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... IRSs have several applications, and, in particular, they are useful for enhancing the coverage in severe non-line-of-sight (NLOS) channel conditions by acting as intelligent mirrors [15]. More in general, IRSs are viewed as a technology enabler for realizing the so-called smart radio environment, i.e., a wireless system in which the environment (e.g., the channel) becomes a variable that can be optimized in addition to the parameters of the communication devices [16]. ...

... where E (V ( ) , B ( ) , G ( )) is the × MSE matrix defined in (15). ...

... From the statistical properties of the information vectors s , we can elaborate (15) as ...

... 2) Performance of IRS-aided large-scale networks: In [22], the network coverage was investigated based on the key result obtained in [23], that is, the probability that an object coated with an IRS could act as a reflector for a given transmitter and receiver pair. However, the path loss model adopted for the reflective path has been shown to be only reasonable in the near-field [24,25]. In [26], using a similar blockage model as in [22], the signal-to-noise ratio (SNR) in a scenario with a direct path and K IRS-assisted paths was analysed, and the system performance under different association criteria was studied. ...

... According to [24,25], and the path loss model for the LoS links in Eq. (2), and denoting u and v the distance from the transmitter to the IRS and the distance from the IRS to the receiver, respectively, the path loss of the reflected path, ζ r , can be formulated as ...

... (17). Moreover, considering the reflective probability of a random incident interfering signal, we can define the equivalent power emitted from one side of a typical IRS located at y 0 as (25) where the fraction 1 2 in Step (a) comes from the probability that the interfering transmitter and the typical receiver locate at the same side of the IRS -the line which passes through the IRS separates all the transmitters in the plane into two parts, and each part has a transmitter density λ b /2-, and G r is the antenna gain between the interfering transmitter and the IRS due to the directional/beamformed antenna deployed in each transmitter. Since the antenna direction is independent of the location of the interfering transmitter, and follows a uniform distribution in [0, 2π), we can compute the average antenna gain as ...

Intelligent reflecting surfaces (IRSs) have been proposed as a promising technology to enhance signal transmissions in high-frequency bands. Up to now, the research on the performance of large networks with IRSs is still in its infancy. In this paper, we study a Poisson bipolar network with line segment blockages and reflectors. By deriving the probability that an IRS can successfully reflect a signal from a transmitter to a receiver and the distribution of the distance traveled by the reflected signal, the performance impact of deploying IRSs on the signal propagation is investigated. The aggregated interference through reflective paths via IRSs is derived by modeling the IRSs as additional interfering sources with non-uniformly distributed interfering power in different directions. With these results, the signal-to-interference-and-noise ratio (SINR) and the achievable rate are further derived, where a characteristic function and the inverse theorem are adopted to handle the complicated channel fading of reflective signals. From the analysis, IRSs have a great potential to enhance the network performance, but the tradeoff between signal enhancement and reflective interference is important. That is, the performance gain suffers from a diminishing return with a large IRS fraction due to the growth of reflective interference.

... For instance, Refs. [19,20] explained that all elements of the finitesized RIS can individually act as diffuse scatters when the transmitter and the receiver both lie in the far-field of the RIS. Similar to a phase shifter, each subwavelength-sized RIS element scatters the incoming signals with a unique phase shift. ...

... Similar to a phase shifter, each subwavelength-sized RIS element scatters the incoming signals with a unique phase shift. By denoting the incident angle from the transmitter to the RIS and assuming the scattered waves from the RIS can reach the maximum value in the observation angle leading to the receiver, Ref. [19] derived the far-field path loss model in terms of physical optics techniques: ...

... As shown in Eqs. (19) and (20), the achievable rate of the RIS-aided system is always larger than that of the traditional SISO system, i.e., , since [27] . Therefore, RIS provides the highest achievable rate if and only if . ...

The reconfigurable intelligent surface (RIS) is an emerging technology, which will hopefully bring a new revolution in wireless communications. The RIS technology can be deployed in an indoor/outdoor environment to dynamically manipulate the propagation environment. The RIS consists of a large number of independently controllable passive elements, and these elements are involved in realizing high passive beamforming gain. Different from the conventional active phased antenna array, there is no dedicated radio-frequency (RF) chain installed at the RIS to perform complex signal processing operations. Therefore, it does not incur additional noise while retransmitting the incident wave, which is substantially a unique feature from the conventional wireless communication systems. Taking advantage of its working principle, RIS has been deployed in various practical scenarios. In this tutorial, at first we will review the latest advances in RIS, including the application scenarios such as the system and channel model, the information theoretic analysis, the physical realization and design, key signal processing techniques such as precoding and channel estimation, and prototyping. Finally, we discuss interesting future research problems for the RIS-aided communications.

... In the sum-distance law, the energy decreases with the square of the distance, in contrast to the fourth power of the distance for the product-distance law. The works in [8], [12]- [14] discussed in detail the near-field and far-field formulations with mirrors and scatterers. In [8], it was introduced that the energy is inversely proportional to the square and the fourth power of the distance for the near-field and far-field cases, respectively. ...

... In [8], it was introduced that the energy is inversely proportional to the square and the fourth power of the distance for the near-field and far-field cases, respectively. The work in [12] used the scalar diffraction theory to prove that the sum-distance and product-distance laws hold in the near and far fields, respectively. In the paper [13], along with verification experiments, it is concluded that the sum-distance and product-distance laws hold for nearfield broadcasting and far-field beamforming, respectively. ...

An accurate and fast prediction technique is necessary for the radiation pattern of the reconfigurable intelligent surface (RIS) to quantitatively and efficiently evaluate the performance of RIS. Based on the uniform theory of diffraction (UTD), this paper proposes a UTD-type solution of the physical optics approximation (PO) for RIS modeled by a continuous planar surface in a two-dimensional environment. The authors validate the proposal under different scenarios in an indoor environment (0.1-20 m) at the terahertz bands (100-300 GHz), by comparing them with those computed using the Fresnel approximation, the Fraunhofer approximation, PO, and the full-wave approach based on the method of moment (MoM). The simulated results show that compared to MoM, the proposal and PO achieve good accuracy with a smaller error of less than 1 dB, while the Fresnel and Fraunhofer approximations present imperfect accuracy with an error of larger than 1 dB in the near-field region. Moreover, the proposal outperforms the PO in terms of faster calculation time by approximately 70%-76%, and the computational time of the proposal is improved by approximately 46,190-125,460 times compared to MoM. Furthermore, the computational complexities of the proposal, the Fresnel approximation and the Fraunhofer approximation are O(N0), compared to that of PO and MoM by O(N) and O(N2), respectively, where N and O(∙) are the number of sampling points and the notation of order, respectively. Therefore, the proposal can achieve a good balance between accuracy and computational cost.

... changed by the change of the propagation environment and user distribution [9], the intelligent reflecting surface (IRS), which can control reflection characteristics such as reflection direction and phase, has been attracting attention [4,6,[10][11][12][13][14][15][16][17][18][19]. ...

... Subsequently, the reflection power and direction of the actual IRS are evaluated. However, since the RCS is defined in the far-field region of the IRS, the measurement system of the RCS pattern is deployed to satisfy far-field conditions, such as the distance between the IRS and each transmitting and receiving antenna [17]. Assuming an IRS with several tens of wavelengths, a distance of more than several tens of thousands of wavelengths is required for each transmitter and receiver. ...

