UAV caching in 6G networks: A Survey on models,techniques, and applications

The rapid development road map of 6G networks has posed a new set of challenges to both industrial and academic sectors. On the one hand, it needs more disruptive technologies and solutions for addressing the threefold issues including enhanced mobile broadband, massive machine-type communications, and ultra-reliable and low-latency communications. On the other hand, the ever-massive number of mobile users and Internet of Things devices conveys the huge volume of traffic throughout the 6G networks. In this context, caching is one of the most feasible technologies and solutions that does not require any system architecture changes nor costly investments, while significantly improve the system performance, i.e., quality of service and resource efficiency. Ground caching models deployed at macro base stations, small-cell base stations, and mobile devices have been successfully studied and currently extended to the air done by unmanned aerial vehicles (UAVs) to deal with the challenges of 6G networks. This paper provides a comprehensive survey of UAV caching models, techniques, and applications in 6G networks. In particular, we first investigate the entire picture of caching models moving from the ground to the air as well as the related surveys on UAV communications. Then, we introduce a typical UAV caching system and describe how it works in connection with all types of the transceivers, end users, and applications and services (A&Ss). After that, we present the recent advancements and analyses of the UAV caching models and common system performance metrics. Furthermore, the UAV caching with assisted techniques, UAV caching-enabled mechanisms, and UAV caching A&Ss are discussed to demonstrate the role of UAV caching system in 6G networks. Finally, we highlight the ongoing challenges and potential research directions toward UAV caching in 6G networks.     

A novel deep deterministic policy gradient model applied to intelligent transportation system security problems in 5G and 6G network scenarios

Traffic congestion has been an actual problem in large cities, causing personal inconvenience and environmental pollution. To solve this problem, new applications for Intelligent Transportation System (ITS) have been created, to monitor actual traffic conditions. Therefore, fast, reliable and safe systems are desirable for creating a real intelligent transportation environment. Deep learning algorithms have been proposed for a better understanding of traffic behavior from a security-related perspective. Thus, we aim to maximize the safety problems using a deep learning algorithm, where a novel policy gradient model is presented for detecting vehicular misuse. The proposed model uses a triple network replay algorithm, maximizing the network convergence speed. Three networks are selected to optimize the policy network variables. Finally, the replay algorithm is partitioned with the aim of obtaining a faster model. Simulations on a real urban map are performed in a scenario with the integration of 5G or 6G networks. An architectural model for the integration of a Vehicular Ad-hoc Network (VANET) and cellular networks is determined in software-defined networking (SDN). The results show that the accuracy prediction of the proposed system presents better performance compared to related studies, where the proposed model increases its convergence speed and cumulative reward. Thus, the ITS improvement by the proposed deep learning algorithm increases the prediction accuracy, and reduces the transmission delay, treating the traffic path according to the congestion.     

Physical layer security using beamforming techniques for 5G and beyond networks: A systematic review

It has been predicted that by the year 2030, 5G and beyond 5G (B5G) networks are expected to provide hundreds of trillions of gigabytes of data for various emerging applications such as augmented, mixed, and virtual reality (AR/MR/VR), wireless computer-brain interfaces (WCBI), connected robotics and autonomous systems. Most of these applications share data with each other using an open channel, i.e., the Internet. The open and broadcast nature of wireless channel makes the communication susceptible to various types of attacks (e.g., eavesdropping, jamming). Thus, there is a strong requirement to enhance the secrecy of wireless channel to maintain the privacy and confidentiality of transmitted data. Physical layer security (PLS) has evolved as a novel concept and robust alternative to cryptography-based techniques, which have a number of drawbacks and practical issues for 5G and beyond networks. Beamforming is an energy-efficient PLS technique, that involves steering of the transmitted signal in a particular direction, while considering that an intruding user attempts to decode the transmitted data. Motivated from these points, this article summarizes various beamforming based PLS techniques for secure data transmission in 5G and B5G networks. We investigate the eight most promising techniques for beamforming in PLS: Non-Orthogonal Multiple Access (NOMA), Full-Duplex Networks, Massive Multiple-Input Multiple-Output (MIMO), Cognitive Radio (CR) Network, Relay Network, Simultaneous Wireless Information and Power Transfer (SWIPT), UAV Communication Networks and Space Information Networks, and Heterogeneous Networks. Moreover, various physical layer threats and countermeasures associated with 5G and B5G networks are subsequently covered. Lastly, we provide insights to the readers about constraints and challenges for the usage of beamforming-based PLS techniques in various upcoming future applications.     

