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Reconfigurable intelligent surfaces (RISs) are an emerging technology for application to wireless networks. We introduce a physics and electromagnetic (EM) compliant communication model for analyzing and optimizing RIS-assisted wireless systems. The proposed model has four main notable attributes: (i) it is
end-to-end
, i.e., it is formulated in terms of an equivalent channel that yields a one-to-one mapping between the voltages fed into the ports of a transmitter and the voltages measured at the ports of a receiver; (ii) it is
EM-compliant
, i.e., it accounts for the generation and propagation of the EM fields; (iii) it is
mutual coupling aware
, i.e., it accounts for the mutual coupling among the sub-wavelength unit cells of the RIS; and (iv) it is
unit cell aware
, i.e., it accounts for the intertwinement between the amplitude and phase response of the unit cells of the RIS.

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... In [18], the authors propose a physics and EM-compliant end-to-end channel model for the RIS-assisted communication systems by considering the mutual coupling among the subwavelength unit cells of the RIS. This mutual coupling and unit cell aware model can be applied to an RIS consisting of closely-spaced scattering elements controlled by tunable impedances. ...

... Inspiring from the impedance-based channel model in [18], an analytical framework and a iterative algorithm are presented to obtain the end-to-end received power in [19]. In [20], a multi-user multiple-input multiple-output (MIMO) interference network is investigated in the presence of multiple RISs by using a circuit-based model for the transmitters, receivers, and RISs. ...

... • Each tile is modeled as an anomalous reflector [18]- [20] • EM-compliant communication model is characterized by considering the mutual coupling among the RIS elements • The entire system is represented with a circuit-based model for all terminals ...

One of the most critical aspects of enabling next-generation wireless technologies is developing an accurate and consistent channel model to be validated effectively with the help of real-world measurements. From this point of view, remarkable research has recently been conducted to model propagation channels involving the modification of the wireless propagation environment through the inclusion of reconfigurable intelligent surfaces (RISs). This study mainly aims to present a vision on channel modeling strategies for the RIS-empowered communications systems considering the state-of-the-art channel and propagation modeling efforts in the literature. Moreover, it is also desired to draw attention to open-source and standard-compliant physical channel modeling efforts to provide comprehensive insights regarding the practical use-cases of RISs in future wireless networks.

... 3) Mutually Coupled Impedance-Modulated Antennas: By interpreting each RIS element as an impedance-modulated backscatter antenna [36], [37], the mutual coupling between transceiving antennas and all RIS elements can be rigorously formulated and related to the end-to-end channel matrix [27]. ...

... PhysFad is built upon an exact analytical formulation. The underlying coupled-dipole formalism is conceptually related to frameworks of mutually coupled antennas [27], [36], [37]. ...

... i) the intertwinment of amplitude and phase in a typical Lorentzian resonator; ii) the frequencydependence of a typical Lorentzian resonator; and iii) the coupling effects between nearby RIS elements. Multiple recent papers on "electromagnetics-compliant" RIS models have discussed how to account for some or all of these aspects in free space [27], [28], [34], [35]. ...

Programmable radio environments parametrized by reconfigurable intelligent surfaces (RISs) are emerging as a new wireless communications paradigm, but currently used channel models for the design and analysis of signal-processing algorithms cannot include fading in a manner that is faithful to the underlying wave physics. To overcome this roadblock, we introduce a physics-based end-to-end model of RIS-parametrized wireless channels with adjustable fading (coined PhysFad) which is based on a first-principles coupled-dipole formalism. PhysFad naturally incorporates the notions of space and causality, dispersion (i.e., frequency selectivity) and the intertwinement of each RIS element's phase and amplitude response, as well as any arising mutual coupling effects including long-range mesoscopic correlations. PhysFad offers the to-date missing tuning knob for adjustable fading. We thoroughly characterize PhysFad and demonstrate its capabilities for a prototypical problem of RIS-enabled over-the-air channel equalization in rich-scattering wireless communications. We also share a user-friendly version of our code to help the community transition towards physics-based models with adjustable fading.

... In [53], the authors have recently introduced a communication model for RIS that explicitly accounts for the mutual coupling among the RIS elements and for the control circuit of the unit cells. The communication model in [53] is based on the theory of mutually coupled tiny antennas and is directly applicable in multiple-antenna communication systems, since it resembles a MIMO communication channel. ...

... In [53], the authors have recently introduced a communication model for RIS that explicitly accounts for the mutual coupling among the RIS elements and for the control circuit of the unit cells. The communication model in [53] is based on the theory of mutually coupled tiny antennas and is directly applicable in multiple-antenna communication systems, since it resembles a MIMO communication channel. In [54] and [43], it has recently been shown that the model is suitable for formulating optimization problems in general wireless networks, such as the MIMO interference channel, and that it can be utilized to optimize an RIS by explicitly taking into account the mutual coupling among the RIS elements. ...

... In [54] and [43], it has recently been shown that the model is suitable for formulating optimization problems in general wireless networks, such as the MIMO interference channel, and that it can be utilized to optimize an RIS by explicitly taking into account the mutual coupling among the RIS elements. In this sub-section, we first introduce the communication model in [53] and then elaborate on the conditions under which it can be utilized. ...

A reconfigurable intelligent surface (RIS) is a planar structure that is engineered to dynamically control the electromagnetic waves. In wireless communications, RISs have recently emerged as a promising technology for realizing programmable and reconfigurable wireless propagation environments through nearly passive signal transformations. With the aid of RISs, a wireless environment becomes part of the network design parameters that are subject to optimization. In this tutorial paper, we focus our attention on communication models for RISs. First, we review the communication models that are most often employed in wireless communications and networks for analyzing and optimizing RISs, and elaborate on their advantages and limitations. Then, we concentrate on models for RISs that are based on inhomogeneous sheets of surface impedance, and offer a step-by-step tutorial on formulating electromagnetically-consistent analytical models for optimizing the surface impedance. The differences between local and global designs are discussed and analytically formulated in terms of surface power efficiency and reradiated power flux through the Poynting vector. Finally, with the aid of numerical results, we discuss how approximate global designs can be realized by using locally passive RISs with zero electrical resistance (i.e., inhomogeneous reactance boundaries with no local power amplification), even for large angles of reflection and at high power efficiency.

... Importantly and unlike all other WFL publications in the literature to date, we do not use a pathloss based channel propagation model or fading model (e.g., Friis and Rayleigh) because such models cannot accurately capture the EM coupling effects caused by the RIS elements (e.g., (beamform, scatter, null) that can completely change the radio map spatial power distribution. Instead, we use a recently proposed end-to-end model [24] based on impedance coupling of thin wire antennas which allows us to accurately test and benchmark our proposed solutions while also gaining realistic engineering insights VOLUME x, 2021 into the design capabilities and challenges related to RISenhanced WFL methods. ...

... Fig. 2 illustrates four representative example of radio maps corresponding to four different configurations of the RIS in an indoor space generated using our simulation approach described in Sec. IV [24]. Thus, by changing the configuration of the RIS, i.e., the load impedance of the dipoles thus applying a phase shift to the reflected EM waves, one can get a much more diverse set of radio maps, i.e., a high dimensional fingerprint by using just one AP and one RIS. ...

... We will use the impedance based model developed in [24] to obtain simulated RSSI values at the MU. While the full power of this model is not required for our simplified WFL setting (see Fig. 1) we believe it is useful to summarize the assumptions made and also how this model is appropriate towards accurately simulating RSSI values for radio maps in the presence of different RIS configurations. ...

Reconfigurable Intelligent Surfaces (RISs) promise improved, secure, and more efficient wireless communications. One less understood aspect relates to the benefits of RIS towards wireless localization and positioning of mobile users and devices. In this paper we propose and demonstrate two practical solutions that exploit the diversity offered by RIS-enhanced indoor environments and to select RIS state configurations that generate easily differentiable radio maps for use with wireless fingerprinting localization estimators. Specifically, we first investigate supervised learning feature selection methods to prune the large state space of the RIS, thus reducing complexity and enhancing localization accuracy and device position acquisition time. We then analytically derive noise correlated heuristics that can further reduce the computational complexity of our proposed solution. Finally, we validate and benchmark our proposed solutions through accurate end-to-end models and computer simulations while demonstrating an average localization accuracy improvement of about 33%. Our explorations thus demonstrate how and why accuracy improvements are achieved and also hint towards how these can be further enhanced in practical localization settings while utilizing more than one RIS.

... Remark 1. It is worthwhile to clarify the differences between our proposed model with the RIS aided communication model proposed in recent work [40]. There are four differences. ...

... There are four differences. First, compared with using impedance parameter in [40], we have found it is more natural to use the reflection coefficient and scattering parameter to account for the scattering mechanism of RIS and derive the RIS aided communication model. Second, our general RIS aided communication model (29) includes the effects of impedance mismatching and mutual coupling at the transmitter, RIS, and receiver, which is more general than [40]. ...

... First, compared with using impedance parameter in [40], we have found it is more natural to use the reflection coefficient and scattering parameter to account for the scattering mechanism of RIS and derive the RIS aided communication model. Second, our general RIS aided communication model (29) includes the effects of impedance mismatching and mutual coupling at the transmitter, RIS, and receiver, which is more general than [40]. Third, we clearly explain the physical significance of the phase shifts and the unit modulus constraint. ...