Intelligent reflecting surfaces (IRSs) have been attracting attention as a solution to coverage hole problems in millimeter-wave communication areas and are considered one of the key technologies of next-generation mobile communication systems. To utilize the IRS for mobile networks, the reflection power of the IRS should be evaluated in advance to estimate the coverage enhancement. Because the IRS becomes large, up to several tens or hundreds of wavelengths, a reflection power evaluation method for a large IRS is required. Although the reflection amplitude and phase of the reflecting element are available for the physical optics (PO)-based evaluation method, they depend on the location of the reflecting element because of the mutual coupling between adjacent reflecting elements, and should be measured at each location of the reflecting element. Since the number of reflecting elements in large IRS becomes several tens of thousands, measurement becomes difficult. In addition, although the radar cross section (RCS) is available for reflection power evaluation in the far field, a massive measurement system of several hundreds of meters is required to satisfy the far-field condition of the IRS. For these reasons, the evaluation of large IRS is challenging. To solve this problem, we propose a practical evaluation method for large IRS by synthesizing the RCS patterns of small IRSs (sub-IRSs). Since the influence of the mutual coupling between sub-IRSs depends on the size of the sub-IRSs, we formulated the mutual coupling on the IRS and evaluated the proposed method by changing the size of the sub-IRSs. The measurement results in an anechoic chamber verified that the proposed method can estimate the RCS pattern of a large IRS with a reflection power difference of less than 1dB and the correlation between the estimated RCS pattern and the actual RCS pattern exceeds more than 0.87.

... Using the scalar theory of diffraction and the Huygens-Fresnel principle, the authors in [46] describe pathloss in RISs in both the near and far fields. RISs are represented as homogenous sheets of EM material with negligible depth. ...

... The received signal power is proportional to the square of the RIS area and inversely proportional to the square product 1∕(r 1 r 2 ) 2 of the distances between transmitter and RIS and between RIS and receiver [46] The Huygens-Fresnel concept and generalized scalar diffraction theory ...

Using reconfigurable intelligent surfaces (RISs) to improve the coverage and the data rate of future wireless networks is a viable option. These surfaces are constituted of a significant number of passive and nearly passive components that interact with incident signals in a smart way, such as by reflecting them, to increase the wireless system's performance as a result of which the notion of a smart radio environment comes to fruition. In this survey, a study review of RIS‐assisted wireless communication is supplied starting with the principles of RIS which include the hardware architecture, the control mechanisms, and the discussions of previously held views about the channel model and pathloss; then the performance analysis considering different performance parameters, analytical approaches and metrics are presented to describe the RIS‐assisted wireless network performance improvements. Despite its enormous promise, RIS confronts new hurdles in integrating into wireless networks efficiently due to its passive nature. Consequently, the channel estimation for, both full and nearly passive RIS and the RIS deployments are compared under various wireless communication models and for single and multi‐users. Lastly, the challenges and potential future study areas for the RIS aided wireless communication systems are proposed.

... By altering the frequency, phase, amplitude, or polarization of the incident EM wave, RIS may intelligently and adaptively rearrange the wireless environment [5]. When there are obstructions in the way of the direct communication path between the transmitter and receiver or when the channel quality between the transmitter and receiver is too low, RIS can be employed in wireless communications as an alternate path provider or as a quality enhancer [6], also in mm-Wave massive multiple-input multiple-output (MIMO) [7], device-to-device communication, simultaneous wireless information and power transfer, enhanced physical layer security, unmanned aerial vehicle communication for smart cities, and intelligent internet of things (IoT) applications for wireless sensor networks [8]. Several studies demonstrate the advantages of the RIS-aided network [9,10]. ...

... As a result, designing and operating a tunable MS will be significantly more difficult. Multiple research projects, including as [3][4][5][6][7][8][9][10][11][12][13][14]15], have examined the probable designs and properties of such programmable MSs, and have made substantial progress in this area. ...

Work on identifying the various techniques for 6G wireless networks has already begun as the present specification for 5G networks nears conclusion. Reconfigurable Intelligent Surfaces (RISs) are one of these potentially useful technologies for 6G service providers. They provide unparalleled levels of freedom in terms of wireless channel engineering, allowing the system to change the channel’s properties whenever and however it chooses. Nonetheless, such qualities need a thorough understanding of the reaction of the related meta-surface under all conceivable operational situations. Analytical models and complete wave simulations may both be used to gain a better knowledge of the radiation pattern features, although both have inaccuracies under specific situations and are exceedingly computationally intensive. As a result, in this study, we offer a unique neural network-based technique for description of the meta-surfaces response that is both rapid and accurate. We look at a variety of scenarios and show how the proposed methodology can be used in them. In particular, we show that our technique is capable of learning and predicting the parameters driving the reflected wave radiation pattern with the accuracy of a complete wave simulation (98.8%–99.8%) while using just a fraction of the time and computer complexity of an analytical simulation. The above finding and approach will be particularly useful in the design, defect tolerance, and servicing of the hundreds of RISs which will be installed in the 6G distributed system.

... Approaches have explored the placement of passive reflectors to increase coverage in a space [63], to employing reflectarrays as active alternatives [61], [62], [64]. The SRE direction consolidated the latter approach, and established the term RIS to denote half-wavelength reflectarrays that are employed for communication purposes [65]. PWEs constituted a distinct approach towards deterministic propagation control, and a departure from the stochastic principles of preceding efforts. ...

... An allelectromagnetic architecture that prescribes PWE-user interaction in the radiative near field should be followed. To this end, it is necessary to rely upon physics-based models for the propagation of EM fields in the proximity of metasurfaces and/or extract circuit models for the problem formulation [65]. Accurate path-loss models for link budget analysis, as well as fading models for sub-wavelength structures, both at the microscopic level, should be developed based on the extension of mathematical physics methods that capture the VOLUME X, XXXX 15 This article has been accepted for publication in IEEE Access. ...

We present a new approach to Extended Reality (XR), denoted as iCOPYWAVES, which seeks to offer naturally low-latency operation and cost effectiveness, overcoming the critical scalability issues faced by existing solutions. iCOPYWAVES is enabled by emerging PWEs, a recently proposed technology in wireless communications. Empowered by intelligent (meta)surfaces, PWEs transform the wave propagation phenomenon into a software-defined process. We leverage PWEs to: i) create, and then ii) selectively copy the scattered RF wavefront of an object from one location in space to another, where a machine learning module, accelerated by FPGAs, translates it to visual input for an XR headset using PWE-driven, RF imaging principles (XR-RF). This makes for an XR system whose operation is bounded in the physical-layer and, hence, has the prospects for minimal end-to-end latency. Over large distances, RF-to-fiber/fiber-to-RF is employed to provide intermediate connectivity. The paper provides a tutorial on the iCOPYWAVES system architecture and workflow. A proof-of-concept implementation via simulations is provided, demonstrating the reconstruction of challenging objects in iCOPYWAVES-produced computer graphics.

... Approaches have explored the placement of passive reflectors to increase coverage in a space [63], to employing reflectarrays as active alternatives [61], [62], [64]. The SRE direction consolidated the latter approach, and established the term RIS to denote half-wavelength reflectarrays that are employed for communication purposes [65]. PWEs constituted a distinct approach towards deterministic propagation control, and a departure from the stochastic principles of preceding efforts. ...

... An allelectromagnetic architecture that prescribes PWE-user interaction in the radiative near field should be followed. To this end, it is necessary to rely upon physics-based models for the propagation of EM fields in the proximity of metasurfaces and/or extract circuit models for the problem formulation [65]. Accurate path-loss models for link budget analysis, as well as fading models for sub-wavelength structures, both at the microscopic level, should be developed based on the extension of mathematical physics methods that capture the VOLUME X, XXXX 15 This article has been accepted for publication in IEEE Access. ...