Deep learning based physical layer security for terrestrial communications in 5G and beyond networks: A survey

The key principle of physical layer security (PLS) is to permit the secure transmission of confidential data using efficient signal-processing techniques. Also, deep learning (DL) has emerged as a viable option to address various security concerns and enhance the performance of conventional PLS techniques in wireless networks. DL is a strong data exploration technique which can be used to learn normal and abnormal behavior of 5G and beyond wireless networks in an insecure channel paradigm. Also, since DL techniques can successfully predict future new instances by learning from existing ones, they can successfully predict new attacks, which frequently involve mutations of earlier attacks. Thus, motivated by the benefits of DL and PLS, this survey provides a comprehensive review that overviews how DL-based PLS techniques can be employed for solving various security concerns in 5G and beyond networks. The survey begins with an overview of physical layer threats and security concerns in 5G and beyond networks. Then, we present a detailed analysis of various DL and deep reinforcement learning (DRL) techniques that are applicable to PLS applications. We present the specific use-cases of PLS design for each type of technique, including attack detection, physical layer authentication (PLA), and other PLS techniques. Then, we present an in-depth overview of the key areas of PLS where DL can be used to enhance the security of wireless networks, such as automatic modulation classification (AMC), secure beamforming, PLA, etc. Performance evaluation metrics for DL-based PLS design are subsequently covered. Finally, we provide insights to the readers about various challenges and future research trends in the design of DL-based PLS for terrestrial communications in 5G and beyond networks.     

Security concerns on machine learning solutions for 6G networks in mmWave beam prediction

6G – sixth generation – is the latest cellular technology currently under development for wireless communication systems. In recent years, machine learning (ML) algorithms have been applied widely in various fields, such as healthcare, transportation, energy, autonomous cars, and many more. Those algorithms have also been used in communication technologies to improve the system performance in terms of frequency spectrum usage, latency, and security. With the rapid developments of ML techniques, especially deep learning (DL), it is critical to consider the security concern when applying the algorithms. While ML algorithms offer significant advantages for 6G networks, security concerns on artificial intelligence (AI) models are typically ignored by the scientific community so far. However, security is also a vital part of AI algorithms because attackers can poison the AI model itself. This paper proposes a mitigation method for adversarial attacks against proposed 6G ML models for the millimeter-wave (mmWave) beam prediction using adversarial training. The main idea behind generating adversarial attacks against ML models is to produce faulty results by manipulating trained DL models for 6G applications for mmWave beam prediction. We also present a proposed adversarial learning mitigation method’s performance for 6G security in mmWave beam prediction application a fast gradient sign method attack. The results show that the defended model under attack’s mean square errors (i.e., the prediction accuracy) are very close to the undefended model without attack.     

罗丹明6G.四溴荧光素双显色体系浮选光度法测定锗的研究

向锗与茜素氨羧络合剂罗丹明６Ｇ形成的Ｇｅ（ＡＷＬＣ３（Ｒ６Ｇ）５甲苯浮选物，加入０．１ｍｏｌ／Ｌ的ＮａＯＨ的溶液，使Ｒ６ＧＹ颜色相同的四溴荧光互，形成等色染料离子对Ｒ６Ｇ＾＋；ＴＢＦ＾－再被甲苯浮选。将浮先物溶于丙酮，于５３０处进行光度测定，由于１０个染料分子同时吸光，使本方法具有很高的灵敏度：ε＝５．８×１０＾５Ｌ．ｍｏｉｌ＾－１，ｃｍ＾－１，锗含量在０．００４０－０．１ｍｇ／Ｌ服从比耳定律。     

A Novel and Adaptive Angle Diversity-Based Receiver for 6G Underground Mining VLC Systems