Reconfigurable intelligent surfaces (RISs) are an emerging technology for future wireless communication. The vast majority of recent research on RIS has focused on system level optimizations. However, developing straightforward and tractable electromagnetic models that are suitable for RIS aided communication modeling remains an open issue. In this paper, we address this issue and derive communication models by using rigorous scattering parameter network analysis. We also propose new RIS architectures based on group and fully connected reconfigurable impedance networks that can adjust not only the phases but also the magnitudes of the impinging waves, which are more general and more efficient than conventional single connected reconfigurable impedance network that only adjusts the phases of the impinging waves. In addition, the scaling law of the received signal power of an RIS aided system with reconfigurable impedance networks is also derived. Compared with the single connected reconfigurable impedance network, our group and fully connected reconfigurable impedance network can increase the received signal power by up to 62%, or maintain the same received signal power with a number of RIS elements reduced by up to 21%. We also investigate the proposed architecture in deployments with distance-dependent pathloss and Rician fading channel, and show that the proposed group and fully connected reconfigurable impedance networks outperform the single connected case by up to 34% and 48%, respectively.

... The modeling of signal propagation in such novel RISempowere conditions appears very challenging [11], [12] involving a number of algorithmic solutions. In [13], a freespace model based on an impedance matrix formalism for RISs with discrete elements has been presented, while the corresponding optimization of the RIS settings for communication purposes is largely disussed in [4], [12]. Additional research directions focus on the challenging task of channel estimation in RIS-empowered communication systems, where multiple users and multiple RISs with large numbers of elements and non-linear hardware characteristics are considered [14]. ...

... The majority of the current research adopts simple communication models that fit farfield communications and incorporate simplified models of the surface [12]. However, the way a metasurface affects wireless propagation properties depends on many characteristics, including the properties of the surface and its unit elements, as well as their interactions [13], their distance to the transmitter and receiver, and the characteristics of the channel. RISE-6G will develop communication models that are accurate and mathematically tractable, and that account for the circuit design of the surface and its EM properties. ...

The design of 6th Generation (6G) wireless networks points towards flexible connect-and-compute technologies capable to support innovative services and use cases. Targeting the 2030 horizon, 6G networks are poised to pave the way for sustainable human-centered smart societies and vertical industries, such that wireless networks will be transformed into a distributed smart connectivity infrastructure, where new terminal types are embedded in the daily environment. In this context, the RISE-6G project aims at investigating innovative solutions that capitalize on the latest advances in the emerging technology of Reconfigurable Intelligent Surfaces (RISs), which offers dynamic and goal-oriented radio wave propagation control, enabling the concept of the wireless environment as a service. The project will focus on: i) the realistic modeling of RIS-assisted signal propagation, ii) the investigation of the fundamental limits of RIS-empowered wireless communications and sensing, and iii) the design of efficient algorithms for orchestrating networking RISs, in order to implement intelligent, sustainable, and dynamically programmable wireless environments enabling diverse services that go well beyond the 5G capabilities. RISE-6G will offer two unprecedented proof-of-concepts for realizing controlled wireless environments in near-future use cases.

... It is obvious that RIS-based communications rely on the design of the reflection coefficients, which is a critical issue in practical hardware implementations. To investigate the reflection from the electromagnetic perspective, we need to study the permittivity and permeability of the reflective elements (REs) and solve Maxwell's equations [39,40,41], which is a difficult task. Considering that the physical size of an RE is smaller than the wavelength of the incident signal, an adequate simplification of Maxwell's equations is transmission line theory [7]. ...

... Generalizations of the results reported in this chapter include the analysis and optimization of RIS-assisted communications based on electromagnetic-compliant communication models, such as that recently introduced in [39] and [40]. ...

Recently, the emergence of reconfigurable intelligent surface (RIS) has attracted heated attention from both industry and academia. A RIS is a planar surface that consists of a large number of low-cost passive reflecting elements. By carefully adjusting the phase shifts of the reflecting elements, an RIS can reshape the wireless environment for better communication. In this thesis, we focus on two subjects: (i) To study the modeling and optimization of RIS-aided communication systems. (ii) To study RIS-aided spatial modulation, especially the detection using deep learning techniques. Chapter 1 introduces the concept of smart radio environments and RIS. In 5G and future communications, RIS is a key technique to achieve seamless connectivity and less energy consumption at the same time. Chapter 2 introduces RIS-aided communication systems. The reflection principle, channel estimation problem and system design problem are introduced in detail. State-of-the-art research on the problems of channel estimation and system design are overviewed. Chapter 3 investigates the distribution of the signal-to-noise ratio (SNR) as a random variable in an RIS-aided multiple-input multiple-output (MIMO) system. Rayleigh fading and line-of-sight propagation are considered separately. The theoretical derivation and numerical simulation prove that the SNR is equivalent in distribution to the product of three (Rayleigh fading) or two (line-of-sight propagation) independent random variables. Chapter 4 studies the behavior of interference in an RIS-aided MIMO system, where each base station serves a user equipment (UE) through an RIS. The interference at a UE is caused by its non-serving RIS. It is proven that the interference-to-noise ratio is equivalent in distribution to the product of a Chi-squared random variable and a random variable which can be approximated with a Gamma distribution. Chapter 5 focuses on RIS-aided spatial modulation. First, we introduce deep learning aided detection for MIMO systems. Then, by generalizing RIS-aided spatial modulation systems as a special case of traditional spatial modulation systems, we investigate deep learning based detection for RIS-aided spatial modulation systems. Numerical results validate the proposed data-based and model-based deep learning detection schemes for RIS-aided spatial modulation systems. Finally, Chapter 6 concludes the thesis and discusses possible future research directions.

... 图 2 (a)信息超表面单元的等效传输线模型 [43] ；(b)信息超表面单元的角度依赖相移器模型 [44] Fig.2 (a) Equivalent transmission line model for the unit cell of the RIS [43] ; (b) Angle-dependent phase shifter model for the unit cell of the RIS [44] 如图2(a)所示，第n个信息超表面单元对应的并 Fig.3 End-to-end mutual-coupling-aware communication model [45] 基于参考文献 [ ...

... 图 2 (a)信息超表面单元的等效传输线模型 [43] ；(b)信息超表面单元的角度依赖相移器模型 [44] Fig.2 (a) Equivalent transmission line model for the unit cell of the RIS [43] ; (b) Angle-dependent phase shifter model for the unit cell of the RIS [44] 如图2(a)所示，第n个信息超表面单元对应的并 Fig.3 End-to-end mutual-coupling-aware communication model [45] 基于参考文献 [ ...

Information metasurfaces have become one of the research hotspots in the field of physics and information, because of the ability of manipulating electromagnetic waves. A series of research progress in the field of wireless communications based on information metasurfaces was introduced. Information metasurface can manipulate electromagnetic waves in real time and directly process digital coding information, and can further perceive, understand, even memorize, learn and recognize information, which makes it show great potential in the field of wireless communications. Firstly, the research progress of channel modeling was introduced and the channel improvement that information metasurfaces could achieve when they worked as a wireless relay. Secondly, the application of information metasurface in the new transmitter system was also introduced, which modulated the amplitude or phase of the carrier waves. Thus several simplified transmitter architectures could be realized. Thirdly, the realization of several new wireless communication systems using the information of the near field, far field and scattering field of the information metasurface was introduced. Finally, the future wireless communication based on information metasurface was summarized and prospected.

... However, in both the cases above, user scheduling/RB allocation and IRS beam routing/passive reflection need to be jointly designed, which is interesting to study in future work. • Third, as our main focus is on the new MBMH routing design, we consider a simplified IRS model in this paper, while a more accurate model may be needed in practical routing design to account for other aspects pertaining to electromagnetic propagation and device hardware imperfections, such as mutual coupling among IRS elements [29], angle-dependent passive beamforming gain [31], near-field effects [38], etc. Nonetheless, the proposed algorithm provides a theoretical bound for the performance of practical MBMH routing designs, which can be calibrated by properly introducing correction factors to account for hardware effects by adjusting the weights in the constructed graphs accordingly. ...

... Similar passive beam search can also be performed in the case with mutual coupling among IRS elements, where the reflection coefficient matrix of each IRS is non-diagonal[29].3 For ease of exposition, we assume that a full amplitude gain of M can be obtained in this paper, while it may be dependent on the incident and reflection angles at each IRS in practice. ...

Intelligent reflecting surface (IRS) is envisioned to play a significant role in future wireless communication systems as an effective means of reconfiguring the radio signal propagation environment. In this paper, we study a new multi-IRS aided massive multiple-input multiple-output (MIMO) system, where a multi-antenna BS transmits independent messages to a set of remote single-antenna users using orthogonal beams that are subsequently reflected by different groups of IRSs via their respective multi-hop passive beamforming over pairwise line-of-sight (LoS) links. We aim to select optimal IRSs and their beam routing path for each of the users, along with the active/passive beamforming at the BS/IRSs, such that the minimum received signal power among all users is maximized. This problem is particularly difficult to solve due to a new type of path separation constraints for avoiding the IRS-reflected signal induced interference among different users. To tackle this difficulty, we first derive the optimal BS/IRS active/passive beamforming solutions based on their practical codebooks given the reflection paths. Then we show that the resultant multi-beam multi-hop routing problem can be recast as an equivalent graph-optimization problem, which is however NP-complete. To solve this challenging problem, we propose an efficient recursive algorithm to partially enumerate the feasible routing solutions, which is able to effectively balance the performance-complexity trade-off. Numerical results demonstrate that the proposed algorithm achieves near-optimal performance with low complexity and outperforms other benchmark schemes. Useful insights into the optimal multi-beam multi-hop routing design are also drawn under different setups of the multi-IRS aided massive MIMO network.