We present a new approach to Extended Reality (XR), denoted as iCOPYWAVES, which seeks to offer naturally low-latency operation and cost-effectiveness, overcoming the critical scalability issues faced by existing solutions. iCOPYWAVES is enabled by emerging PWEs, a recently proposed technology in wireless communications. Empowered by intelligent (meta)surfaces, PWEs transform the wave propagation phenomenon into a software-defined process. We leverage PWEs to i) create, and then ii) selectively copy the scattered RF wavefront of an object from one location in space to another, where a machine learning module, accelerated by FPGAs, translates it to visual input for an XR headset using PWEdriven, RF imaging principles (XR-RF). This makes for an XR system whose operation is bounded in the physical layer and, hence, has the prospects for minimal end-to-end latency. Over large distances, RF-to-fiber/fiber-to-RF is employed to provide intermediate connectivity. The paper provides a tutorial on the iCOPYWAVES system architecture and workflow. A proof-of-concept implementation via simulations is provided, demonstrating the reconstruction of challenging objects in iCOPYWAVES produced computer graphics.

... Ref. [19] studies the path loss model of RIS-assisted wireless communication under different conditions. Ref. [20] uses the Huygens-Fresnel principle to study the wireless channel of reflective RIS and gives a closed expression for calculating the received power of RISs. Ref. [21] verifies the proposed RIS free space path loss model experimentally, and the measurement results show that the established model has strong credibility. ...

... Equation (20) can be vectorized as ...

Terahertz communication has been proposed as one of the basic key technologies of the sixth-generation wireless network (6G) due to its significant advantages, such as ultra-large bandwidth, ultra-high transmission rates, high-precision positioning, and high-resolution perception. In terahertz-enabled 6G communication systems, the intelligent reconfiguration of wireless propagation environments by deploying reconfigurable intelligent surfaces (RIS) will be an important research direction. This paper analyzes the far field and near field of RIS-assisted wireless communication and a detailed system description is presented. Subsequently, this paper presents a specific study of the channel model for an RIS-assisted 6G communication system in the far-field and near-field cases, respectively. Finally, an integrated simulation of the channel models for the far-field and near-field cases is carried out, and the performance of the RIS auxiliary link measured in terms of signal-to-noise ratio (SNR) is compared and analyzed. The results show that increasing the size of the RIS surface to improve the SNR is an effective method to enhance the coverage performance of the 6G THz communication system under the strong guarantee of the ultra-large bandwidth of THz.

... In this sub-section, we consider models for RISs that abstract their microscopic structure and that are focused on the specific wave transformations that the metasurface, as a whole, is intended to realize. More precisely, a metamaterialbased RIS whose unit cells have sizes and inter-distances much smaller than the wavelength is homogenizable and can be modeled as a continuous surface sheet through appropriate surface functions, e.g., surface impedances [17], [36], [43], [45], [46], [47], [49], [58], [59], [63], [64], [65]. This modeling approach is not dissimilar from the characterization of bulk (three-dimensional) metamaterials, which are usually represented through effective permittivity and permeability functions that determine the wave phenomena based on Maxwell's equations. ...

... From (67), we conclude that the amplitude R (r Rx , y, r Tx ) and the total phase Ψ (r Rx , y, r Tx ) of the surface reflection coefficient are intertwined, and they are not, in general, independent of each other if a lossless RIS needs to have a locally unitary power efficiency. By definition, (65) and (67) are equivalent. Therefore, imposing (Z(r Rx , y, r Tx )) = 0 ∀y ∈ [−L y , L y ] is equivalent to imposing a well-defined relation between the amplitude and the phase of the field reflection coefficient, as obtained in (67). ...

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 article, 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.

... The scaling laws of the path loss as a function of the transmission distances are discussed numerically but no explicit characterization of the unit cells of planar RISs is given. In [25], integral and approximated closed-form expressions of the path loss of a one-dimensional RIS in the far-field and near-field regions are given. The results are obtained by leveraging the general scalar theory of diffraction. ...

... Different scaling laws as a function of the transmission distances and the size of the RIS are observed in the near-field and far-field regions. In [26], the analysis in [25] is generalized to two-dimensional RISs by using the vector generalization of Green's theorem. In particular, the scaling laws of the electric and magnetic fields as a function of the transmission distance and the size of the RIS are characterized. ...

Reconfigurable intelligent surfaces (RISs) provide an interface between the electromagnetic world of wireless propagation environments and the digital world of information science. Simple yet sufficiently accurate path loss models for RISs are an important basis for theoretical analysis and optimization of RIS-assisted wireless communication systems. In this paper, we refine our previously proposed free-space path loss model for RISs to make it simpler, more applicable, and easier to use. The impact of the antenna’s directivity of the transmitter, receiver, and the unit cells of the RIS on the path loss is explicitly formulated as an angle-dependent loss factor. The refined model gives more accurate estimates of the path loss of RISs comprised of unit cells with a deep sub-wavelength size. Based on the proposed model, the properties of a single unit cell are evaluated in terms of scattering performance, power consumption, and area, which allows us to unveil fundamental considerations for deploying RISs in high frequency bands. Two fabricated RISs operating in the millimeter-wave (mmWave) band are utilized to carry out a measurement campaign. The measurement results are shown to be in good agreement with the proposed path loss model. In addition, the experimental results suggest an effective form to characterize the power radiation pattern of the unit cell for path loss modeling.

... Using the scalar theory of diffraction and the Huygens-Fresnel principle, the authors in [44] describe pathloss in IRSs in both the near and far fields. IRSs are represented as homogenous sheets of electromagnetic material with negligible depth. ...

... The received signal power is proportional to the square of the IRS area and inversely proportional to the square product 1/ (r 1 r 2 ) 2 of the distances between TX and RIS and RIS and the RX [44] The Huygens-Fresnel concept and generalized scalar diffraction theory ...

Using intelligent reflecting surfaces (IRSs) to improve the coverage and the data rate of future wireless networks is a viable option. These surfaces are constituted of a significant number of passive and nearly passive components that interact with incident signals in a smart way, such as by reflecting them, to increase the wireless system's performance as a result of which the notion of a smart radio environment comes to fruition. In this survey we supply a study review of IRS-assisted wireless communication starting with the principles of IRS which include the hardware architecture, the control mechanisms, and the discussions of previously held views about the channel model and pathloss, then the performance analysis considering different performance parameters, analytical approaches and metrics are presented to describe the IRS-assisted wireless network performance improvements. Despite its enormous promise, IRS confronts new hurdles in integrating into wireless networks efficiently due to its passive nature. Consequently, the channel estimation for, both full and nearly passive IRS and the IRS deployments are compared under various wireless communication models and for single and multi-users. Lastly, we propose the challenges and potential future study areas for the IRS aided wireless communication systems.

... RIS-assisted communications provide network planning engineers with new system design freedom, becoming one of the potential key technologies for sixth generation (6G) wireless mobile networks. At present, both academia and industry are striving to explore and evaluate the performance of RIS-assisted wireless communication networks by means of path loss models [3] and experimental measurements [4] of RIS-assisted links. ...

Reconfigurable intelligent surface (RIS) is emerging as a promising technology to achieve coverage enhancement. This paper develops a tractable analytical framework based on stochastic geometry for performance analysis of RIS-assisted millimeter wave networks. Based on the framework, a two-step cell association criterion is proposed, and the analytical expressions of the user association probability and the coverage probability in general scenarios are derived. In addition, the closed-form expressions of the two performance metrics in special cases are also provided. The simulation results verify the accuracy of the theoretically derived analytical expressions, and reveal the superiority of deploying RISs in millimeter wave networks and the effectiveness of the proposed cell association scheme to improve coverage. Furthermore, the effects of the RIS parameters and the BS density on coverage performance are also investigated.

... Therefore, the users or receivers can be located in either the far-field or the near-field region of an RIS. The authors of [14], [15] derive closed-form expressions for computing the intensity of the electric field (E-field) in two asymptotic regimes that are representative of the farfield and near-field regions of an RIS. They also characterize the scaling laws of the EM field scattered by an RIS as a function of its size, the transmission distances, and the wave transformations. ...