Visible light communication (VLC) is considered an enabling technology for future 6G wireless systems. Among the many applications in which VLC systems are used, one of them is harsh environments such as Underground Mining (UM) tunnels. However, these environments are subject to degrading environmental and intrinsic challenges for optical links. Therefore, current research should focus on solutions to mitigate these problems and improve the performance of Underground Mining Visible Light Communication (UM-VLC) systems. In this context, this article presents a novel solution that involves an improvement to the Angle Diversity Receivers (ADRs) based on the adaptive orientation of the Photo-Diodes (PDs) in terms of the Received Signal Strength Ratio (RSSR) scheme. Specifically, this methodology is implemented in a hemidodecahedral ADR and evaluated in a simulated UM-VLC scenario. The performance of the proposed design is evaluated using metrics such as received power, user data rate, and bit error rate (BER). Furthermore, our approach is compared with state-of-the-art ADRs implemented with fixed PDs and with the Time of Arrival (ToA) reception method. An improvement of at least 60% in terms of the analyzed metrics compared to state-of-the-art solutions is obtained. Therefore, the numerical results demonstrate that the hemidodecahedral ADR, with adaptive orientation PDs, enhances the received optical signal. Furthermore, the proposed scheme improves the performance of the UM-VLC system due to its optimum adaptive angular positioning, which is completed according to the strongest optical received signal power. By improving the performance of the UM-VLC system, this novel method contributes to further consideration of VLC systems as potential and enabling technologies for future 6G deployments.     

Degradation of a cationic dye (Rhodamine 6G) using hydrodynamic cavitation coupled with other oxidative agents: Reaction mechanism and pathway

In the present study, decolorization and mineralization of a cationic dye, Rhodamine 6G (Rh6G), has been carried out using hydrodynamic cavitation (HC). Two cavitating devices such as slit and circular venturi were used to generate cavitation in HC reactor. The process parameters such as initial dye concentration, solution pH, operating inlet pressure, and cavitation number were investigated in detail to evaluate their effects on the decolorization efficiency of Rh6G. Decolorization of Rh6G was marginally higher in the case of slit venturi as compared to circular venturi. The kinetic study showed that decolorization and mineralization of the dye fitted first-order kinetics. The loadings of H₂O₂ and ozone have been optimized to intensify the decolorization and mineralization efficiency of Rh6G using HC. Nearly 54% decolorization of Rh6G was obtained using a combination of HC and H₂O₂ at a dye to H₂O₂ molar ratio of 1:30. The combination of HC with ozone resulted in 100% decolorization in almost 5–10 min of processing time depending upon the initial dye concentration. To quantify the extent of mineralization, total organic carbon (TOC) analysis was also performed using various processes and almost 84% TOC removal was obtained using HC coupled with 3 g/h of ozone. The degradation by-products formed during the complete degradation process were qualitatively identified by liquid chromatography-mass spectrometry (LC-MS) and a detailed degradation pathway has been proposed.     

A contemporary review on user scheduling techniques and feedback reduction strategies towards the development of 5G and beyond communications

User scheduling (US) is the process of dynamic selection of the set of active users out of all available users to serve in each time slot. This is done to optimize the system performance, such as maximizing the sum rate, achieving better fairness, and quality of service or minimizing the interference. The choice of US method depends on the desired system performance and the trade-off between fairness and efficiency. In order to achieve these performance metrics base station (BS) needs channel state information (CSI) of each user for efficient US. Moreover, US and CSI feedback are closely related in the context of conventional multiple-input multiple-output (MIMO) to massive MIMO (mMIMO) systems based on full and limited CSI, as feedback information is often used to make informed decisions on US. To address these objectives simultaneously, this survey deals with exploring different algorithms used for efficient US, various criteria for US considering different scenarios, key methods for user grouping, methods for reduced feedback, and different standard codebook based feedback methods. To be more specific and concise, this article provides a comprehensive survey on state of the art methods used for US in single cell single tier, dual stage (double tier), multi cell scenarios and feedback mechanisms used in various contexts, e.g., multiuser (MU)-MIMO, MU-mMIMO, frequency division duplexing (FDD) mMIMO framework. Moreover, a synopsis of the recently proposed advanced codebook and non-codebook based methods for the long term evolution standards, fifth generation, and beyond communications are discussed. Finally the research gaps as the future scopes are discussed in this article.     

一种简单的方法制备SERS基底用于染料分子的富集、降解与检测

用一种简单的方法制备银纳米粒子, 研究了此纳米粒子作为SERS基底、吸附剂和光催化剂的多功能性。在光照条件下研究其对染料分子的光催化性能, 用紫外光谱和表面增强拉曼光谱对整个光催化过程进行动态跟踪检测, 实验结果表明染料分子光照条件下确实被催化降解了。本实验不仅合成了多功能的基底材料, 还赋予了表面增强拉曼光谱新的应用价值, 为光催化实验提供了新的动态跟踪检测方法。     

A cobalt (II) complex with 6-methylpicolinate: Synthesis,characterization, second- and third-order nonlinear optical properties,and DFT calculations