... Hence, the ability to control the RIS in a precise and known manner is essential for ISLAC applications, which necessitates the availability of accurate and simple RIS phase control models. Such models should ideally account for the per-element response [36], the finite quantization of the control [14], [37], mutual coupling [38], calibration effects, and power losses. Most studies on RIS localization have considered ideal phase shifters (e.g. ...

... Output: Location estimate p. (a) Find an estimate of azimuthθ by solving(38). (b) Usingθ, find an estimate of elevationφ by solving(39). ...

We investigate the problem of reconfigurable intelligent surface (RIS)-aided near-field localization of a user equipment (UE) served by a base station (BS) under phase-dependent amplitude variations at each RIS element. Through a misspecified Cram\'{e}r-Rao bound (MCRB) analysis and a resulting lower bound (LB) on localization, we show that when the UE is unaware of amplitude variations (i.e., assumes unit-amplitude responses), severe performance penalties can arise, especially at high signal-to-noise ratios (SNRs). Leveraging Jacobi-Anger expansion to decouple range-azimuth-elevation dimensions, we develop a low-complexity approximated mismatched maximum likelihood (AMML) estimator, which is asymptotically tight to the LB. To mitigate performance loss due to model mismatch, we propose to jointly estimate the UE location and the RIS amplitude model parameters. The corresponding Cram\'{e}r-Rao bound (CRB) is derived, as well as an iterative refinement algorithm, which employs the AMML method as a subroutine and alternatingly updates individual parameters of the RIS amplitude model. Simulation results indicate fast convergence and performance close to the CRB. The proposed method can successfully recover the performance loss of the AMML under a wide range of RIS parameters and effectively calibrate the RIS amplitude model online with the help of a user that has an a-priori unknown location.

... Secondly, metamaterial elements are regularly arranged at sub-wavelength intervals on the waveguides, which indicates that an HMA-based array can accommodate more antenna elements than a conventional array, e.g., a patch antenna array, with the same aperture. By contrast, for the conventional array, antenna elements are usually distributed with half wavelength to reduce the mutual coupling, leading to huge sizes of antenna arrays in XL-MIMO systems [11], [12]. Thus, HMAs are more conducive to the layout of large-scale antenna arrays compared to conventional antennas, especially in the circumstance of a limited area. ...

... Typically, the conventional antennas are half-wavelength dipoles [40] while the metamaterial elements are dipoles of 1/32 wavelength [12]. The off-diagonal entry of the mutual impedance matrix Z is given by [39] ...

Extremely large-scale multiple-input multiple-output (XL-MIMO) is the development trend of future wireless communications. However, the extremely large-scale antenna array could bring inevitable nearfield and dual-wideband effects that seriously reduce the transmission performance. This paper proposes an algorithmic framework to design the beam combining for the near-field wideband XL-MIMO uplink transmissions assisted by holographic metasurface antennas (HMAs). Firstly, we introduce a spherical-wave-based channel model that simultaneously takes into account both the near-field and dual-wideband effects. Based on such a model, we then formulate the HMA-based beam combining problem for the proposed XL-MIMO communications, which is challenging due to the nonlinear coupling of high dimensional HMA weights and baseband combiners. We further present a sum-mean-square-error-minimization-based algorithmic framework. Numerical results showcase that the proposed scheme can effectively alleviate the sum-rate loss caused by the near-field and dual-wideband effects in HMA-assisted XL-MIMO systems. Meanwhile, the proposed HMA-based scheme can achieve a higher sum rate than the conventional phase-shifter-based hybrid analog/digital one with the same array aperture.

... Once the hardware model has been selected, the final step to reconcile physical implementations with communication theory is to adopt a channel model for determining the received signal power. There are various physics-based approaches that can be used to develop channel models for STAR-IOSs [13]- [15], hence below we critically appraise five promising approaches 2 . 2 We would like to point out that there are other existing research works on the topic of RIS channel modeling. Those works studied the RIS channel in specific application scenarios based on the conventional ray tracing method. ...

... 3) Equivalent Circuit Based Channel Models: Instead of studying the propagation or generation of the EM wave, the equivalent circuit based channel models characterize the channel between the STAR-IOS and the receivers using a linear transformation [13]. Explicitly, in this model, each element and receiver is represented by specific ports of the circuit. ...

Given the rapid development of advanced electromagnetic manipulation technologies, researchers have turned their attentions to the investigation of smart surfaces for enhancing the radio coverage. Simultaneously transmitting and reflecting intelligent omni-surfaces (STAR-IOSs) constitute one of the most promising categories. Although previous research contributions have demonstrated the benefits of STAR-IOSs in terms of its wireless communication performance gains, several important issues remain unresolved, including both their practical hardware implementations and their accurate physical models. In this paper, we address these issues by discussing four practical hardware implementations of STAR-IOSs, as well as three hardware modeling techniques and five channel modeling methods. We clarify the taxonomy of the smart surface technologies in support of further investigating the family of STAR-IOSs.

... ARGUMENTS Once the hardware model has been selected, the final step to reconcile physical implementations with communication theory is to adopt a channel model for determining the received signal power. There are various physics-based approaches that can be used to develop channel models for STAR-IOSs [13]- [15], hence below we critically appraise five promising approaches 2 . ...

... 3) Equivalent Circuit Based Channel Models: Instead of studying the propagation or generation of the EM wave, the equivalent circuit based channel models characterize the channel between the STAR-IOS and the receivers using a linear transformation [13]. Explicitly, in this model, each element and receiver is represented by specific ports of the circuit. ...

Given the rapid development of advanced electromagnetic manipulation technologies, researchers have turned their attention to the investigation of smart surfaces for enhancing the radio coverage. Simultaneously transmitting and reflecting intelligent omni-surfaces (STAR-IOSs) constitute one of the most promising categories. Although previous research contributions have demonstrated the benefits of STAR-IOSs in terms of its wireless communication performance gains, several important issues remain unresolved, including both their practical hardware implementations and their accurate physical models. In this paper, we address these issues by discussing four practical hardware implementations of STAR-IOSs, as well as three hardware modeling techniques and five channel modeling methods. We clarify the taxonomy of the smart surface technologies in support of further investigating the family of STAR-IOSs.

... The horizontal and vertical lengths of the holographic RIS are L x and L z , with element spacing of d x and d z , respectively. Each element in the holographic RIS is modeled as a cylindrical thin wire of perfectly conducting material, and is connected to a tunable load, where the load can be a positive-intrinsic-negative diode whose inductance and capacitance are adaptable to reconfigure the response of each element [39]. with respect to the associated coordinate system. ...

... When the elements are small and resonant, such as dipoles, the first-order result of MC is to alter the impedance of each of the array elements [27]. Thus, the coupling can be described in terms of mutual impedance between elements (when higher order effects can be neglected), which is also a common practice in plenty of previous research work (e.g., [35,37,39]). The mutual impedance and MC models in this paper are intended to be illustrative; for arrays composed of dipoles with other layouts or a different type of elements, it is necessary to employ more suitable mutual impedance/MC models, or to measure these parameters in the actual array, which is deferred to future work. ...

As a prospective key technology for the next-generation wireless communications, reconfigurable intelligent surfaces (RISs) have gained tremendous research interest in both the academia and industry in recent years. Only limited knowledge, however, has been obtained about the channel eigenvalue characteristics and spatial degrees of freedom (DoF) of systems containing RISs, especially when mutual coupling (MC) is present between the array elements. In this paper, we focus on the small-scale spatial correlation and eigenvalue properties excluding and including MC effects, for RISs with a quasi-continuous aperture (i.e., holographic RISs). Specifically, asymptotic behaviors of far-field and near-field eigenvalues of the spatial correlation matrix of holographic RISs without MC are first investigated, where the counter-intuitive observation of a lower DoF with more elements is explained by leveraging the power spectrum of the spatial correlation function. Second, a novel metric is proposed to quantify the inter-element correlation or coupling strength in RISs and ordinary antenna arrays. Furthermore, in-depth analysis is performed regarding the MC effects on array gain, effective spatial correlation, and eigenvalue architectures for a variety of element intervals when a holographic RIS works in the radiation and reception mode, respectively. The analysis and numerical results demonstrate that a considerable amount of the eigenvalues of the spatial correlation matrix correspond to evanescent waves that are promising for near-field communication and sensing. More importantly, holographic RISs can potentially reach an array gain conspicuously larger than conventional arrays by exploiting MC, and MC has discrepant impacts on the effective spatial correlation and eigenvalue structures at the transmitter and receiver.

