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End-to-End Mutual Coupling Aware Communication Model for Reconfigurable Intelligent Surfaces: An Electromagnetic-Compliant Approach Based on Mutual Impedances
Abstract
Reconfigurable intelligent surfaces (RISs) are an emerging technology for application to wireless networks. We introduce a physics and electromagnetic (EM) compliant communication model for analyzing and optimizing RIS-assisted wireless systems. The proposed model has four main notable attributes: (i) it is
end-to-end
, i.e., it is formulated in terms of an equivalent channel that yields a one-to-one mapping between the voltages fed into the ports of a transmitter and the voltages measured at the ports of a receiver; (ii) it is
EM-compliant
, i.e., it accounts for the generation and propagation of the EM fields; (iii) it is
mutual coupling aware
, i.e., it accounts for the mutual coupling among the sub-wavelength unit cells of the RIS; and (iv) it is
unit cell aware
, i.e., it accounts for the intertwinement between the amplitude and phase response of the unit cells of the RIS.
... However, this strong assumption cannot be easily achieved in practice, given that RIS usually consists of numerous densely spaced elements within a limited aperture to provide sufficient beamforming gain [8], [101]. There have been existing works on the modeling and analysis of the mutual coupling between D-RIS elements [18], [102], [103], which have been recently extended to BD-RIS-aided channels [104]- [106]. Below, we will briefly revisit the modeling of mutual coupling aware BD-RIS-aided channels, and how the existence of mutual coupling impacts the system performance. ...
... Consider a BD-RIS-aided MIMO system consisting of an N -antenna transmitter, an M -element BD-RIS, and an N r receiver, as also illustrated in Section IV-B. To capture explicitly the mutual coupling at BD-RIS, [18], [35], [103], [104] have made physics-consistent assumptions and derived the following three equivalent wireless channel models 4 ...
... However, as discussed above, it is difficult to achieve such a strong assumption in practice. That is, the off-diagonal entries of Z II are generally nonzero, and can be modeled as functions of inter-element spacing [18], [103]. Specifically, [103] has modeled each offdiagonal entry of Z II assuming isotropic radiators, that is ...
Written by its inventors, this first tutorial on Beyond-Diagonal Reconfigurable Intelligent Surfaces (BD-RISs) provides the readers with the basics and fundamental tools necessary to appreciate, understand, and contribute to this emerging and disruptive technology. Conventional (Diagonal) RISs (D-RISs) are characterized by a diagonal scattering matrix such that the wave manipulation flexibility of D-RIS is extremely limited. In contrast, BD-RIS refers to a novel and general framework for RIS where its scattering matrix is not limited to be diagonal (hence, the ``beyond-diagonal'' terminology) and consequently, all entries of can potentially help shaping waves for much higher manipulation flexibility. This physically means that BD-RIS can artificially engineer and reconfigure coupling across elements of the surface thanks to inter-element reconfigurable components which allow waves absorbed by one element to flow through other elements. Consequently, BD-RIS opens the door to more general and versatile intelligent surfaces that subsumes existing RIS architectures as special cases. In this tutorial, we share all the secret sauce to model, design, and optimize BD-RIS and make BD-RIS transformative in many different applications. Topics discussed include physics-consistent and multi-port network-aided modeling; transmitting, reflecting, hybrid, and multi-sector mode analysis; reciprocal and non-reciprocal architecture designs and optimal performance-complexity Pareto frontier of BD-RIS; signal processing, optimization, and channel estimation for BD-RIS; hardware impairments (discrete-value impedance and admittance, lossy interconnections and components, wideband effects, mutual coupling) of BD-RIS; benefits and applications of BD-RIS in communications, sensing, power transfer.
... These and other non-ideal effects are difficult to model, and can only be characterized using full-wave simulations or extensive experimental measurements. Furthermore, the reflection coefficients created by the varactor biasing may not be perfectly modeled, as varactor characteristics may vary due to environmental (thermal), fabrication, and electrical conditions [16], as well as mutual coupling between elements [17]. The metasurface response also varies according to the angle of arrival of the incoming signal [18]. ...
... We simulated two cases involving beam-and nullforming using the same SA algorithm as before, except that the power calculated in each direction by the MLP in the NN system is defined as in (17). The simulated system is allowed to sample the power in any given direction rather than being confined to a discrete grid. ...