A cobalt(II) complex of 6-methylpicolinic acid, [Co(6-Mepic)₂(H₂O)₂]·2H₂O, was prepared and fully determined by single crystal X-ray crystal structure analysis as well as FT-IR, FT-Raman. UV–vis spectra were recorded within different solvents, to illustrate electronic transitions and molecular charge transfer within complex 1. The coordination sphere of complex 1 is a distorted octahedron according to single crystal X-ray results. Moreover, DFT (density functional theory) calculations with HSEH1PBE/6-311 G(d,p) level were carried out to back up the experimental results, and form base for future work in advanced level. Hyperconjugative interactions, intramolecular charge transfer (ICT), molecular stability and bond strength were researched by the using natural bond orbital (NBO) analysis. X-ray and NBO analysis results demonsrate that O−H···O hydrogen bonds between the water molecules and carboxylate oxygen atoms form a 2D supramolecular network, and also adjacent 2D networks connected by C−H···π and π···π interactions to form a 3D supramolecular network. Additionally, the second− and third−order nonlinear optical parameters of complex 1 were computed at DFT/HSEH1PBE/6-311 G(d,p) level. The refractive index (n) was calculated by using the Lorentz−Lorenz equation in order to investigate polarization behavior of complex 1 in different solvent polarities. The first−order static hyperpolarizability (β) value is found to be lower than pNA value because of the inversion symmetry around Co (II). But the second−order static hyperpolarizability (γ) value is 2.45 times greater than pNA value (15×10⁻³⁰ esu). According to these results, Co(II) complex can be considered as a candidate to NLO material. Lastly molecular electrostatic potential (MEP), frontier molecular orbital energies and related molecular parameters for complex 1 were evaluated.     

RuSin（n=1～6）团簇的结构、稳定性和电子性质的密度泛函研究

运用杂化密度泛函理论方法在(U)B3LYP/LanL2DZ水平研究了RuSin(n=1~6)团簇体系的稳定结构及电子性质．结果发现：RuSin(n=1~6)团簇基本保持了纯硅团簇的框架.对原子平均束缚能和分裂能的计算表明,RuSi6团簇是RuSin(n=1~6)团簇中热力学稳定性最强的.对自然电荷分布的研究结果发现,RuSin(n=2,4～6)团簇的最低能结构出现电荷反转现象. HOMO-LUMO能隙的研究结果表明掺入钌原子后团簇的化学活性增强了,且RuSi的化学活性是RuSin(n=1~6)团簇最强的。通过对团簇磁矩的研究发现,RuSi和RuSi3团簇具有了磁性,其余团簇的总磁矩为零,且RuSin(n=1～6)团簇中各原子对团簇总磁矩的贡献不同.     

RuSi_n(n=1～6)团簇的结构、稳定性和电子性质的密度泛函研究

运用杂化密度泛函理论方法在(U)B3LYP/Lan L2DZ水平研究了Ru Sin(n=1~6)团簇体系的稳定结构及电子性质.结果发现:Ru Sin(n=1~6)团簇基本保持了纯硅团簇的框架.对原子平均束缚能和分裂能的计算表明,Ru Si6团簇是Ru Sin(n=1~6)团簇中热力学稳定性最强的.对自然电荷分布的研究结果发现,Ru Sin(n=2,4~6)团簇的最低能结构出现电荷反转现象.HOMO-LUMO能隙的研究结果表明掺入钌原子后团簇的化学活性增强了,且Ru Si的化学活性是Ru Sin(n=1~6)团簇最强的.通过对团簇磁矩的研究发现,Ru Si和Ru Si3团簇具有了磁性,其余团簇的总磁矩为零,且Ru Sin(n=1~6)团簇中各原子对团簇总磁矩的贡献不同.     

Theoretical study of M6X2 and M6XX' structure (M = Au,Ag; X,X' = S,Se): Electronic and optical properties,ability of photocatalytic water splitting,and tunable properties under biaxial strain

MoS$_{2}$, a transition metal dichalcogenide (TMDC), has attracted significant amount of attention due to its direct bandgap, tunability and optical properties. Recently, a novel structure consisting of MoS$_{2}$ and noble metal nanoclusters has been reported. Inspired by this, first principle calculations are implemented to predict the structures of $M_{6}X_{2}$ and $M_{6}XX'$ ($M= {rm Au}$, Ag; $X$, $X' ={rm S}$, Se). The calculated bandgap, band edge position, and optical absorption of these structures prove that the silver compounds (Ag$_{6}X_{2 }$ and Ag$_{6}XX'$) have great potential for catalytic water splitting. In addition, biaxial strain (tensile strain and compressive strain) is applied to adjust the properties of these materials. The bandgap presents a quasi-linear trend with the increase of the applied strain. Moreover, the transition between the direct and indirect bandgap is found. The outstanding electronic and optical properties of these materials provide strong evidence for their application in microelectronic devices, photoelectric devices, and photocatalytic materials.     