... Regarding future work, it would be interesting to model each IRS element as a transmission line and investigate the wideband design problem. Another promising direction would be to consider the mutual coupling between closely-spaced reflecting elements and its impact on system performance [23]. ...

In this paper, we study the performance of wideband terahertz (THz) communications assisted by an intelligent reflecting surface (IRS). Specifically, we first introduce a generalized channel model that is suitable for electrically large THz IRSs operating in the near-field. Unlike prior works, our channel model takes into account the spherical wavefront of the emitted electromagnetic waves and the spatial-wideband effect. We next show that conventional frequency-flat beamfocusing significantly reduces the power gain due to beam squint, and hence is highly suboptimal. More importantly, we analytically characterize this reduction when the spacing between adjacent reflecting elements is negligible, i.e., holographic reflecting surfaces. Numerical results corroborate our analysis and provide important insights into the design of future IRS-aided THz systems.

... For thin radiating elements, such as short dipole antennas, there exists no simple relationship between their physical size and their effective area. However, if such dipoles are densely cast into a planar array, mutual coupling effects need to be taken into account for ensuring that the principle of energy conservation is fulfilled, which results in the failure of the mentioned relation between D m and A m , similarly to the foregoing case of aperture antennas [15]. ...

Reconfigurable intelligent surfaces (RISs) have attracted attention in the last year as nearly-passive, planar structures that can dynamically change their reflection or refraction characteristics, and therefore realize anomalous reflection, focalization, or other radiowave or signal transformations, to engineer and optimize complex propagation environments. Evaluating the performance and optimizing the deployment of RISs in wireless networks need physically sound frameworks that account for the actual electromagnetic and physical characteristics of engineered metasurfaces. In this paper, we introduce a general macroscopic model for the realistic evaluation of RIS scattering, based on its decomposition into multiple scattering mechanisms. Since state-of-the-art ray models can already efficiently simulate specular interactions (reflection, diffraction) and diffuse scattering, but not anomalous reradiation, we complement them with a Huygens principle approach implemented using either an integral formulation, or a simpler antenna-array-like formulation. The different scattering mechanisms are combined through a generalization of the Effective Roughness model using a suitable power conservation equation. Notably, multiple reradiation modes can be modeled through the proposed approach. In addition, we validate the overall model accuracy by benchmarking it against several case studies available in the literature, either based on analytical models, full-wave simulations, or experimental measurements.

... To facilitate the IRS passive beamforming design in the presence of mutual coupling, the authors in [188] proposed an end-to-end electromagnetic-compliant communication channel model based on Maxwell's equations, which incorporates the effects of mutual coupling at the transmitter, receiver, and IRS. This impedance-based channel model resembles the communicationtheoretic models [18] in terms of the received SNR, while it is more complicated to deal with due to the phase-dependent amplitude as well as the existence of self-impedance and mutual coupling. ...

Intelligent reflecting surface (IRS) has emerged as a key enabling technology to realize smart and reconfigurable radio environment for wireless communications, by digitally controlling the signal reflection via a large number of passive reflecting elements in real time. Different from conventional wireless communication techniques that only adapt to but have no or limited control over dynamic wireless channels, IRS provides a new and cost-effective means to combat the wireless channel impair-ments in a proactive manner. However, despite its great potential, IRS faces new and unique challenges in its efficient integration into wireless communication systems, especially its channel estimation and passive beamforming design under various practical hardware constraints. In this paper, we provide a comprehensive survey on the up-to-date research in IRS-aided wireless communications, with an emphasis on the promising solutions to tackle practical design issues. Furthermore, we discuss new and emerging IRS architectures and applications as well as their practical design problems to motivate future research.

... Recently, it was shown that the amplitude and phase responses are intertwined[22],[23], which suggests an interesting idea for extension of the current work, i.e., to study the impact of active (additive transceiver distortion) and passive (IRS phase noise) HIs by accounting for this intertwinement. ...

We focus on the realistic maximization of the uplink minimum signal-to-interference-plus-noise ratio (SINR) of a general multiple-input single-output (MISO) system assisted by an intelligent reflecting surface (IRS) in the large system limit accounting for HIs. In particular, we introduce the HIs at both the IRS (IRS-HIs) and the transceiver HIs (AT-HIs), usually neglected despite their inevitable impact. Specifically, the deterministic equivalent analysis enables the derivation of the asymptotic weighted maximum-minimum SINR with HIs by jointly optimizing the HIs-aware receiver, the transmit power, and the reflect beamforming matrix (RBM). Notably, we obtain the optimal power allocation and reflect beamforming matrix with low overhead instead of their frequent necessary computation in conventional MIMO systems based on the instantaneous channel information. Monte Carlo simulations verify the analytical results which show the insightful interplay among the key parameters and the degradation of the performance due to HIs.

... An RIS is usually made of a large number of passive scattering elements whose response to electromagnetic waves can be adaptively configured through simple and low-cost electronic circuits such as PIN diodes or varactors. Conceptually, an RIS can be thought of being made of many sub-wavelength antenna dipoles (or patch antenna elements), which can be controlled by tunable lumped loads [193]. By tuning the load, the scattered field can be optimized and, for instance, a plane wave that impinges upon an RIS from a given direction can be steered towards a direction of reflection, different from that of incidence and corresponding to the location of an intended user [194], [195]. ...

What will the future of UAV cellular communications be? In this tutorial article, we address such a compelling yet difficult question by embarking on a journey from 5G to 6G and sharing a large number of realistic case studies supported by original results. We start by overviewing the status quo on UAV communications from an industrial standpoint, providing fresh updates from the 3GPP and detailing new 5G NR features in support of aerial devices. We then show the potential and the limitations of such features. In particular, we demonstrate how sub-6 GHz massive MIMO can successfully tackle cell selection and interference challenges, we showcase encouraging mmWave coverage evaluations in both urban and suburban/rural settings, and we examine the peculiarities of direct device-to-device communications in the sky. Moving on, we sneak a peek at next-generation UAV communications, listing some of the use cases envisioned for the 2030s. We identify the most promising 6G enablers for UAV communication, those expected to take the performance and reliability to the next level. For each of these disruptive new paradigms (non-terrestrial networks, cell-free architectures, artificial intelligence, reconfigurable intelligent surfaces, and THz communications), we gauge the prospective benefits for UAVs and discuss the main technological hurdles that stand in the way. All along, we distil our numerous findings into essential takeaways, and we identify key open problems worthy of further study.

... Regarding future work, it would be interesting to model each IRS element as a transmission line and investigate the wideband design problem. Another promising direction would be to consider the mutual coupling between closely-spaced reflecting elements and its impact on system performance [23]. ...

In this paper, we study the performance of wideband terahertz (THz) communications assisted by an intelligent reflecting surface (IRS). Specifically, we first introduce a generalized channel model that is suitable for electrically large THz IRSs operating in the near-field. Unlike prior works, our channel model takes into account the spherical wavefront of the emitted electromagnetic waves and the spatial-wideband effect. We next show that conventional frequency-flat beamfocusing significantly reduces the power gain due to beam squint, and hence is highly suboptimal. More importantly, we analytically characterize this reduction when the spacing between adjacent reflecting elements is negligible, i.e., holographic reflecting surfaces. Numerical results corroborate our analysis and provide important insights into the design of future IRS-aided THz systems.

... With the considered fading spatial correlation model and for a size of the RIS elements no smaller than λ/3, we do not observe a significant difference of the achievable net throughput. Further studies are, however, necessary for deep sub-wavelength RIS structures, for different optimization criteria of the phase shifts of the RISs, and in the presence of mutual coupling in addition to the fading spatial correlation[36],[37].VI. CONCLUSIONCell-Free Massive MIMO and RIS are two disruptive technologies for boosting the system performance of future wireless networks. ...

Cell-Free Massive multiple-input multiple-output (MIMO) and reconfigurable intelligent surface (RIS) are two promising technologies for application to beyond-5G networks. This paper considers Cell-Free Massive MIMO systems with the assistance of an RIS for enhancing the system performance under the presence of spatial correlation among the scattering elements of the RIS. Distributed maximum-ratio processing is considered at the access points (APs). We introduce an aggregated channel estimation approach that provides sufficient information for data processing with the main benefit of reducing the overhead required for channel estimation. The considered system is studied by using asymptotic analysis which lets the number of APs and/or the number of RIS elements grow large. A lower bound for the channel capacity is obtained for a finite number of APs and scattering elements of the RIS, and closed-form expressions for the uplink and downlink ergodic net throughput are formulated in terms of only the channel statistics. Based on the obtained analytical frameworks, we unveil the impact of channel correlation, the number of RIS elements, and the pilot contamination on the net throughput of each user. In addition, a simple control scheme for controlling the configuration of the scattering elements of the RIS is proposed, which is shown to increase the channel estimation quality, and, hence, the system performance. Numerical results demonstrate the effectiveness of our system design and performance analysis. In particular, the performance benefits of using RISs in Cell-Free Massive MIMO systems are confirmed, especially if the direct links between the APs and the users are of insufficient quality with a high probability.

... Hence, we limit our overview to design methods in which only the phase shift can be adjusted. It is worth noting that some works considered practical RIS reflection models with phase-dependent amplitude [75]- [77] or reflection models that account for the mutual coupling among the reflecting elements [78]- [80]. For simplicity, we only consider the case study with phase-independent and element-independent model for S 1 and S 2 . ...