... It is observed from the plots that the offline and adaptive data-based optimizations successfully create radiation patterns that satisfy the criteria defined by the objective functions, creating peaks and nulls at the desired directions. However, peaks are also created in unintended directions, especially in the broadside (0 • ) direction and at angles symmetric with the desired beams, which may lead to undesirable behavior in Algorithm 3 Adaptive Optimization and Lookup for each θ b in θ beam do 5: (17) of θ b in training dataset. 6: if P b > P max then 7: Define an empty objective function C based on the SLNR measure from (12), initially not taking into account any beam or null directions. ...
A promising type of Reconfigurable Intelligent Surface (RIS) employs tunable control of its varactors using biasing transmission lines below the RIS reflecting elements. Biasing standing waves (BSWs) are excited by a time-periodic signal and sampled at each RIS element to create a desired biasing voltage and control the reflection coefficients of the elements. A simple rectifier can be used to sample the voltages and capture the peaks of the BSWs over time. Like other types of RIS, attempting to model and accurately configure a wave-controlled RIS is extremely challenging due to factors such as device non-linearities, frequency dependence, element coupling, etc., and thus significant differences will arise between the actual and assumed performance. An alternative approach to solving this problem is data-driven: Using training data obtained by sampling the reflected radiation pattern of the RIS for a set of BSWs, a neural network (NN) is designed to create an input-output map between the BSW amplitudes and the resulting sampled radiation pattern. This is the approach discussed in this paper. In the proposed approach, the NN is optimized using a genetic algorithm (GA) to minimize the error between the predicted and measured radiation patterns. The BSW amplitudes are then designed via Simulated Annealing (SA) to optimize a signal-to-leakage-plus-noise ratio measure by iteratively forward-propagating the BSW amplitudes through the NN and using its output as feedback to determine convergence. The resulting optimal solutions are stored in a lookup table to be used both as settings to instantly configure the RIS and as a basis for determining more complex radiation patterns.
... To capture MC effects in RIS, microwave network theory is often applied. Current approaches to microwave network-based MC modeling in communications are typically classified into impedance matrix-based models [28] and scattering matrixbased models [23], [29], [30]. In [28], an EM-compliant, MC-aware communication model is introduced by leveraging mutual impedance analysis between RIS elements. ...
... Current approaches to microwave network-based MC modeling in communications are typically classified into impedance matrix-based models [28] and scattering matrixbased models [23], [29], [30]. In [28], an EM-compliant, MC-aware communication model is introduced by leveraging mutual impedance analysis between RIS elements. In contrast, [29] investigates, for the first time, a scattering matrix-based model using scattering parameter network analysis. ...
... 2 Although we approximate the RIS phase profile in (28) for the sake of algorithm development, we will employ the exact definition in the CRB calculation and generating data in simulations section to evaluate the performance of the proposed algorithms. whereγ n denotes the estimated value for γ n obtained by substituting b (0) n in (25). ...
Integrated sensing and communication (ISAC) is recognized as a promising approach to address the growing spectrum requirements for seamless sensing and communication. This paper investigates the deployment of reconfigurable intelligent surface (RIS) in ISAC systems under line-of-sight (LoS) obstructions, addressing the limited attention given to mutual coupling (MC) among RIS elements and its impact on localization performance. We tackle the joint estimation of the 3D location of a single-antenna user equipment (UE) and MC coefficients in challenging multipath and LoS-blocked environments. To enhance MC estimation, we extend our analysis to scenarios where signals from multiple UE locations are available, leveraging the stability of MC values over extended time intervals. Our methodology encompasses several key steps: first, we estimate the delay using the multiple signal classification (MUSIC) algorithm to mitigate multipath effects; second, we employ an efficient MC-unaware maximum likelihood (ML) approach for initial 2D angle-of-departure (2D-AOD) estimation; third, we propose a novel closed-form solution for the initial estimation of MC coefficients relying on a scattering matrix-based realistic MC modeling; and finally, we introduce a low-complexity alternating optimization algorithm for the joint refinement of the 2D-AODs and MC values. Simulation results demonstrate the effectiveness of the proposed method, outperforming classical MC-unaware ML techniques.
... Upon considering the unit cells' equivalent scattering model, such aspects can be adequately taken into consideration adopting multiport network models for the MTP. The initial multiport model for RIS-aided channels, which is non-linear with respect to the reflection coefficient, was introduced in [19], where the authors modeled the unit cells response of a metasurface by using thin wire dipoles, motivated by the discrete dipole approximation. A similar approach, based on the coupled dipoles formalism, is discussed in [20]. ...
