AN transmission scheme is proposed to reduce the impact of clipping distortion, thus improving the secrecy performance. The proposed scheme exploits the typical structure of LED luminaries that are composed of multiple light-emitting chips. Specifically, LED chips in each luminaire are divided into two groups driven by separate driver circuits. One group is used to transmit the information-bearing signal, while the other group transmits the AN. Numerical results show that while clipping distortion can significantly reduce the secrecy level, with proper design AN significantly improves the secrecy performance using the proposed design methodology.

Federated learning (FL)-enabled digital twin (DT) has recently attracted research attention to bring intelligent applications. However, enabling the FL-enabled DT in vehicular networks becomes challenging due to vehicle mobility’s impact on communication channels. In this regard, we propose to deploy an unmanned aerial vehicle (UAV) as a relay node to support the vehicular network. The objective is to minimize energy consumption under the trade-off with the latency and accuracy constraints of the DT model via a joint optimization of local accuracy, the local computation frequency, relay decision, and transmission power. To do so, we derive instantaneous formulas to update the accuracy and latency constraints, then solve the proposed problem using an iterative algorithm with convex optimization techniques. Numerical results show that the proposed dynamic optimization for UAV-aided vehicular networks can reduce up to 39.9% of consumption energy compared to conventional methods.

Though visible light communication (VLC) systems are contained in a given room, ensuring their security amongst users in a room is essential. In this paper, the design of artificial noise (AN) to enhance physical layer security in VLC systems is studied in the context of input signals with no explicit amplitude constraint (such as multicarrier systems). In such systems, clipping is needed to constrain the input signals within the limited linear ranges of the LEDs. However, this clipping process gives rise to non-linear clipping distortion, which must be incorporated into the AN design. To facilitate the solution of this problem, a sub-optimal design approach is presented using the Charnes-Cooper transformation and the convex-concave procedure (CCP). Numerical results show that the clipping distortion significantly reduces the secrecy level, and using AN is advantageous over the no-AN scheme in improving the secrecy performance.

Physical layer security (PLS) offers a unique approach to protecting information confidentiality against eavesdropping by malicious users. This paper studies a joint design of adaptive M−ary pulse amplitude modulation (PAM) and precoding for performance improvement of PLS in visible light communications (VLC). It is known that higher-order modulation results in a better secrecy capacity at the expense of a higher bit-error rate (BER). On the other hand, a proper precoding design can also enhance secrecy performance. The proposed design, therefore, aims at the optimal PAM modulation order and precoder to maximize a utility function that takes into account the secrecy capacity and BERs of the legitimate user (Bob)’s and the eavesdropper (Eve)’s channel. Due to the lack of a closed-form expression for the utility function, a Q-learning-based design is proposed and evaluated. Compared to the non-adaptive approach under all different settings of Bob’s and Eve’s positions, simulation results verify that the proposed joint adaptive design achieves a good balance between the secrecy capacity and BER of Bob’s channel while maintaining a sufficiently high BER of Eve’s channel.

In this paper, we newly present a closed-form expression for the bit-error rate (BER) of an M-ary pulse-amplitude modulation (M-PAM) over additive white Gaussian noise (AWGN) channels by analytically characterizing the bit decision regions and positions. The obtained expression is then used to derive the conditional BER of a rectangular quadrature amplitude modulation (QAM) for a given value of phase noise. Numerical results show that the impact of phase noise on the conditional BER performance is proportional to the constellation size. Moreover, it is observed that given a constellation size, the square QAM is more resilient to phase noise in the sense that it achieves the lowest phase noise-induced performance loss compared to other rectangular constellations.

In this paper, an energy-efficient precoding scheme is designed for multi-user visible light communication (VLC) systems in the context of physical layer security, where users' messages are kept mutually confidential. The design problem is shown to be non-convex fractional programming, therefore Dinkelbach algorithm and convex-concave procedure (CCCP) based on the first-order Taylor approximation are utilized to tackle the problem. Numerical results are performed to show the convergence behaviors and the performance of the proposed solution for different parameter settings.

Physical layer security (PLS) has recently gained a lot of attention in the research and development of visible light communication (VLC). In this article, we study the designs of PLS in VLC systems in the presence of multiple unauthorized users (i.e. eavesdroppers) using artificial noise (AN)-aided precoding. The design objective focuses on minimizing the total transmit power subject to specific constraints on the signal-to-interference-plus-noise ratios (SINRs) of the legitimate and unauthorized users. In particular, two design approaches are investigated considering the availability of unauthorized users' channel state information (CSI) at the transmitter. In the case of unknown CSI, the AN is constructed to lie on the null-space of the legitimate user's channel. The design problem is convex, thus, can be effectively solved. When the CSI is available, the design additionally imposes constraints on the maximum allowable unauthorized users' SINRs. The design problem, in this case, is, nevertheless, non-convex. Therefore, instead of finding the optimal solution, we examine two different sub-optimal yet low-complexity approaches to solve the problem, namely: Concave-Convex Procedure (CCP) and Semidefinite Relaxation (SDR). Additionally, robust designs that take into account channel uncertainty are also investigated. Extensive numerical results are shown to demonstrate the feasibility and performance of each design with practical parameters.