In the past as well as present wireless communication systems, the wireless propagation environment is regarded as an uncontrollable black box that impairs the received signal quality, and its negative impacts are compensated for by relying on the design of various sophisticated transmission/reception schemes. However, the improvements through applying such schemes operating at two endpoints (i.e., transmitter and receiver) only are limited even after five generations of wireless systems. Reconfigurable intelligent surface (RIS) or intelligent reflecting surface (IRS) have emerged as a new and revolutionary technology that can configure the wireless environment in a favorable manner by properly tuning the phase shifts of a large number of passive and low-cost reflecting elements, thus standing out as a promising candidate technology for the next-/sixth-generation (6G) wireless system. However, to reap the performance benefits promised by RIS/IRS, efficient signal processing techniques are crucial, for a variety of purposes such as channel estimation, transmission design, radio localization, and so on. In this paper, we provide a comprehensive overview of recent advances on RIS/IRS-aided wireless systems from the signal processing perspective. We also highlight promising research directions that are worthy of investigation in the future.

... The second class, taking a discrete perspective, calculates the response of RISs as a summation of the scattering from all unit cells [2], [8], [33]. A widely used but greatly oversimplified model is to assume that unit cells act as diffusive scatterers able to change the amplitude and phase of the incident EM waves, i.e., E s = γe jΩ E i , (I. 1) where E i and E s are the incident and reflected scalar electric fields, respectively, γ ∈ (0, 1] is the reflection coefficient, and Ω ∈ [0, 2π) is the phase shifting to be optimized [34], [35]. For the transmission model of RIS-aided systems, consider communication from a single-antenna source to a singleantenna destination as an example. ...

Physically accurate and mathematically tractable models are presented to characterize scattering and reflection properties of reconfigurable intelligent surfaces (RISs). We take continuous and discrete strategies to model a single patch and patch array and their interactions with multiple incident electromagnetic (EM) waves. The proposed models consider the effect of the incident and scattered angles, polarization features, and the topology and geometry of RISs. Particularly, a simple system of linear equations can describe the multiple-input multiple-output (MIMO) behaviors of RISs under reasonable assumptions. It can serve as a fundamental model for analyzing and optimizing the performance of RIS-aided systems in the far-field regime. The proposed models are employed to identify the advantages and limitations of three typical configurations. One important finding is that complicated beam reshaping functionality can not be endowed by popular phase compensation configurations. A possible solution is the simultaneous configurations of collecting area and phase shifting. We finally discuss the inherent inverse sensing capabilities of RISs. The reconfigurability is crucial for wireless environmental sensing. Numerical simulations verify the effectiveness of the proposed inverse sensing scheme.

... With the considered fading spatial correlation model and for a size of the RIS elements no smaller than /3, we do not observe a significant difference on the average net throughput. Further studies are, however, necessary for deep sub-wavelength RIS structures, for different optimization criteria of the phase shifts of the RIS, and in the presence of mutual coupling in addition to the fading spatial correlation [40], [41]. ...

Cell-Free Massive multiple-input multiple-output (MIMO) and reconfigurable intelligent surface (RIS) are two promising technologies for application to beyond-5G networks. This paper considers Cell-Free Massive MIMO systems with the assistance of an RIS for enhancing the system performance under the presence of spatial correlation among the engineered scattering elements of the RIS. Distributed maximum-ratio processing is considered at the access points (APs). We introduce an aggregated channel estimation approach that provides sufficient information for data processing with the main benefit of reducing the overhead required for channel estimation. The considered system is studied by using asymptotic analysis which lets the number of APs and/or the number of RIS elements grow large. A lower bound for the channel capacity is obtained for a finite number of APs and engineered scattering elements of the RIS, and closed-form expressions for the uplink and downlink ergodic net throughput are formulated in terms of only the channel statistics. Based on the obtained analytical frameworks, we unveil the impact of channel correlation, the number of RIS elements, and the pilot contamination on the net throughput of each user. In addition, a simple control scheme for optimizing the configuration of the engineered scattering elements of the RIS is proposed, which is shown to increase the channel estimation quality, and, hence, the system performance. Numerical results demonstrate the effectiveness of the proposed system design and performance analysis. In particular, the performance benefits of using RISs in Cell-Free Massive MIMO systems are confirmed, especially if the direct links between the APs and the users are of insufficient quality with high probability.

... Future works should study the effect of the clutter on the system design and the joint design of the emitted space-time waverforms, the RISs phase shifts, and the receive filter; also, they might consider how to point the RISs towards multiple spots (widely or closely spaced). Moreover, the impact of the mutual coupling among the RIS elements and among the RIS and radar arrays should be investigated; initial efforts in this direction have been done in [49], [50], where a circuit-based end-to-end model is developed for an RIS-aided communication channel; however, the RIS-aided radar channel may be substantially different, as it entails additional hops and passes through a non-cooperative object (namely, the target). Future developments might also investigate applications involving a high-resolution radar where the direct and indirect echoes have resolvable delays or a passive/opportunistic radar exploiting an RIS to redirect the signal emitted by another (possibly non directional) source. ...

... The mutual coupling between unit cells of metasurfaces is a well-known problem that has been thoroughly studied in the literature [8]. This effect has a significant impact on RIS channel propagation models [9], because it infuences the scattering properties of the RIS. This motivated the use of full-wave analysis in [10], where the Method of Moments was employed to compute the path loss in a free-space communication link including an RIS. ...

We present a hybrid numerical method that combines full-wave analysis with ray-tracing to efficiently model propagation in reconfigurable intelligent surface (RIS)-enabled communication channels. Full-wave simulation is used to obtain the radiation pattern of the transmitter and the complex radar cross-section (RCS) of the RIS. Then, the RIS is imported into a ray-tracer as a secondary transmitter. That enables the modeling of the interaction of the RIS with complex environments. We present the formulation of the proposed technique and its validation against full-wave (finite element) results in representative scenarios of indoor propagation in the presence of an RIS.

... As limitações teóricas resultam de suposições simplificadas, como a análise da interação da RIS com a onda eletromagnética pela perspectiva daóptica geométrica. Mesmo que essa perspectiva resulte em projetos eficazes, aindaé preferível analisar esta interação pela perspectiva daóptica física [33], [34]. As limitações de implementação resultam principalmente das características do hardware, como o número de elementos queé possível integrar no substrato e consequentemente a quantidade de níveis de quantização das mudanças de fase da RIS [35]- [38]. ...

New technologies, applications, and services demand high throughput, robustness, reliability, massive connections support, and low latency. This quality of service (QoS) requirements imply the redefinition of networks and wireless communication systems. However, the mobile network does not exploit the maximum channel capacity due to the effects of signal propagation in free space. Therefore, it is necessary to improve wireless communication through the evolution of the current systems by adding new technologies such as reconfigurable intelligent surfaces (RIS). RIS comprises surface arranged elements used to control impinging signal's phase and amplitude towards a predefined direction, allowing mitigating propagation effects such as attenuation and multipath propagation phenomena. This article presents a study about RIS-related aspects such as operation principles, propagation models, and potential application scenarios. First, it highlights the metasurface basic concepts and their limitations related to implementation. Second, the propagation models are discussed and compared concerning their parameters. Finally, some RIS application scenarios are described.

... Hence, the ability to control in a precise and known manner is essential for ISLAC applications, which necessitates the availability of accurate and simple RIS phase control models. Such models should ideally account for the per-element response [22], the finite quantization of the control [13], [23], mutual coupling [24], calibration effects, as well as power losses. Most studies on RIS localization have considered ideal phase shifters (e.g. ...

We investigate a reconfigurable intelligent surface (RIS)-aided near-field localization system with single-antenna user equipment (UE) and base station (BS) under hardware impairments by considering a practical phase-dependent RIS amplitude variations model. To analyze the localization performance under the mismatch between the practical model and the ideal model with unit-amplitude RIS elements, we employ the misspecified Cram\'{e}r-Rao bound (MCRB). Based on the MCRB derivation, the lower bound (LB) on the mean-squared error for estimation of UE position is evaluated and shown to converge to the MCRB at low signal-to-noise ratios (SNRs). Simulation results indicate more severe performance degradation due to the model misspecification with increasing SNR. In addition, the mismatched maximum likelihood (MML) estimator is derived and found to be tight to the LB in the high SNR regime. Finally, we observe that the model mismatch can lead to an order-of-magnitude localization performance loss at high SNRs.

... Therefore, we neglect any inter-RIS channel contribution in the received signal model given by (3). 4 When d RIS λ/2 (i.e., non-negligible mutual coupling), Φm will be a full or banded matrix. For those cases, Φm can be expressed as Cmdiag{φ m }, where Cm represents the mutual coupling matrix [140], [141] of the RISm structure. This matrix can be then absorbed in the channel matrix g m,k in (2), rendering the cascaded channel model in this expression mutual-coupling aware. ...