The ability of reconfigurable intelligent surfaces (RIS) to produce complex radiation patterns in the far-field is determined by various factors, such as the unit cell’s design, spatial arrangement, tuning mechanism, the communication and control circuitry’s complexity, and the illuminating source’s type (point/planewave). Research on RIS has been mainly focused on two areas: first, the optimization and design of unit cells to achieve desired electromagnetic responses within a specific frequency band, and second, exploring the applications of RIS in various settings, including system-level performance analysis. The former does not assume any specific full radiation pattern on the surface level, while the latter does not consider any particular unit cell design. Both approaches largely ignore the complexity and power requirements of the RIS control circuitry. As we progress toward the fabrication and use of RIS in real-world settings, it is becoming increasingly necessary to consider the interplay between the unit cell design, the required surface-level radiation patterns, the control circuit’s complexity, and the power requirements concurrently. In this paper, we propose a benchmarking framework comprising a set of simple and complex radiation patterns. Using full-wave simulations, we compare the relative performance of various RISs made from unit cell designs that use PIN diodes as control elements in producing the full radiation patterns in the far-field of the RIS under point/planewave source assumptions. We also analyze the control circuit complexity and power requirements and explore the tradeoffs of various designs.

... Importantly, this is consistent (and provides a link) with path-loss models (see for example [46,47]), and provides an assessment of the impedance model for arbitrary RIS structures. The small error of the channel capacity obtained using the proposed expression stems from the effect of the mutual coupling among transmitting antennas, receiving antennas and the RIS that is neglected in its formulation. ...

We devise an end-to-end communication channel model that describes the performance of RIS-assisted MIMO wireless links. The model borrows the impedance (interaction) matrix formalism from the Method of Moments and provides a physics-based communication model. In configurations where the transmit and receive antenna arrays are distant from the RIS beyond a wavelength, a reduced model provides accurate results for arbitrary RIS unit cell geometry. Importantly, the simplified model configures as a cascaded channel transfer matrix whose mathematical structure is compliant with widely accepted, but less accurate, system level RIS models. A numerical validation of the communication model is presented for the design of binary RIS structures with scatterers of canonical geometry. Attained results are consistent with path-loss models: For obstructed line-of-sight between transmitter and receiver, the channel capacity of the (optimised) RIS-assisted link scales as $R^{-2}$, with $R$ RIS-receiver distance at fixed transmitter position. Our results shows that the applicability of communication models based on mutual impedance matrices is not restricted to canonical minimum scattering RIS unit cells.

... In addition, a physically accurate formula was introduced to calculate the scattered electric field of rectangular metal patches and several mathematically easy-to-handle models are proposed to characterize the input/output behavior of the array. Based on general scalar diffraction theory and the Huygens-Fresnel principle, [98] proposed a calculating method for the received power of RIS in closed form. [99] proposed an end-to-end and EM-compliant electromagnetic compatibility model considering the mutual coupling between cells of RIS. ...

Existing literature reviews predominantly focus on the theoretical aspects of reconfigurable intelligent surfaces (RISs), such as algorithms and models, while neglecting a thorough examination of the associated hardware components. To bridge this gap, this research paper presents a comprehensive overview of the hardware structure of RISs. The paper provides a classification of RIS cell designs and prototype systems, offering insights into the diverse configurations and functionalities. Moreover, the study explores potential future directions for RIS development. Notably, a novel RIS prototype design is introduced, which integrates seamlessly with a communication system for performance evaluation through signal gain and image formation experiments. The results demonstrate the significant potential of RISs in enhancing communication quality within signal blind zones and facilitating effective radio wave imaging.

... In addition, the path loss (PL) scaling law for RIS-assisted channel, which is also inseparable from phase shift designs, acts as one crucial role in RIS-related research. In existing works, such as [13], [14], [27]- [32], the authors formulated that the PL scaling law in the far field is proportional to (d 1 d 2 ) 2 , where d 1 and d 2 are the distance from transmitter (Tx) and receiver (Rx) to the center of RIS, respectively. However, the existing studies were mainly analyzed under ideal continuous phase shifts of RIS. ...

Reconfigurable intelligent surface (RIS) has aroused a surge of interest in recent years. In this paper, we investigate the joint phase alignment and phase quantization on discrete phase shift designs for RIS-assisted single-input single-output (SISO) system. Firstly, the phenomena of phase distribution in far field and near field are respectively unveiled, paving the way for discretization of phase shift for RIS. Then, aiming at aligning phases, the phase distribution law and its underlying degree-of-freedom (DoF) are characterized, serving as the guideline of phase quantization strategies. Subsequently, two phase quantization methods, dynamic threshold phase quantization (DTPQ) and equal interval phase quantization (EIPQ), are proposed to strengthen the beamforming effect of RIS. DTPQ is capable of calculating the optimal discrete phase shifts with linear complexity in the number of unit cells on RIS, whilst EIPQ is a simplified method with a constant complexity yielding sub-optimal solution. Simulation results demonstrate that both methods achieve substantial improvements on power gain, stability, and robustness over traditional quantization methods. The path loss (PL) scaling law under discrete phase shift of RIS is unveiled for the first time, with the phase shifts designed by DTPQ due to its optimality. Additionally, the field trials conducted at 2.6 GHz and 35 GHz validate the favourable performance of the proposed methods in practical communication environment.

... Given an RIS with M elements, its codeword ψ ∈ C M×1 , where for the element m with a phase shift φ, ψ m = e jφ [60]. Codewords determine the RIS behaviors, which generally include two categories: anomalous reflection and focusing [61,62], as shown in Figure 2. Concretely, anomalous reflection means that the RIS reflects the impinging signals towards arbitrary directions in parallel, thereby also including the common specular reflection (the angle of incidence equals the angle of reflection). Focusing would converge the reflected signals to one point, which is very effective for a single DOI, but at the same time means low versatility. ...

Reconfigurable Intelligent Surfaces (RISs) not only enable software-defined radio in modern wireless communication networks but also have the potential to be utilized for localization. Most previous works used channel matrices to calculate locations, requiring extensive field measurements, which leads to rapidly growing complexity. Although a few studies have designed fingerprint-based systems, they are only feasible under an unrealistic assumption that the RIS will be deployed only for localization purposes. Additionally, all these methods utilize RIS codewords for location inference, inducing considerable communication burdens. In this paper, we propose a new localization technique for RIS-enhanced environments that does not require RIS codewords for online location inference. Our proposed approach extracts codeword-independent representations of fingerprints using a domain adversarial neural network. We evaluated our solution using the DeepMIMO dataset. Due to the lack of results from other studies, for fair comparisons, we define oracle and baseline cases, which are the theoretical upper and lower bounds of our system, respectively. In all experiments, our proposed solution performed much more similarly to the oracle cases than the baseline cases, demonstrating the effectiveness and robustness of our method.

... In the research of RIS-assisted wireless communication, some of the existing works take a simple scalar RIS model with a diagonal matrix composed of the phase shift of each element [4], which leads to the absence of some important characteristics such as polarization. Some of the physical models proposed for reflective RIS thus far are based on the Huygens-Fresnel principle [2,5] or antenna theory [6][7][8] under physical optics approximation [9][10][11][12]. Different electromagnetic characteristics of an RIS can be achieved by different implementation schemes, which may be evaluated by full wave approaches such as the method of moment (MoM) [13,14]. ...

Reconfigurable intelligent surfaces (RISs) are one of the potential technologies for 6th generation (6G) mobile communication systems with superior electromagnetic (EM) wave-steering capability to effectively control the phase, amplitude, and polarization of the incident EM wave. An implementation-independent physical RIS model with key EM characteristics is especially crucial to RIS channel modeling considering the trade-off between complexity and accuracy. In this paper, a reflective RIS physical model is proposed to facilitate channel modeling in a system simulation. Based on the impinging EM wave of the last bounce to the RIS, the scattering field intensity of the target point is obtained using geometric optics and the electric field surface integration method of physical optics. The feasibility of the model is verified by a comparison of the simulation and test results.