Lancaster delftware: a Raman spectroscopy,electron microscopy and Mössbauer spectroscopy compositional study

In 2008, excavations were conducted by the Northern Ceramic Society at the site of the former Lancaster delftware potworks, which operated between 1754 and about 1790. The recovered sherds have been non‐destructively examined by Raman and electron microscopies and the iron phases in the biscuit by Mössbauer spectroscopy. These methods have provided a new understanding of the mineralogy of the delftware produced at Lancaster using clay imported from Carrickfergus in Ireland and blended with the local ferruginous‐aluminous clays. This has implications for the attribution of delftware produced at Liverpool, Bristol, Scotland and Ireland. The Carrickfergus clay has been found to be highly dolomitic resulting in the body of the delftware forming diopside and the magnesian olivine forsterite, when fired. Brookite had not converted to rutile, nor had tridymite, nor cristobalite formed; the K‐feldspars did not undergo further chemical reactions, and the observation of metakaolin would suggest that the biscuit firing temperature was in the order of 800–900 °C. Chalcedony containing moganite was established as the silica source. A cobalt‐containing lead‐tin glaze was applied to the biscuit body and, after decorating, was fired. The mineralogy of the pigments used to decorate the objects indicate the yellow to be the PbSbSn triple oxide, the green to be a copper silicate mixed with lead‐tin yellow, the purple and browns to be manganese silicates and the blue to contain cobalt spinels and cobalt pyroxenes. Diopside crystals together with recrystallised tin agglomerates have been observed floating within the glaze. Copyright © 2015 John Wiley & Sons, Ltd.     

富勒烯衍生物C60(CF3)n(n=2,4,6,10)几何结构和电子性质变化规律的密度泛函研究

采用密度泛函理论中的广义梯度近似对C60(CF3)n (n=2,4,6,10)几何结构和电子性质的变化规律进行了计算研究.发现在C60(CF3)4可能稳定存在的三种同分异构体中,具有p-p-p加成方式的衍生物热力学性质最为稳定;在C60(CF3)6可能稳定存在的三种同分异构体中,具有p-p-p-m-p加成方式的衍生物热力学性质最为稳定.对C60(CF3)2,C60(CF3)4,C60(CF3)6和C60(CF3)10四种加成衍生物的几何结构分析可知:随着CF3加成个数的增加,C60中的C-C平均键长逐渐变大,笼子与CF3之间连接键CC60-CCF3逐渐变大.对它们的电子结构分析可知,随着CF3加成数目的增多,反应热几乎是线性增加.而C60(CF3)n(n=2,4,6,10)分子的平均反应热在n=6处为极大值,说明C60(CF3)6应该是最容易得到的加成产物.由Mulliken电荷可知,加成的CF3个数越多,CF3与笼子的相互作用也就越强,每个CF3转移到笼子上电荷数也就越多.C60(CF3)n的自旋聚居数分布表明它们均为闭壳层结构.最后,从CF3对分子的前线轨道贡献可知,四种分子的得电子情况和失电子情况均发生在碳笼本身,并不随着CF3个数的增加而发生明显的改变.     

Cavitation based cleaner technologies for biodiesel production and processing of hydrocarbon streams: A perspective on key fundamentals,missing process data and economic feasibility – A review