The emerging technology of Reconfigurable Intelligent Surfaces (RISs) is provisioned as an enabler of smart wireless environments, offering a highly scalable, low-cost, hardware-efficient, and almost energy-neutral solution for dynamic control of the propagation of electromagnetic signals over the wireless medium, ultimately providing increased environmental intelligence for diverse operation objectives. One of the major challenges with the envisioned dense deployment of RISs in such reconfigurable radio environments is the efficient configuration of multiple metasurfaces with limited, or even the absence of, computing hardware. In this paper, we consider multi-user and multi-RIS-empowered wireless systems, and present a thorough survey of the online machine learning approaches for the orchestration of their various tunable components. Focusing on the sum-rate maximization as a representative design objective, we present a comprehensive problem formulation based on Deep Reinforcement Learning (DRL). We detail the correspondences among the parameters of the wireless system and the DRL terminology, and devise generic algorithmic steps for the artificial neural network training and deployment, while discussing their implementation details. Further practical considerations for multi-RIS-empowered wireless communications in the sixth Generation (6G) era are presented along with some key open research challenges. Differently from the DRL-based status quo, we leverage the independence between the configuration of the system design parameters and the future states of the wireless environment, and present efficient multi-armed bandits approaches, whose resulting sum-rate performances are numerically shown to outperform random configurations, while being sufficiently close to the conventional Deep Q-Network (DQN) algorithm, but with lower implementation complexity.

... To facilitate the IRS passive beamforming design in the presence of mutual coupling, the authors in [194] proposed an end-to-end electromagnetic-compliant communication channel model based on Maxwell's equations, which incorporates the effects of mutual coupling at the transmitter, receiver, and IRS. This impedance-based channel model resembles the communication-theoretic models [18] in terms of the received SNR, while it is more complicated to deal with due to the phase-dependent amplitude as well as the existence of selfimpedance and mutual coupling. ...

Intelligent reflecting surface (IRS) has emerged as a key enabling technology to realize smart and reconfigurable radio environment for wireless communications, by digitally controlling the signal reflection via a large number of passive reflecting elements in real time. Different from conventional wireless communication techniques that only adapt to but have no or limited control over dynamic wireless channels, IRS provides a new and cost-effective means to combat the wireless channel impairments in a proactive manner. However, despite its great potential, IRS faces new and unique challenges in its efficient integration into wireless communication systems, especially its channel estimation and passive beamforming design under various practical hardware constraints. In this paper, we provide a comprehensive survey on the up-to-date research in IRS-aided wireless communications, with an emphasis on the promising solutions to tackle practical design issues. Furthermore, we discuss new and emerging IRS architectures and applications as well as their practical design problems to motivate future research.

... The analysis of different small scale fading models in the near-and far-field regions of RIS-assisted systems is postponed to a future research work.2 The generalization of the proposed analytical framework in the presence of channel correlation[52] (i.e., B is a non-diagonal matrix) is left for future research. ...

In this paper, we investigate the performance of an RIS-aided wireless communication system subject to outdated channel state information that may operate in both the near- and far-field regions. In particular, we take two RIS deployment strategies into consideration: (i) the centralized deployment, where all the reflecting elements are installed on a single RIS and (ii) the distributed deployment, where the same number of reflecting elements are placed on multiple RISs. For both deployment strategies, we derive accurate closed-form approximations for the ergodic capacity, and we introduce tight upper and lower bounds for the ergodic capacity to obtain useful design insights. From this analysis, we unveil that an increase of the transmit power, the Rician-K factor, the accuracy of the channel state information and the number of reflecting elements help improve the system performance. Moreover, we prove that the centralized RIS-aided deployment may achieve a higher ergodic capacity as compared with the distributed RIS-aided deployment when the RIS is located near the base station or near the user. In different setups, on the other hand, we prove that the distributed deployment outperforms the centralized deployment. Finally, the analytical results are verified by using Monte Carlo simulations.

... Real-life experimentations -Conducting testbed experiments for evaluation of RIS-enhanced systems. [14], random shadowing and interference from terrestrial stations in satellite communications [15], etc. ...

The next generation of wireless systems will take the concept of communications and networking to another level and turn the vision of Internet of Everything (IoE) into reality. Everywhere connectivity through the integration of terrestrial, aerial, satellite, maritime, and underwater communications is expected in 6G-enabled IoE systems, where various services with satisfying performance are proffered in an uninterrupted universal manner. The successful realization of this ambitious goal relies on the development of pioneering solutions which can revolutionize the future of wireless technologies, while being secure, scalable, and reliable. Reconfigurable intelligent surface (RIS) is a novel paradigm which has recently been on the research spotlight and shown promising signs to expedite the evolution of 6G-enabled integrated terrestrial/non-terrestrial (INTENT) IoE networks. Motivated by the unparalleled properties of this innovatory technology, we herein set forth the architecture of RIS-enhanced 6G-enabled INTENT IoE networks and clarify the decisive role of RIS in such an integrated environment. We also present the key challenges which need to be addressed for the successful realization of RIS-enhanced 6G systems in all dimensions.

... • We propose three practical PSC strategies for STAR-RISs with correlated phase shifts, namely the primary-secondary PSC (PS-PSC), diversity preserving PSC (DP-PSC), and T/Rgroup PSC (TR-PSC) strategies. We show that the PS-PSC strategy is suitable for generating channels with different channel gains for the users on different sides of the STAR-RIS, while 1 Note that the correlation investigated in this work is not due to mutual coupling, as studied in [16]. Here, we study the correlation between the transmission and reflection coefficients of a given STAR-RIS element. ...

A correlated transmission and reflection (T&R) phase-shift model is proposed for passive lossless simultaneously transmitting and reflecting reconfigurable intelligent surfaces (STAR-RISs). A STAR-RIS-aided two-user downlink communication system is investigated for both orthogonal multiple access (OMA) and non-orthogonal multiple access (NOMA). To evaluate the impact of the correlated T&R phase-shift model on the communication performance, three phase-shift configuration strategies are developed, namely the primary-secondary phase-shift configuration (PS-PSC), the diversity preserving phase-shift configuration (DP-PSC), and the T/R-group phase-shift configuration (TR-PSC) strategies. Furthermore, we derive the outage probabilities for the three proposed phase-shift configuration strategies as well as for those of the random phase-shift configuration and the independent phase-shift model, which constitute performance lower and upper bounds, respectively. Then, the diversity order of each strategy is investigated based on the obtained analytical results. It is shown that the proposed DP-PSC strategy achieves full diversity order simultaneously for users located on both sides of the STAR-RIS. Moreover, power scaling laws are derived for the three proposed strategies and for the random phase-shift configuration. Numerical simulations reveal a performance gain if the users on both sides of the STAR-RIS are served by NOMA instead of OMA. Moreover, it is shown that the proposed DP-PSC strategy yields the same diversity order as achieved by STAR-RISs under the independent phase-shift model and a comparable power scaling law with only 4 dB reduction in received power.

... Capitalizing on the circuit theory of communications [65] and its applications in tunable impedance systems (e.g., in beamforming with single-RF electronically steerable parasitic array radiators [66]), an end-to-end mutual-coupling-aware channel model for free-space signal propagation empowered by an RIS was presented in [113]. The model is based on the mutual impedances between all existing radiating elements, i.e., the transmit/receive antennas and the passive scatterers which are all modeled as dipoles. ...

The demanding objectives for the future sixth generation (6G) of wireless communication networks have spurred recent research efforts on novel materials and radio-frequency front-end architectures for wireless connectivity, as well as revolutionary communication and computing paradigms. Among the pioneering candidate technologies for 6G belong the reconfigurable intelligent surfaces (RISs), which are artificial planar structures with integrated electronic circuits that can be programmed to manipulate the incoming electromagnetic field in a wide variety of functionalities. Incorporating RISs in wireless networks has been recently advocated as a revolutionary means to transform any wireless signal propagation environment to a dynamically programmable one, intended for various networking objectives, such as coverage extension and capacity boosting, spatiotemporal focusing with benefits in energy efficiency and secrecy, and low electromagnetic field exposure. Motivated by the recent increasing interests in the field of RISs and the consequent pioneering concept of the RIS-enabled smart wireless environments, in this paper, we overview and taxonomize the latest advances in RIS hardware architectures as well as the most recent developments in the modeling of RIS unit elements and RIS-empowered wireless signal propagation. We also present a thorough overview of the channel estimation approaches for RIS-empowered communications systems, which constitute a prerequisite step for the optimized incorporation of RISs in future wireless networks. Finally, we discuss the relevance of the RIS technology in the latest wireless communication standards, and highlight the current and future standardization activities for the RIS technology and the consequent RIS-empowered wireless networking approaches.

... Such an analysis has previously been done for antenna arrays. The special case of canonical minimum-scattering (CMS) antennas [47] allows expressing the mutual impedance as a closed-form function of the distance and orientations of two antennas [48], [49]. ...

Reconfigurable intelligent surface (RIS), one of the key enablers for the sixth-generation (6G) mobile communication networks, is considered by designers to smartly reconfigure the wireless propagation environment in a controllable and programmable manner. Specifically, an RIS consists of a large number of low-cost and passive reflective elements (REs) without radio frequency chains. The system gain of RIS wireless systems can be achieved by adjusting the phase shifts and amplitudes of the REs so that the desired signals can be added constructively at the receiver. However, an RIS typically has limited signal processing capability and cannot perform active transmitting/receiving in general, which leads to new challenges in the physical layer design of RIS wireless systems. In this paper, we provide an overview of the RIS-aided wireless systems, including the reflection principle, channel estimation, and system design. In particular, two types of emerging RIS systems are considered: RIS-aided wireless communications (RAWC) and RIS-based information transmission (RBIT), where the RIS plays the role of the reflector and the transmitter, respectively. We also envision the potential applications of RIS in 6G networks.