... We also assume that the intensity of the scattered electromagnetic field decays with the inverse of the distance, and that the IRS are uniformly illuminated by the BS; our model is intended to hold in the far-field regime [32], [24] and when the angular aperture of the IRS, as observed from the BS, is small when compared to the beamwidth of the BS signal. ...

We consider the optimization of a smart radio environment where meta-surfaces are employed to improve the performance of multiuser wireless networks working at sub-THz frequencies. Motivated by the extreme sparsity of the THz channel we propose to model each meta-surface as an electronically steerable reflector, by using only two parameters, regardless of its size. This assumption, although suboptimal in a general multiuser setup, allows for a significant complexity reduction when optimizing the environment and, despite its simplicity, is able to provide high communication rates. We derive a set of asymptotic results providing insight on the system behavior when both the number of antennas at the transmitter and the meta-surfaces area grow large. For the optimization we propose an algorithm based on the Newton-Raphson method and a simpler, yet effective, heuristic approach based on a map associating meta-surfaces and users. Through numerical results we provide insights on the system behavior and we assess the performance limits of the network in terms of supported users and spatial density of the meta-surfaces.

... Follow up works were then published over the years, for example [9-11], but the topic remained of little interest to the wireless community, until a series of papers were published in late 2018 and 2019 [11][12][13][14][15]. From there, the idea of smart environments using electronically reconfigurable surfaces, coined Reconfigurable Intelligent Surfaces (RIS) emerged as a credible major technological advancement for 6G and has attracted an enormous and growing interest in the wireless communications community. Associated to RIS there are numerous research topics ranging from energy efficient wireless communication [16] to channel modeling [17,18], RIS based signal modulation and encoding [19], MIMO channel estimation and beamforming [20][21][22], telecommunication performance evaluation [23], mathematical model and optimization method for wavefront shaping with RIS [24-26] and even stochastic analysis approaches [27]. Of the numerous works proposed, a very large proportion are concerned with theoretical and mathematical approaches, and very few deal with experimental demonstrations of RIS [28]. ...

We exploit multi-path fading propagation to improve both the signal-to-interference-plus-noise-ratio and the stability of wireless communications within electromagnetic environments that support rich multipath propagation. Quasi-passive propagation control with multiple binary reconfigurable intelligent surfaces is adopted to control the stationary waves supported by a metallic cavity hosting a software-defined radio link. Results are demonstrated in terms of the error vector magnitude minimization of a quadrature phase-shift modulation scheme under no-line-of-sight conditions. It is found that the magnitude of fluctuation of received symbols is reduced to a stable constellation by increasing the number of individual surfaces, or elements, thus demonstrating channel hardening. By using a second software-defined radio device as a jammer, we demonstrate the ability of the RIS to mitigate the co-channel interference by channel hardening. Results are of particular interest in smart radio environments for mobile network architectures beyond 5G.

... A recent work [23] considered double-Rayleigh fading and approximated the composite channel gain as the Gamma distribution. Besides, based on a tractable linear RIS model proposed in [26], the authors in [24] and [25] analyzed the coverage probability and rate performance. ...

The simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) is capable of providing full-space coverage of smart radio environments. This work investigates STAR-RIS aided downlink non-orthogonal multiple access (NOMA) multi-cell networks, where the energy of incident signals at STAR-RISs is split into two portions for transmitting and reflecting. We first propose a fitting method to model the distribution of composite small-scale fading power as the tractable Gamma distribution. Then, a unified analytical framework based on stochastic geometry is provided to capture the random locations of RIS-RISs, base stations (BSs), and user equipments (UEs). Based on this framework, we derive the coverage probability and ergodic rate of both the typical UE and the connected UE. In particular, we obtain closed-form expressions of the coverage probability in interference-limited scenarios. We also deduce theoretical expressions in conventional RIS aided networks for comparison. The analytical results show that there exist optimal energy splitting coefficients of STAR-RISs to simultaneously maximize the system coverage and ergodic rate. The numerical results demonstrate that: 1) STAR-RISs are able to meet different demands of UEs located at different sides; 2) in low RIS density regions, STAR-RISs outperform conventional RISs while in dense regions the conclusion is opposite.

... In [88], a simple path loss model was proposed for RIS communications based on the general scalar theory of diffraction and the Huygens-Fresnel principle. The RIS was modeled as a sheet of electromagnetic material of negligible thickness. ...

Reconfigurable intelligent surfaces (RISs) are two dimensional (2D) metasurfaces which can intelligently manipulate electromagnetic waves by low-cost near passive reflecting elements. RIS is viewed as a potential key technology for the sixth generation (6G) wireless communication systems mainly due to its advantages in tuning wireless signals, thus smartly controlling propagation environments. In this paper, we aim at addressing channel characterization and modeling issues of RIS-assisted wireless communication systems. At first, the concept, principle, and potential applications of RIS are given. An overview of RIS based channel measurements and experiments is presented by classifying frequency bands, scenarios, system configurations, RIS constructions, experiment purposes, and channel observations. Then, RIS based channel characteristics are studied, including reflection and transmission, Doppler effect and multipath fading mitigation, channel reciprocity, channel hardening, rank improvement, far field and near field, etc. RIS based channel modeling works are investigated, including largescale path loss models and small-scale multipath fading models. At last, future research directions related to RIS-assisted channels are also discussed.

... So far, several techniques have been theoretically proposed for the design of the desired RIS properties [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and relevant experiments have been performed in order to verify the predicted RIS performance [12][13][14][15][21][22][23][24][25][26][27]. To achieve the desired wave manipulation, the design involves the determination of the appropriate surface properties, such as surface impedance (or effective electric and magnetic surface conductivities). ...

A Reconfigurable Intelligent Surface (RIS) redirects and possibly modifies the properties of incident waves, with the aim to restore non-line-of-sight communication links. Composed of elementary scatterers, the RIS has been so far treated as a collection of point scatterers with properties similar to antennas in an equivalent massive MIMO communication link. Despite the discrete nature of the RIS, current design approaches often treat the RIS as a continuous radiating surface, which is subsequently discretized. Here we investigate the connection between the two approaches in an attempt to bridge the two seemingly opposite perspectives. We analytically find the factor that renders the two approaches equivalent and we demonstrate our findings with examples of RIS elements modeled as antennas with commonly used radiation patterns and properties consistent with antenna theory. The equivalence between the two theoretical approaches is analyzed with respect to design aspects of the RIS elements, such as gain and directivity, with the aim to provide insight into the observed discrepancies, the understanding of which is crucial for assessing the RIS efficiency.

... In Ref. [108], an analytical channel model for pointto-point RIS-assisted free-space optical (FSO) systems was developed, which is based on the Huygens-Fresnel principle for the intermediate and the far-field. The model determines the reflected electric field and captures the impact of the size, position, and orientation of the RIS, as well as its phase shift profile on the end-to-end channel. ...

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 have 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.

... The existing works for path loss model estimation are mainly based on either analytical models [3,7,8] or empirical models [9] which rely on data collected in specific propagation scenarios. Although the empirical models are computationally efficient and easy to implement, the actual path loss at a specific location cannot be accurately computed especially in more general environments [10]. ...

... Thus, the beamforming gain of RIS is distance-dependent, in addition to the angles of the incident and scattered waves. As a result of this effect, the conventional collimated beamforming, which only depends on the directions and is optimal in the far-field, suffers from notable performance degradation in the near-field [6], [7]. More specifically, the effective beamforming gain has a limit which is independent of the RIS size or the distance between the RIS and the receiver. ...