... According to this model each scattering element includes a radiation element, an accessible port, and a frequency dependent static load. The whole analysis is carried out leveraging the Sparameter model discussed in [19]. Assuming, for simplicity, a SISO scenario, the system transfer function from the incident wave at the transmitter port to the outgoing wave at the receiver port is expressed as ...
... To obtain the pole at the desired frequency f n,p in (19) we impose the conditionL n,pCn,p = 1 2πf n,p , ...
Recent advancements in smart radio environment technologies aim to enhance wireless network performance through the use of low-cost electromagnetic (EM) devices. Among these, reconfigurable intelligent surfaces (RIS) have garnered attention for their ability to modify incident waves via programmable scattering elements. An RIS is a nearly passive device, in which the tradeoff between performance, power consumption, and optimization overhead depend on how often the RIS needs to be reconfigured. This paper focuses on the metaprism (MTP), a static frequency-selective metasurface which relaxes the reconfiguration requirements of RISs and allows for the creation of different beams at various frequencies. In particular, we address the design of an ideal MTP based on its frequency-dependent reflection coefficients, defining the general properties necessary to achieve the desired beam steering function in the angle-frequency domain. We also discuss the limitations of previous studies that employed oversimplified models, which may compromise performance. Key contributions include a detailed exploration of the equivalence of the MTP to an ideal S-parameter multiport model and an analysis of its implementation using Foster's circuits. Additionally, we introduce a realistic multiport network model that incorporates aspects overlooked by ideal scattering models, along with an ad hoc optimization strategy for this model. The performance of the proposed optimization approach and circuits implementation are validated through simulations using a commercial full-wave EM simulator, confirming the effectiveness of the proposed method.
... The general idea of MNT is that each network element, whether it is a transmitter, a receiver, or a scattering object, can be modeled as a multiport circuit whose ports are appropriately loaded. The first application of MNT to RISaided networks was reported in [6]. A recent tutorial on MNT applied to RIS-aided networks can be found in [7]. ...
... As mentioned, the first application of MNT to RIS-aided networks is reported in [6]. The proposed approach is based on impedance parameters. ...
... In [10], the MNT model is generalized for application to multipath channels, by representing general scattering objects as multiport networks. In [11], the authors extend the work in [6], by considering Chu's theory. The authors of [12], [13] and [14] propose the use of scattering parameters in lieu of the impedance parameters, and the structural scattering of RIS is discussed in the latter two papers. ...
Multiport network theory (MNT) is a powerful analytical tool for modeling and optimizing complex systems based on circuit models. We present an overview of current research on the application of MNT to the development of electromagnetically consistent models for programmable metasurfaces, with focus on reconfigurable intelligent surfaces for wireless communications.
... Modeling the RIS is under ongoing research and different models for RISs have already been proposed in the literature. In, e.g., [21], a RIS model has been introduced that is based on impedance matrices. Impedance-based descriptions have already been shown to provide a powerful description for conventional communication systems without the RIS (see [22]). ...
... Impedance-based descriptions have already been shown to provide a powerful description for conventional communication systems without the RIS (see [22]). The model in [21] allows to include the effect of mutual coupling as well as different RIS architectures. Furthermore, in [17], the RIS has been modeled based on scattering parameters which can also include the effects of mutual coupling (see [23]). ...
... The transmission is supported by a RIS, consisting of N reflecting elements. By using the impedance representation, the channel from the BS to the receiver reads as (see [21], [20]) ...
We propose decoupling networks for the reconfigurable intelligent surface (RIS) array as a solution to benefit from the mutual coupling between the reflecting elements. In particular, we show that when incorporating these networks, the system model reduces to the same structure as if no mutual coupling is present. Hence, all algorithms and theoretical discussions neglecting mutual coupling can be directly applied when mutual coupling is present by utilizing our proposed decoupling networks. For example, by including decoupling networks, the channel gain maximization in RIS-aided single-input single-output (SISO) systems does not require an iterative algorithm but is given in closed form as opposed to using no decoupling network. In addition, this closed-form solution allows to analytically analyze scenarios under mutual coupling resulting in novel connections to the conventional transmit array gain. In particular, we show that super-quadratic (up to quartic) channel gains w.r.t. the number of RIS elements are possible and, therefore, the system with mutual coupling performs significantly better than the conventional uncoupled system in which only squared gains are possible. We consider diagonal as well as beyond diagonal (BD)-RISs and give various analytical and numerical results, including the inevitable losses at the RIS array. In addition, simulation results validate the superior performance of decoupling networks w.r.t. the channel gain compared to other state-of-the-art methods.