Reconfigurable intelligent surfaces (RISs) have attracted the attention of academia and industry circles because of their ability to control the electromagnetic characteristics of channel environments. However, it has been found that the introduction of an RIS may bring new and more serious network coexistence problems. It may even further deteriorate the network performance if these new network coexistence problems cannot be effectively solved. In this paper, an RIS network coexistence model is proposed and discussed in detail, and these problems are deeply analysed. Two novel RIS design mechanisms, including a novel multilayer RIS structure with an out-of-band filter and an RIS blocking mechanism, are further explored. Finally, numerical results and a discussion are given.

In this paper, we introduce a physics-consistent analytical characterization of the free-space path-loss of a wireless link in the presence of a reconfigurable intelligent surface. The proposed approach is based on the vector generalization of Green’s theorem. The obtained path-loss model can be applied to two-dimensional homogenized metasurfaces, which are made of sub-wavelength scattering elements and that operate either in reflection or transmission mode. The path-loss is formulated in terms of a computable integral that depends on the transmission distances, the polarization of the radio waves, the size of the surface, and the desired surface transformation. Closed-form expressions are obtained in two asymptotic regimes that are representative of far-field and near-field deployments. Based on the proposed approach, the impact of several design parameters and operating regimes is unveiled.

Reconfigurable intelligent surfaces (RISs) have attracted the attention of academia and industry circles because of their ability to control the electromagnetic characteristics of channel environments. However, it has been found that the introduction of an RIS may bring new and more serious network coexistence problems. It may even further deteriorate the network performance if these new network coexistence problems cannot be effectively solved. In this paper, an RIS network coexistence model is proposed and discussed in detail, and these problems are deeply analysed. Two novel RIS design mechanisms, including a novel multilayer RIS structure with an out-of-band filter and an RIS blocking mechanism, are further explored. Finally, numerical results and a discussion are given.
Our contributions: Based on our previous studies [21], this paper makes two contributions: (1) to deeply analyse and model RIS network coexistence for the first time and (2) to further analyse and evaluate two novel RIS structures, including a novel multilayer RIS structure with an out-of-band filter and an RIS blocking mechanism.

This Roadmap takes the reader on a journey through the research in electromagnetic wave propagation control via reconfigurable intelligent surfaces. Meta-surface modelling and design methods are reviewed along with physical realisation techniques. Several wireless applications are discussed, including beam-forming, focusing, imaging, localisation, and sensing, some rooted in novel architectures for future mobile communications networks towards 6G.

This research report is the first systematic technical report on RIS technology in the industry, and is released by the IMT-2030 propulsion group. It first briefly reviews the evolution history and current situation of RIS technology, and then introduces the foundational principle of RIS technology. The typical application scenarios and key enabling technologies of RIS are the focus of this report. As for potential application scenarios, the report gives 7 traditional communication scenarios enhanced by RIS and 10 new application scenarios enabled by RIS. This report further divides the potential key enabling technologies into three categories: hardware structure and regulation mechanism, baseband algorithm and system architecture and deployment. Among them, the hardware structure and regulation mechanism includes two key technologies, the baseband algorithm includes nine key technologies, and the system architecture and deployment include three key technologies. Then, the report analyzes the maturity and challenges of RIS technology. Finally, the report gives a prospect for the development of RIS technology.

Reconfigurable intelligent surface (RIS) is an emerging technology that is under investigation for different applications in wireless communications. RISs are often analyzed and optimized by considering simplified electromagnetic reradiation models. In this chapter, we aim to study the impact of realistic reradiation models for RISs as a function of the sub-wavelength inter-distance between nearby elements of the RIS, the quantization levels of the reflection coefficients, the interplay between the amplitude and phase of the reflection coefficients, and the presence of electromagnetic interference. We consider both case studies in which the users may be located in the far-field and near-field regions of an RIS. Our study shows that, due to design constraints, such as the need of using quantized reflection coefficients or the inherent interplay between the phase and the amplitude of the reflection coefficients, an RIS may reradiate power towards unwanted directions that depend on the intended and interfering electromagnetic waves. Therefore, it is in general important to optimize an RIS by considering the entire reradiation pattern by design to maximize the reradiated power towards the desired directions of reradiation while keeping the power reradiated towards other unwanted directions at a low level. Our study shows that a 2-bit digitally controllable RIS with an almost constant reflection amplitude as a function of the applied phase shift, and whose scattering elements have a size and an inter-distance between (1/8)th and (1/4)th of the signal wavelength may be a good tradeoff between performance, implementation complexity and cost. However, the presented results are preliminary and pave the way for further research into the performance of RISs based on accurate and realistic electromagnetic reradiation models.

The diverse and stringent requirements of 6G networks, detailed in the present book, give rise to fully flexible, end-to-end, software-defined network paradigm, where every part of the network can be configured and controlled via software. However, the wireless environment per se – i.e. the wireless medium or channel – is generally assumed uncontrollable, thus, imposing inherent limitations to 6G networks, that arise by the very nature of wireless operation. To this end, the emergence of the newly introduced concept of reconfigurable intelligent surfaces (RISs) challenges the fundamental status quo that the wireless environment is fixed by nature, paving the way for the realization of end-to-end fully reconfigurable 6G networks.
RISs are network devices that can control and manipulate the radio waves traversing through the wireless channel. Since RISs reside within the wireless channel and not at the communication endpoints, they can control the wireless channels from within. In this context, the present chapter introduces the concept of RISs within the 6G framework, elaborating on their advantages and limitations. RISs are then compared with other transmission technologies, e.g. phased arrays, multi-antenna transmitters, and relays, while demonstrating the trade-offs governing their operation and applicability. Subsequently, the different types of RIS implementations are presented from a theoretical standpoint, along the available prototypes in the literature; thus, demonstrating how the RIS technology is already a reality, ushering wireless networks into the 6G era.

Reconfigurable intelligent surfaces (RISs), also known as intelligent reflecting surfaces (IRSs), or large intelligent surfaces (LISs),
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have received significant attention for their potential to enhance the capacity and coverage of wireless networks by smartly reconfiguring the wireless propagation environment. Therefore, RISs are considered a promising technology for the sixth-generation (6G) of communication networks. In this context, we provide a comprehensive overview of the state-of-the-art on RISs, with focus on their operating principles, performance evaluation, beamforming design and resource management, applications of machine learning to RIS-enhanced wireless networks, as well as the integration of RISs with other emerging technologies. We describe the basic principles of RISs both from physics and communications perspectives, based on which we present performance evaluation of multiantenna assisted RIS systems. In addition, we systematically survey existing designs for RIS-enhanced wireless networks encompassing performance analysis, information theory, and performance optimization perspectives. Furthermore, we survey existing research contributions that apply machine learning for tackling challenges in dynamic scenarios, such as random fluctuations of wireless channels and user mobility in RIS-enhanced wireless networks. Last but not least, we identify major issues and research opportunities associated with the integration of RISs and other emerging technologies for applications to next-generation networks.
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Without loss of generality, we use the name of RIS in the remainder of this paper.
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The optimal planning of electromagnetic skins (EMSs) installed on the building facades to enhance the received signal strength, thus the wireless coverage and/or the quality-of-service (QoS) in large-scale urban areas, is addressed. More specifically, a novel instance of the System-by-Design (SbD) paradigm is proposed towards the implementation of a smart electromagnetic environment (SEME) where low-cost passive static reflective skins are deployed to enhance the level of the power received within selected regions-of-interest (RoIs). Thanks to the ad-hoc customization of the SbD functional blocks, which includes the exploitation of a digital twin (DT) for the accurate yet fast assessment of the wireless coverage condition, effective solutions are yielded. Numerical results, dealing with real-world test-beds, are shown to assess the capabilities, the potentialities, and the current limitations of the proposed EMSs planning strategy.

div>The use of reconfigurable intelligent surfaces (RISs) for optimization of propagation channels is one of the most promising and revolutionizing techniques for improving the efficiency of the next generation of communications systems. In this work, we combine the physical optics approximation and the theory of diffraction gratings to study the scattering properties of finite-size metasurfaces mounted on partially reflecting walls and illuminated by directive antennas. We consider both reflective and refractive metasurfaces designed to control both reflection and transmission of waves. We start the analysis under the assumption of uniform, plane-wave illumination, and then discuss non-uniform illuminations by directive antennas.</div

We introduce algorithms for optimizing a single-input single-output reconfigurable intelligent surface (RIS) assisted system. The RIS is modeled by using an electromagnetic-compliant framework based on mutual impedances and its reconfigurability is realized through tunable lumped impedances. In the absence of mutual coupling among the scattering elements of the RIS, we derive a closed-form expression for the optimal tunable impedances, which accounts for the interplay between the amplitude and phase of the lumped loads of the RIS. In the presence of mutual coupling, we introduce an iterative algorithm for optimizing the tunable impedances of the RIS. The algorithm is proved to be convergent by showing that the objective function is non-decreasing and upper bounded. Numerical results reveal that the mutual coupling significantly affects the end-to-end received power. If the RIS is optimized by taking the mutual coupling into account, the received power can be increased.