Beamformer design for large-dimension reconfig-urable intelligent surface (RIS) is investigated. The challenge arises from the expanded near-field of RIS where its beam-forming gain is, in general, distance-dependent due to near-field diffraction. To gain more insights into this effect, we first analyse the performance of conventional collimated beamforming using Fresnel integrals, and compare it with that of focused beam-forming. Then, a two-step beamforming scheme is proposed. The principle of the proposed scheme is to divide the RIS into multiple subarrays followed by steering the sub-beams of the individual subarrays to focus. Providing properly chosen subarray size, the proposed scheme retains the low complexity of collimated beamforming and achieves a near-optimal performance, as shown both analytically and numerically.

... Considering an RIS modeled as a sheet of EM material of negligible thickness, and leveraging the general scalar theory of diffraction as well as the Huygens-Fresnel principle in [109], closed-form expressions for the power reflected from an RIS are presented as functions of the size of the RIS, the distance between the transmitter/receiver and the RIS, and the phase shift matrix configured by the RIS. With the aid of the stationary phase method, the authors identify sufficient conditions under which an RIS acts as an anomalous mirror, indicating that the received power decays as a function of the reciprocal of the sum of the distances between the transmitter/receiver and the RIS. ...

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.

This chapter starts with the state-of-the-art technology of the intelligent reflecting surface (IRS) which is emerged as a promising new paradigm to achieve smart and reconfigurable wireless propagation environment for beyond fifth-generation (B5G)/sixth-generation (6G) wireless communication systems. The motivation as well as the research background of the IRS is first presented. Then, the potential applications of the IRS in wireless information transmission and wireless energy transmission are highlighted and discussed. The unique property of IRS as well as its difference compared to the other technologies are studied. Next, we introduce the fundamental signal processing technique for IRS to show how it works. In addition, several types of IRS hardware architectures and hardware constraints are introduced and compared. Through the discussion, it is revealed that the IRS can provide significant high passive beamforming gain by adjusting its phase shifts, which motivates the main theme of this monograph.

Reconfigurable intelligent surfaces (RISs) are programmable metasurface structures that can control the propagation of electromagnetic waves by changing the electrical and magnetic properties of the surface. They can be used to intelligently reconfigure the wireless environment to improve the capacity and coverage of wireless networks. In recent years, numerous theoretical innovations and prototype tests have demonstrated that the RIS has the advantages of low cost, low power consumption, and easy deployment, and creates many potential opportunities and broad application prospects in 5G and future 6G networks. In this paper, starting from the technological development of RISs, we discussed the technical issues of RISs. The standardization of RISs, types of RISs according to operation modes, channel modeling, considerations for hardware implementation, differences from existing communication modules and the need for active RIS implementation, noise and power characteristics to ensure the efficiency of RISs, and performance parameters of RISs and field test results of RISs in indoor and outdoor environments were reviewed. By resolving the current technical issues of RISs, it is expected that RISs will be successfully used for B5G/6G communication through commercialization.

Intelligent reflecting surfaces (IRSs) have been proposed in recent years as a promising technology to enhance signal quality at high frequencies and save energy. In this paper, a Poisson bipolar network model with line segments is used to analyze the energy efficiency (EE) of an IRS-assisted, large-scale network. Specifically, we investigate the performance impact of the IRS configuration, in particular, the number of IRS elements and the phase-shifting resolution of each element. Using customized energy consumption and channel estimation models, we obtain the theoretical trade-off between signal quality and energy consumption as a function of these IRS configurations. The optimal number of elements and phase-shifting resolution of the IRS are also derived. Our results show that IRS technology has great potential for improving the EE of dense networks if their static energy consumption is small enough. Simulation results verify the accuracy of the obtained theoretical results.

Metasurfaces enable efficient manipulation of electromagnetic radiation. In practice, control over reflection direction is possibly the most useful. Extensive research has been done in the field of anomalous reflectors over the past years, resulting in numerous introduced geometries and several distinct design approaches. Without a comprehensive comparison between design methods, it is difficult to properly select the most appropriate method and the most suitable metasurface geometry. Here, we consider four main approaches that can be used to design anomalous reflectors for large deviations from specular reflection within the same basic structure topology for microwave and millimeter-wave applications. These approaches include the phase-gradient design, which is well-suited for small deviation angles due to its simplicity in design and realization. The second and third approaches involve optimization-based methods at the level of input and grid impedances, respectively. The fourth method is a non-local approach that optimizes supercells of the structure. We analyze and discuss a wide range of performance aspects, such as the power efficiency and losses, angular response, and the scattering pattern of finite-size structures. We believe that our study is particularly interesting for researchers working on metasurfaces, communication technologies, and reconfigurable intelligent surfaces.

The need for unrestricted, high-quality, and high-speed communications in planned sixth generation (6G) wireless systems drives the development and research towards the sub-terahertz (sub-THz) bands which so far have been relatively unused for wireless communications applications. Additionally, the sub-THz bands have gained an increasing interest as a potential spectral region at which to go even beyond the well-known Shannon limits. This review paper provides a technological overview on some of the key hardware aspects of sub-THz wireless communications (at 100–300 GHz), namely antennas, reconfigurable intelligent surfaces (RISs), and reconfigurable antenna systems based on state-of-the-art technologies reported in recent literature. Different technologies of antennas and RISs are compared to understand their possibilities and limitations, and to identify the most promising technological approaches to transform 6G from a vision into a commercially viable solution. The paper also presents the authors’ interpretations of possible hardware and design trends that can shape the future research directions.

Metasurfaces enable efficient manipulation of electromagnetic radiation. In particular, control over plane-wave reflection is one of the most useful features in many applications. Extensive research has been done in the field of anomalous reflectors over the past years, resulting in numerous introduced geometries and several distinct design approaches. Anomalously reflecting metasurfaces designed using different methods show different performances in terms of reflection efficiency, angular response, frequency bandwidth, etc. Without a comprehensive comparison between known design approaches, it is difficult to properly select the most appropriate design method and the most suitable metasurface geometry. Here, we consider four main approaches that can be used to design anomalous reflectors within the same basic topology of the structure and study the designed metasurfaces first on the level of the input impedance and then consider and compare the performance of the realized structures. We cover a wide range of performance aspects, such as the power efficiency and losses, angular response, and the scattering pattern of finite-size structures. We anticipate that this study will prove useful for developing new engineering methods and designing more sophisticated structures that include reconfigurable elements. Furthermore, we believe that this study can be considered referential since it provides comparative physical insight into anomalous reflectors in general.

This paper deals with line-of-sight (LOS) MIMO communication via an intelligent reflecting surface (IRS). It is shown that the number of spatial degrees of freedom (DOF) afforded by this setting grows in proportion with the IRS aperture, as opposed to being dictated by the transmit and receive apertures; this buttresses the interest in IRS deployments at mmWave and terahertz frequencies, with wavelengths and transmission ranges small enough to enable LOS MIMO. Explicit and simple-to-implement IRS phase shifts are put forth that achieve, not only the maximum number of DOF, but the capacity, under a certain geometrical condition. The insights leading to the proposed phase shifts, and to the optimality condition itself, are asymptotic in nature, yet extensive simulations confirm that the performance is excellent for a broad range of settings and even if the optimality condition is not strictly met.

Despite various intelligent reconfigurable surface (IRS)‐assisted use cases in the existing literature, there is no strong consensus to identify the killer applications that effectively exploit the potential of RISs to control the transmission medium with intelligent reflections for enhanced end‐to‐end system performance. The first step in clearing this ambiguity is to form a unified and physical RIS‐assisted channel model that can be adapted to different use cases and operating frequencies, taking into account the physical characteristics of RISs. As intelligent reflection is the art of manipulating the channel characteristics brilliantly and dynamically, modeling the RIS‐assisted transmission link is essential to provide detailed insights into the practical use cases. This chapter mainly aims to present a vision of channel modeling strategies for the RIS‐empowered communications systems considering the state‐of‐the‐art channel and propagation modeling efforts in the literature. Another objective of the chapter is 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. Furthermore, the extensive numerical results are provided via the SimRIS Channel Simulator MATLAB package for the detailed evaluation of how RISs can be effectively used in future wireless networks to enrich and improve the existing communication systems.