The present review emphasizes the role of hydrodynamic cavitation (HC) and acoustic cavitation in clean and green technologies for selected fuels (of hydrocarbon origins such as gasoline, naphtha, diesel, heavy oil, and crude oil) processing applications including biodiesel production. Herein, the role of cavitation reactors, their geometrical parameters, physicochemical properties of liquid media, liquid oxidants, catalyst loading, reactive oxygen species, and different types of emulsification and formation of radicals, formation as well as extraction of formed by-products are systematically reviewed. Among all types of HC reactors, vortex diode and single hole orifices revealed more than 95 % desulfurization yield and a 20 % viscosity reduction in heavy oil upgrading, while multi-hole orifice (100 holes) and slit Venturi allowed obtaining the best biodiesel production processes in terms of high (%) yield, low cost of treatment, and short processing time (5 min; 99 % biodiesel; 4.80 USD/m³). On the other hand, the acoustic cavitation devices are likely to be the most effective in biodiesel production based on ultrasonic bath (90 min; 95 %; 6.7 $/m³) and desulfurization treatment based on ultrasonic transducers (15 min; 98.3 % desulfurization; 10.8 $/m³). The implementation of HC-based processes reveals to be the most cost-effective method over acoustic cavitation-based devices. Finally, by reviewing the ongoing applications and development works, the limitations and challenges for further research are addressed emphasizing the cleaner production and guidelines for future scientists to assure obtaining comprehensive data useful for the research community.     

Solution of the unanimity rule on exponential, uniform and scalefree networks: A simple model for biodiversity collapse in foodwebs

We solve the Unanimity Rule on networks with exponential, uniform and scalefree degree distributions. In particular we arrive at equations relating the asymptotic number of nodes in one of two states to the initial fraction of nodes in this state. The solutions for exponential and uniform networks are exact, the analytical approximation for the scalefree case is in perfect agreement with simulation results. We use these solutions to provide a theoretical understanding for biodiversity loss in experimental data of foodwebs, which is available for the three network types discussed. The model allows in principle to estimate the critical value of species that have to be removed from the system to induce a complete diversity collapse.     

Bio-refinery of orange peels waste: A new concept based on integrated green and solvent free extraction processes using ultrasound and microwave techniques to obtain essential oil,polyphenols and pectin

In this study, extraction of essential oil, polyphenols and pectin from orange peel has been optimized using microwave and ultrasound technology without adding any solvent but only “in situ” water which was recycled and used as solvent. The essential oil extraction performed by Microwave Hydrodiffusion and Gravity (MHG) was optimized and compared to steam distillation extraction (SD). No significant changes in yield were noticed: 4.22 ± 0.03% and 4.16 ± 0.05% for MHG and SD, respectively. After extraction of essential oil, residual water of plant obtained after MHG extraction was used as solvent for polyphenols and pectin extraction from MHG residues. Polyphenols extraction was performed by ultrasound-assisted extraction (UAE) and conventional extraction (CE). Response surface methodology (RSM) using central composite designs (CCD) approach was launched to investigate the influence of process variables on the ultrasound-assisted extraction (UAE). The statistical analysis revealed that the optimized conditions of ultrasound power and temperature were 0.956 W/cm² and 59.83 °C giving a polyphenol yield of 50.02 mg GA/100 g dm. Compared with the conventional extraction (CE), the UAE gave an increase of 30% in TPC yield. Pectin was extracted by conventional and microwave assisted extraction. This technique gives a maximal yield of 24.2% for microwave power of 500 W in only 3 min whereas conventional extraction gives 18.32% in 120 min. Combination of microwave, ultrasound and the recycled “in situ” water of citrus peels allow us to obtain high added values compounds in shorter time and managed to make a closed loop using only natural resources provided by the plant which makes the whole process intensified in term of time and energy saving, cleanliness and reduced waste water.     

Studies of the spin-Hamiltonian parameters, d–d transitions and defect structures for two tetragonal Cu centers in Ba2ZnF6:Cu crystal

Two theoretical methods, the perturbation theory method (PTM) and the complete diagonalization (of energy matrix) method (CDM), are applied to calculate the spin-Hamiltonian parameters (g-factors g, g and hyperfine structure constants A, A, obtained from electron paramagnetic resonance (EPR) spectra) and d–d transitions (obtained from optical spectra) for two tetragonal Cu²⁺ centers in Ba₂ZnF₆:Cu²⁺ crystals. The Cu²⁺(I) ion replaces the Zn²⁺ ion at tetragonally compressed octahedral coordination and has the ground state ²A₁(|d_z²), whereas the Cu²⁺(II) ion is at an interstitial site with a square-planar F⁻coordination and has the ground state ²B₂(|d_x²-y²). The calculated spin-Hamiltonian parameters and d–d transitions from the PTM and CDM coincide and are in reasonable agreement with the experimental values. This suggests that both methods are effective for the theoretical studies of EPR and optical spectral data for 3d⁹ ions in tetragonal symmetry with different ground states. The defect structures of the two Cu²⁺ centers in Ba₂ZnF₆:Cu²⁺ are also estimated.