Reconfigurable intelligent surfaces (RISs) comprised of tunable unit cells have recently drawn significant attention due to their superior capability in manipulating electromagnetic waves. In particular, RIS-assisted wireless communications have the great potential to achieve significant performance improvement and coverage enhancement in a cost-effective and energy-efficient manner, by properly programming the reflection coefficients of the unit cells of RISs. In this paper, free-space path loss models for RIS-assisted wireless communications are developed for different scenarios by studying the physics and electromagnetic nature of RISs. The proposed models, which are first validated through extensive simulation results, reveal the relationships between the free-space path loss of RIS-assisted wireless communications and the distances from the transmitter/receiver to the RIS, the size of the RIS, the near-field/far-field effects of the RIS, and the radiation patterns of antennas and unit cells. In addition, three fabricated RISs (metasurfaces) are utilized to further corroborate the theoretical findings through experimental measurements conducted in a microwave anechoic chamber. The measurement results match well with the modeling results, thus validating the proposed free-space path loss models for RIS, which may pave the way for further theoretical studies and practical applications in this field.

Reconfigurable intelligent surfaces (RISs) have the potential of realizing the emerging concept of smart radio environments by leveraging the unique properties of metamaterials and large arrays of inexpensive antennas. In this article, we discuss the potential applications of RISs in wireless networks that operate at high-frequency bands, e.g., millimeter wave (30-100 GHz) and sub-millimeter wave (greater than 100 GHz) frequencies. When used in wireless networks, RISs may operate in a manner similar to relays. The present paper, therefore, elaborates on the key differences and similarities between RISs that are configured to operate as anomalous reflectors and relays. In particular, we illustrate numerical results that highlight the spectral efficiency gains of RISs when their size is sufficiently large as compared with the wavelength of the radio waves. In addition, we discuss key open issues that need to be addressed for unlocking the potential benefits of RISs for application to wireless communications and networks.

Intelligent reflecting surface (IRS) that enables the control of wireless propagation environment has recently emerged as a promising cost-effective technology for boosting the spectral and energy efficiency of future wireless communication systems. Prior works on IRS are mainly based on the ideal phase shift model assuming full signal reflection by each of its elements regardless of the phase shift, which, however, is practically difficult to realize. In contrast, we propose in this paper a practical phase shift model that captures the phase-dependent amplitude variation in the element-wise reflection design. Based on the proposed model and considering an IRS-aided multiuser system with one IRS deployed to assist in the downlink communications from a multi-antenna access point (AP) to multiple single-antenna users, we formulate an optimization problem to minimize the total transmit power at the AP by jointly designing the AP transmit beamforming and the IRS reflect beamforming, subject to the users’ individual signal-to-interference-plus-noise ratio (SINR) constraints. Iterative algorithms are proposed to find suboptimal solutions to this problem efficiently by utilizing the alternating optimization (AO) as well as penalty-based optimization techniques. Moreover, to draw essential insight, we analyze the asymptotic performance loss of the IRS-aided system that employs practical phase shifters but assumes the ideal phase shift model for beamforming optimization, as the number of IRS elements goes to infinity. Simulation results unveil substantial performance gains achieved by the proposed beamforming optimization based on the practical phase shift model as compared to the conventional ideal model.

Future wireless networks are expected to constitute a distributed intelligent wireless communications, sensing, and computing platform, which will have the challenging requirement of interconnecting the physical and digital worlds in a seamless and sustainable manner. Currently, two main factors prevent wireless network operators from building such networks: (1) the lack of control of the wireless environment, whose impact on the radio waves cannot be customized, and (2) the current operation of wireless radios, which consume a lot of power because new signals are generated whenever data has to be transmitted. In this paper, we challenge the usual “more data needs more power and emission of radio waves” status quo, and motivate that future wireless networks necessitate a smart radio environment: a transformative wireless concept, where the environmental objects are coated with artificial thin films of electromagnetic and reconfigurable material (that are referred to as reconfigurable intelligent meta-surfaces), which are capable of sensing the environment and of applying customized transformations to the radio waves. Smart radio environments have the potential to provide future wireless networks with uninterrupted wireless connectivity, and with the capability of transmitting data without generating new signals but recycling existing radio waves. We will discuss, in particular, two major types of reconfigurable intelligent meta-surfaces applied to wireless networks. The first type of meta-surfaces will be embedded into, e.g., walls, and will be directly controlled by the wireless network operators via a software controller in order to shape the radio waves for, e.g., improving the network coverage. The second type of meta-surfaces will be embedded into objects, e.g., smart t-shirts with sensors for health monitoring, and will backscatter the radio waves generated by cellular base stations in order to report their sensed data to mobile phones. These functionalities will enable wireless network operators to offer new services without the emission of additional radio waves, but by recycling those already existing for other purposes. This paper overviews the current research efforts on smart radio environments, the enabling technologies to realize them in practice, the need of new communication-theoretic models for their analysis and design, and the long-term and open research issues to be solved towards their massive deployment. In a nutshell, this paper is focused on discussing how the availability of reconfigurable intelligent meta-surfaces will allow wireless network operators to redesign common and well-known network communication paradigms.

A procedure to achieve near-field multiple input multiple output (MIMO) communication with equally strong channels is demonstrated in this paper. This has applications in near-field wireless communications, such as Chip-to-Chip (C2C) communication or wireless links between printed circuit boards. Designing the architecture of these wireless C2C networks is, however, based on standard engineering design tools. To attain this goal, a network optimization procedure is proposed, which introduces decoupling and matching networks. As a demonstration, this optimization procedure is applied to a 2-by-2 MIMO with dipole antennas. The potential benefits and design trade-offs are discussed for implementation of wireless radio-frequency interconnects in chip-to-chip or device-to-device communication such as in an Internet-of-Things scenario.

In this paper, we introduce a physics-consistent analytical characterization of the free-space path-loss of a wireless link in the presence of a reconfigurable intelligent surface. The proposed approach is based on the vector generalization of Green’s theorem. The obtained path-loss model can be applied to two-dimensional homogenized metasurfaces, which are made of sub-wavelength scattering elements and that operate either in reflection or transmission mode. The path-loss is formulated in terms of a computable integral that depends on the transmission distances, the polarization of the radio waves, the size of the surface, and the desired surface transformation. Closed-form expressions are obtained in two asymptotic regimes that are representative of far-field and near-field deployments. Based on the proposed approach, the impact of several design parameters and operating regimes is unveiled.

We consider a fading channel in which a multi-antenna transmitter communicates with a multi-antenna receiver through a reconfigurable intelligent surface (RIS) that is made of N reconfigurable passive scatterers impaired by phase noise. The beamforming vector at the transmitter, the combining vector at the receiver, and the phase shifts of the N scatterers are optimized in order to maximize the signal-to-noise-ratio (SNR) at the receiver. By assuming Rayleigh fading (or line-of-sight propagation) on the transmitter-RIS link and Rayleigh fading on the RIS-receiver link, we prove that the SNR is a random variable that is equivalent in distribution to the product of three (or two) independent random variables whose distributions are approximated by two (or one) gamma random variables and the sum of two scaled non-central chi-square random variables. The proposed analytical framework allows us to quantify the robustness of RIS-aided transmission to fading channels. For example, we prove that the amount of fading experienced on the transmitter-RIS-receiver channel linearly decreases with N1. This proves that RISs of large size can be effectively employed to make fading less severe and wireless channels more reliable.

Reconfigurable intelligent surfaces (RISs) are an emerging transmission technology for application to wireless communications. RISs can be realized in different ways, which include (i) large arrays of inexpensive antennas that are usually spaced half of the wavelength apart; and (ii) metamaterial-based planar or conformal large surfaces whose scattering elements have sizes and inter-distances much smaller than the wavelength. Compared with other transmission technologies, e.g., phased arrays, multi-antenna transmitters, and relays, RISs require the largest number of scattering elements, but each of them needs to be backed by the fewest and least costly components. Also, no power amplifiers are usually needed. For these reasons, RISs constitute a promising software-defined architecture that can be realized at reduced cost, size, weight, and power (C-SWaP design), and are regarded as an enabling technology for realizing the emerging concept of smart radio environments (SREs). In this paper, we (i) introduce the emerging research field of RIS-empowered SREs; (ii) overview the most suitable applications of RISs in wireless networks; (iii) present an electromagnetic-based communication-theoretic framework for analyzing and optimizing metamaterial-based RISs; (iv) provide a comprehensive overview of the current state of research; and (v) discuss the most important research issues to tackle. Owing to the interdisciplinary essence of RIS-empowered SREs, finally, we put forth the need of reconciling and reuniting C. E. Shannon’s mathematical theory of communication with G. Green’s and J. C. Maxwell’s mathematical theories of electromagnetism for appropriately modeling, analyzing, optimizing, and deploying future wireless networks empowered by RISs.

A communication model for large intelligent surfaces

- R J Williams

R. J. Williams et al., "A communication model for large intelligent
surfaces", IEEE Int. Conf. Commun., Jun. 2020.