This work exploits ultra-low cost, commodity, radio frequency identification (RFID) tags as elements of a reconfigurable intelligent surface (RIS). Such batteryless tags are powered and controlled by a software-defined radio reader, with properly modified software, so that a source-destination link is assisted, operating at a different band. Signal model includes small-scale and large-scale fading, direct link, as well as specific parameters relevant to reflection (i.e., backscatter) radio, such as antenna structural mode and reflection efficiency, typically overlooked in the literature. An algorithm is offered that computes the optimal RIS configuration with complexity of
O
(
M
log
M
) in number of elements
M
, instead of intractable exponential complexity of exhaustive search, while accommodating any number
K
≥ 2 of loads. With the proposed algorithm, it is shown that performance gains reach a plateau for constant element spacing and increasing number of elements, suggesting that the weak, passive nature of backscattered links limits the performance gains, even with perfect channel estimation. Channel estimation with linear minimum mean squared error (LMMSE) estimator is shown to be effective, provided that there are sufficient number of pilot symbols. A concrete way is offered to design and prototype a wireless, batteryless, RF-powered, reconfigurable surface and a proof-of-concept is experimentally demonstrated.

Reconfigurable Intelligent Surface (RIS) has grown rapidly due to its performance improvement for wireless networks, and the integration of unmanned aerial vehicle (UAV) and RIS has obtained widespread attention. In this paper, the downlink of non-orthogonal multiple access (NOMA) UAV networks equipped with RIS is considered. The objective is to optimize the UAV trajectory with RIS phase shift to maximize the system capacity under the UAV energy consumption constraint. By deep reinforcement learning, a capacity maximization scheme under energy consumption constraints based on double deep Q-Network (DDQN) is proposed. The joint optimization of UAV trajectory with RIS phase shift design is achieved by DDQN algorithm. From the numerical results, the proposed optimization scheme can increase the system capacity of the RIS-UAV-assisted NOMA networks.

The reconfigurable intelligent surface (RIS) is a promising technology that is anticipated to enable high spectrum and energy efficiencies in future wireless communication networks. This paper investigates optimum location-based RIS selection policies in RIS-aided wireless networks to maximize the end-to-end signal-to-noise ratio for product-scaling and sum-scaling path-loss models where the received power scales with the
product
and
sum
of the transmitter-to-RIS and RIS-to-receiver distances, respectively. These scaling laws cover the important cases of end-to-end path-loss models in RIS-aided wireless systems. The random locations of all available RISs are modeled as a Poisson point process. To quantify the network performance, the outage probabilities and average rates attained by the proposed RIS selection policies are evaluated by deriving the distance distribution of the chosen RIS node as per the selection policies for both product-scaling and sum-scaling path-loss models. We also propose a limited-feedback RIS selection framework to achieve distributed network operation. The outage probabilities and average rates obtained by the limited-feedback RIS selection policies are derived for both path-loss models as well. The numerical results show notable performance gains obtained by the proposed RIS selection policies.

Reconfigurable intelligent surfaces (RISs) are gaining huge momentum in the field of wireless communications due to the paradigm shift that they bring. Indeed, they allow making any environment electromagnetically smart and dynamically reconfigurable for more efficient and greener wireless communications. As physicists, we proposed to use electronically tunable metasurfaces to shape the electromagnetic waves carrying our wireless communications in reflection almost ten years ago, inspired by some works that we and colleagues did in the field of wave control in complex media. In this article, we review the seminal works that led us to propose this concept, starting from the original one that is time reversal. Then, we propose a physicist’s point of view of RISs using a comparison with phase conjugation. Finally, we highlight what we think are their limitations, relying on both our knowledge of wave control and our study of them over a decade.

Reconfigurable intelligent surfaces (RISs) are 2-D metasurfaces, which can intelligently manipulate electromagnetic waves by low-cost near passive reflecting elements. RIS is viewed as a potential key technology for the sixth-generation (6G) wireless communication systems mainly due to its advantages in tuning wireless signals, thus smartly controlling propagation environments. In this article, we aim at addressing channel characterization and modeling issues of RIS-assisted wireless communication systems. First, the concept, principle, and potential applications of RIS are given. An overview of RIS-based channel measurements and experiments is presented by classifying frequency bands, scenarios, system configurations, RIS constructions, experiment purposes, and channel observations. Then, RIS-based channel characteristics are studied, including reflection and transmission, the Doppler effect and multipath fading mitigation, channel reciprocity, channel hardening, rank improvement, far field, near field, and so on. RIS-based channel modeling works are investigated, including large-scale path loss models and small-scale multipath fading models. Finally, future research directions related to RIS-assisted channels are also discussed.

Reconfigurable intelligent surfaces (RISs) have attracted major attention in the last few years, due to their useful characteristics. An RIS is a nearly passive thin surface that can dynamically change the reradiated field and can therefore realize anomalous reflection, refraction, focalization, or other wave transformations for engineering the radio propagation environment or realizing novel surface-type antennas. Evaluating the performance and optimizing the deployment of RISs in wireless networks need physically consistent frameworks that account for the electromagnetic characteristics of dynamic metasurfaces. In this article, we introduce a general macroscopic model for evaluating the scattering from an RIS. The proposed method decomposes the wave reradiated from an RIS into multiple scattering contributions and is aimed at being embedded into ray-based models. Since state-of-the-art ray-based models can already efficiently simulate specular wave reflection, diffraction, and diffuse scattering but not anomalous reradiation, we enhance them with an approach based on Huygens’ principle and propose two possible implementations for it. Multiple reradiation modes can be modeled through the proposed approach using the power conservation principle. We validate the accuracy of the proposed model by benchmarking it against several case studies available in the literature, which are based on analytical models, full-wave simulations, and measurements.

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.

Future wireless networks are expected to evolve toward an intelligent and software reconfigurable paradigm enabling ubiquitous communications between humans and mobile devices. They will also be capable of sensing, controlling, and optimizing the wireless environment to fulfill the visions of low-power, high-throughput, massively-connected, and low-latency communications. A key conceptual enabler that is recently gaining increasing popularity is the HMIMOS that refers to a low-cost transformative wireless planar structure comprised of sub-wavelength metallic or dielectric scattering particles, which is capable of shaping electromagnetic waves according to desired objectives. In this article, we provide an overview of HMIMOS communications including the available hardware architectures for reconfiguring such surfaces, and highlight the opportunities and key challenges in designing HMIMOS-enabled wireless communications.

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.

The future 5G networks are expected to use millimeter wave (mmWave) frequency bands to take advantage of the large unused spectrum. However, due to the high path loss at mmWave frequencies, coverage of mmWave signals can get severely reduced, especially for non-line-of-sight (NLOS) scenarios as mmWave signals are severely attenuated when going through obstructions. In this work, we study the use of passive metallic reflectors of different shapes/sizes to improve 28 GHz mmWave signal coverage for both indoor and outdoor NLOS scenarios. We quantify the gains that can be achieved in the link quality with metallic reflectors using measurements, analytical expressions, and ray tracing simulations. In particular, we provide an analytical model for the end-to-end received power in an NLOS scenario using reflectors of different shapes and sizes. For a given size of the flat metallic sheet reflector approaching to the size of the incident beam, we show that the reflected received power for the NLOS link is the same as line-of-sight (LOS) free space received power of the same link distance. Extensive results are provided to study the impact of environmental features and reflector characteristics on NLOS link quality.

Intelligent reflecting surfaces can improve the communication between a source and a destination. The surface contains metamaterial that is configured to “reflect” the incident wave from the source towards the destination. Two incompatible pathloss models have been used in prior work. In this letter, we derive the far-field pathloss using physical optics techniques and explain why the surface consists of many elements that individually act as diffuse scatterers but can jointly beamform the signal in a desired direction with a certain beamwidth. We disprove one of the previously conjectured pathloss models.