In this paper, we study the performance of unmanned aerial vehicle (UAV)-based free-space optical (FSO) systems over atmospheric turbulence channels considering the pointing misalignment and UAV hovering. The Gamma-Gamma distribution is used for modeling the turbulence-induced fading and the Gaussian beam is assumed for laser beam between two UAVs at the low and high altitudes. A closed-form expression for the symbol error probability is derived and validated by Monte-Carlo simulations. The selected results show the impact of some key factors such as UAV position and beam-waist on the system performance so that the practical system parameters can be determined.

This paper focuses on the free-space optics (FSO) links between high-altitude platforms (HAPs) and unmanned aerial vehicles (UAVs) which have not been addressed in the literature. In the considered system model, a HAP and a UAV play the roles as a transmitter and a receiver, respectively. The UAV is in operation when it is within the beam coverage of the HAP. This work aims to model the HAP-UAV FSO channel taking into account the effects of both the atmospheric turbulence and the pointing error caused by the UAV's hovering. A Gaussian beam model is assumed for the laser transmitted from the HAP and the log-normal distribution is adopted for the atmospheric turbulence-induced fading. For performance analysis, the outage probability and outage capacity versus the distance from the UAV to the center of the received Gaussian beam footprint are numerically investigated. Moreover, Monte-Carlo simulations are also performed to verify the numerical results.

This paper studies multi-user multi-cell visible light communications networks in which each cell is composed of multiple light emitting diode (LED) arrays. The use of multiple LED transmitters enables each cell to support multiple users by means of precoding techniques. In such multi-user multi-cell networks, the signal for each user can be severely interfered not only by the signals that are intended to other users in the same cell, i.e., intra-cell interference, but also by the signals for users of the other cells, i.e., inter-cell interference. While intra-cell interference can be handled by the underlying precoding scheme, it is hard to deal with the inter-cell one. This paper focuses on cell coordination/cooperation strategies and their corresponding coordinated/cooperative precoder designs as the approaches to alleviate, or possibly, to cancel out the inter-cell interference. We first derive lower and upper bounds on the capacity of Gaussian interference channels with amplitude constraints on the input and the interference. Capitalizing on derived bounds and the zero-forcing scheme as the underlying precoding technique, optimal coordinated/cooperative precoding designs to maximize users' sum-rate are investigated under the non-negativity and amplitude-limited constraints on the channel inputs. The comprehensive numerical results are presented to compare the performance of the considered coordination/cooperation strategies.

This paper investigated the comparative performance of different cell cooperation strategies for multi-cell multi-user visible light communications (VLC) networks. In practical deployment of VLC, multiple LED arrays are deployed to provide sufficient illumination for large rooms/offices. As a consequence, multi-cell configurations are a natural progression for indoor VLC networks. In this study, to support multiple users simultaneously by means of precoding technique, each VLC cell is formed by 4 separated LED arrays. In such multi-cell networks, a user can be severely interfered not only by the signals that are intended to other users within the cell (intra-cell interference) but also by the signals for users of the other cells (inter-cell interference). In order to suppress these interferences, cell cooperation can be applied for precoder designs. We consider several strategies of cell cooperation and investigate the design of optimal precoding matrix corresponding to each cooperative strategy to maximize the achievable sum capacity of users. Comprehensive numerical results are shown to compare the performance of the considered cooperation strategies.

This paper studies zero-forcing (ZF) precoding designs for multi-user multiple-input single-output visible light communication (VLC) broadcast channels. In such broadcast systems, the main challenging issue arises from the presence of multi-user interference (MUI) among non-coordinated users. In order to completely suppress the MUI, ZF precoding, which is originally designed for radio frequency (RF) communications, is adopted. Different from RF counterpart, VLC signal is inherently non-negative and has a limited linear range, which leads to an amplitude constraint on the input data signal. Unlike the average power constraint, obtaining the exact capacity for an amplitude-constrained channel is more cumbersome. In this paper, we first investigate lower and upper bounds on the capacity of an amplitude-constrained Gaussian channel, which are especially tight in the high signal-to-noise regime. Based on the derived bounds, optimal beamformer designs for the max-min fairness sum-rate and the maximum sum-rate problems are formulated as convex optimization problems, which then can be efficiently solved by using standard optimization packages.

We study the use of moment generating function (MGF) method to approximate the distribution of the sum of independent, but not necessarily identical, Gamma-Gamma variables, which is crucial in performance evaluation of multiple- input multiple-output (MIMO) free-space optical (FSO) systems. We show that the MGF-based approximation method can flexibly provide sufficient accuracy in the upper and lower tails of the cumulative distribution function (CDF) for both identically and non- identically distributed cases. Comparisons to highlight the advantages of the proposed method over existing ones are also presented. We then apply the proposed method to analytically derive closed-form expressions for the outage probability and average bit-error rate of MIMO-FSO systems. Monte-Carlo simulations are also performed to validate analytical results.

This study studies the performance of multihop free‐space optical systems using the subcarrier binary phase‐shift keying modulation over atmospheric turbulence channels. The authors propose a modified relaying strategy, termed ‘amplify–decode‐and‐forward’, realised by using avalanche photodiode (APD) receivers. The outage probability of the proposed system is analytically derived considering the atmospheric turbulence and the receiver noise, including APD shot noise and thermal noise. The analytical results are verified by Monte Carlo simulations, and a good agreement between the analytical and simulation results is confirmed. In the authors’ analysis, they quantitatively discuss the impact of turbulence strength, number of relay nodes, relaying configuration, system bit rate and receiver parameters on the system outage probability. In addition, the optimal value of APD gain for achieving the lowest outage probability in different cases of relaying configuration, number of relays and receiver parameters is also discussed.