The future of mobile communications looks exciting with the potential new use cases and challenging requirements of future 6th generation (6G) and beyond wireless networks. Since the beginning of the modern era of wireless communications, the propagation medium has been perceived as a randomly behaving entity between the transmitter and the receiver, which degrades the quality of the received signal due to the uncontrollable interactions of the transmitted radio waves with the surrounding objects. The recent advent of reconfigurable intelligent surfaces in wireless communications enables, on the other hand, network operators to control the scattering, reflection, and refraction characteristics of the radio waves, by overcoming the negative effects of natural wireless propagation. Recent results have revealed that reconfigurable intelligent surfaces can effectively control the wavefront, e.g., the phase, amplitude, frequency, and even polarization, of the impinging signals without the need of complex decoding, encoding, and radio frequency processing operations. Motivated by the potential of this emerging technology, the present article is aimed to provide the readers with a detailed overview and historical perspective on state-of-the-art solutions, and to elaborate on the fundamental differences with other technologies, the most important open research issues to tackle, and the reasons why the use of reconfigurable intelligent surfaces necessitates to rethink the communication-theoretic models currently employed in wireless networks. This article also explores theoretical performance limits of reconfigurable intelligent surface-assisted communication systems using mathematical techniques and elaborates on the potential use cases of intelligent surfaces in 6G and beyond wireless networks.

This work deals with the use of emerging deep learning techniques in future wireless communication networks. It will be shown that data-driven approaches should not replace, but rather complement traditional design techniques based on mathematical models. Extensive motivation is given for why deep learning based on artificial neural networks will be an indispensable tool for the design and operation of future wireless communication networks, and our vision of how artificial neural networks should be integrated into the architecture of future wireless communication networks is presented. A thorough description of deep learning methodologies is provided, starting with the general machine learning paradigm, followed by a more in-depth discussion about deep learning and artificial neural networks, covering the most widely-used artificial neural network architectures and their training methods. Deep learning will also be connected to other major learning frameworks such as reinforcement learning and transfer learning. A thorough survey of the literature on deep learning for wireless communication networks is provided, followed by a detailed description of several novel case-studies wherein the use of deep learning proves extremely useful for network design. For each case-study, it will be shown how the use of (even approximate) mathematical models can significantly reduce the amount of live data that needs to be acquired/measured to implement data-driven approaches. Finally, concluding remarks describe those that in our opinion are the major directions for future research in this field.

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.

Electromagnetic metasurfaces can be characterized as intelligent if they are able to perform multiple tunable functions, with the desired response being controlled by a computer influencing the individual electromagnetic properties of each metasurface inclusion. In this paper, we present an example of an intelligent metasurface that operates in the reflection mode in the microwave frequency range. We numerically show that, without changing the main body of the metasurface, we can achieve tunable perfect absorption and tunable anomalous reflection. The tunability features can be implemented using mixed-signal integrated circuits (ICs), which can independently vary both the resistance and reactance, offering complete local control over the complex surface impedance. The ICs are embedded in the unit cells by connecting two metal patches over a thin grounded substrate and the reflection property of the intelligent metasurface can be readily controlled by a computer. Our intelligent metasurface can have a significant influence on future space-time modulated metasurfaces and a multitude of applications, such as beam steering, energy harvesting, and communications.

Programmable wireless environments use unique customizable software processes rather than traditional rigid channel models.

Electromagnetic waves undergo multiple uncontrollable alterations as they propagate within a wireless environment. Free space path loss, signal absorption, as well as reflections, refractions, and diffractions caused by physical objects within the environment highly affect the performance of wireless communications. Currently, such effects are intractable to account for and are treated as probabilistic factors. This article proposes a radically different approach, enabling deterministic, programmable control over the behavior of wireless environments. The key enabler is the so-called HyperSurface tile, a novel class of planar meta-materials that can interact with impinging electromagnetic waves in a controlled manner. The HyperSurface tiles can effectively re-engineer electromagnetic waves, including steering toward any desired direction, full absorption, polarization manipulation, and more. Multiple tiles are employed to coat objects such as walls, furniture, and overall, any objects in indoor and outdoor environments. An external software service calculates and deploys the optimal interaction types per tile to best fit the needs of communicating devices. Evaluation via simulations highlights the potential of the new concept.

Conventional optical components rely on gradual phase shifts accumulated during light propagation to shape light beams. New
degrees of freedom are attained by introducing abrupt phase changes over the scale of the wavelength. A two-dimensional array
of optical resonators with spatially varying phase response and subwavelength separation can imprint such phase discontinuities
on propagating light as it traverses the interface between two media. Anomalous reflection and refraction phenomena are observed
in this regime in optically thin arrays of metallic antennas on silicon with a linear phase variation along the interface,
which are in excellent agreement with generalized laws derived from Fermat’s principle. Phase discontinuities provide great
flexibility in the design of light beams, as illustrated by the generation of optical vortices through use of planar designer
metallic interfaces.

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.

In this work we address the distance dependence of reconfigurable intelligent surfaces (RIS). As differentiating factor to other works in the literature, we focus on the array near-field, what allows us to comprehend and expose the promising potential of RIS. The latter mostly implies an interplay between the physical size of the RIS and the size of the Fresnel zones at the RIS location, highlighting the major role of the phase. To be specific, the point-like (or zero-dimensional) conventional scattering characterization results in the well-known dependence with the fourth power of the distance. On the contrary, the characterization of its near-field region exposes a reflective behavior following a dependence with the second and third power of distance, respectively, for a two-dimensional (planar) and one-dimensional (linear) RIS. Furthermore, a smart RIS implementing an optimized phase control can result in a power exponent of four that, paradoxically, outperforms free-space propagation when operated in its near-field vicinity. All these features have a major impact on the practical applicability of the RIS concept. As one contribution of this work, the article concludes by presenting a complete signal characterization for a wireless link in the presence of RIS on all such regions of operation.

Contents: Green's Functions in Mathematical Physics: Time-Independent Green's Functions. Time-Dependent Green's Functions.- Green's Functions in One-Body Quantum Problems: Physical Significance of G. Application to the Free-Particle Case. Green's Functions and Perturbation Theory. Green's Functions for Tight-Binding Hamiltonians. Single Impurity Scattering. Two or More Impurities Disordered Systems.- Green's Functions in Many-Body Systems: Definitions. Properties and Use of the Green's Functions. Calculational Methods for g. Applications.- Appendix A: Analytic Behavior of G(z) Near a Band Edge.- Appendix B: The Renormalized Perturbation Expansion (RPE).- Appendix C: Second Quantization.- References.- Subject Index.

Non-uniform metasurfaces (electrically thin composite layers) can be used for shaping refracted and reflected electromagnetic waves. However, known design approaches based on the generalized refraction and reflection laws do not allow realization of perfectly performing devices: there are always some parasitic reflections into undesired directions. In this paper we introduce and discuss a general approach to the synthesis of metasurfaces for full control of transmitted and reflected fields and show that perfect performance can be realized. The method is based on the use of an equivalent impedance matrix model which connects the tangential field components at the two sides on the metasurface. With this approach we are able to understand what physical properties of the metasurface are needed in order to perfectly realize the desired response. Furthermore, we determine the required polarizabilities of the metasurface unit cells and discuss suitable cell structures. It appears that only spatially dispersive metasurfaces allow realization of perfect refraction and reflection of incident plane waves into arbitrary directions. In particular, ideal refraction is possible only if the metasurface is bianisotropic, and ideal reflection without polarization transformation requires spatial dispersion with a specific, strongly non-local response to the fields.

Reconfigurable intelligent surfaces vs. relaying: Differences, similarities, and performance comparison

- Di Renzo

Beyond max-SNR: Joint encoding for reconfigurable intelligent surfaces

- R Karasik