... Accurate modeling of RIS-aided wireless channels is crucial for designing and optimizing RIS-aided systems, including a single or multiple RISs implemented through D-RIS or BD-RIS architectures. To rigorously model wireless channels in the presence of a single RIS, multiport network theory has been successfully utilized [23], [24], [16]. Specifically, previous works used multiport network theory to derive physics-compliant RIS-aided channel models accounting for the impedance mismatch and mutual coupling effects at the transmitter, receiver, and RIS. ...
... Specifically, previous works used multiport network theory to derive physics-compliant RIS-aided channel models accounting for the impedance mismatch and mutual coupling effects at the transmitter, receiver, and RIS. Different models have been proposed based on three equivalent formalisms, i.e., impedance (or Z) parameters [23], admittance (or Y ) parameters [24], and scattering (or S) parameters [16]. The relationship between impedance and scattering parameters has been more recently analyzed in [25], [26], [27], [28], and a universal framework has been derived in [29] highlighting the connection between impedance, admittance, and scattering parameters. ...
... Consider a MIMO communication system between an N Tantenna transmitter and an N R -antenna receiver aided by L RISs, each having N I elements, as represented in Fig. 1. Following previous literature [16], [23], [24], [25], [26], [27], [28], [29], we model the wireless channel as an N -port network, with N = N T + LN I + N R . ...
Reconfigurable intelligent surface (RIS) enables the control of wireless channels to improve coverage. To further extend coverage, multi-RIS aided systems have been explored, where multiple RISs steer the signal via a multi-hop path. However, deriving a physics-compliant channel model for multi-RIS aided systems is still an open problem. In this study, we fill this gap by modeling multi-RIS aided systems through multiport network theory, and deriving a channel model accounting for impedance mismatch, mutual coupling, and structural scattering. The derived physics-compliant model differs from the model widely used in literature, which omits the RIS structural scattering. To quantify this difference, we derive the channel gain scaling laws of the two models under line-of-sight (LoS) and multipath channels. Theoretical insights, validated by numerical results, show an important discrepancy between the physics-compliant and the widely used models, increasing with the number of RISs and multipath richness. In a multi-hop system aided by four 128-element RISs with multipath channels, optimizing the RISs using the widely used model and applying their solutions to the physics-compliant model achieves only 7% of the maximum channel gain. This highlights how severely mismatched channel models can be, calling for more accurate models in communication theory.
... When a RIS element is excited with a current, it generates an EM field that can induce currents in neighboring elements, thereby altering their excitation. These mutual coupling effects at the RIS complicate the expression of the RIS-aided channel [12], [13], [14]. For this reason, mutual coupling is commonly neglected in the literature on D-RIS and BD-RIS. ...
... MUTUAL COUPLING Consider a communication system between a single-antenna transmitter and a single-antenna receiver, aided by an N Ielement RIS. This system can be modeled by using the multiport network theory [3], [12], [14], and its wireless channel can be regarded as an N -port network, with N = 2 + N I , as represented in Fig. 1. ...
... To obtain a tractable expression of the channel h ∈ C relating the voltage v T (transmitted signal) and the voltage v R (received signal) through v R = hv T , we make the following two assumptions, commonly considered in related literature [3], [12], [14]. First, the transmission distances from the transmitter to RIS, from the RIS to receiver, and from the transmitter to receiver are assumed to be large enough such that we can neglect the effect of the feedback channels, i.e., we can consider z T I = 0, z IR = 0, and z T R = 0, which is also known as the unilateral approximation [31]. ...
Reconfigurable Intelligent Surface (RIS) is a breakthrough technology enabling the dynamic control of the propagation environment in wireless communications through programmable surfaces. To improve the flexibility of conventional diagonal RIS (D-RIS), beyond diagonal RIS (BD-RIS) has emerged as a family of more general RIS architectures. However, D-RIS and BD-RIS have been commonly explored neglecting mutual coupling effects, while the global optimization of RIS with mutual coupling, its performance limits, and scaling laws remain unexplored. This study addresses these gaps by deriving global optimal closed-form solutions for BD-RIS with mutual coupling to maximize the channel gain, specifically fully- and tree-connected RISs. Besides, we provide the expression of the maximum channel gain achievable in the presence of mutual coupling and its scaling law in closed form. By using the derived scaling laws, we analytically prove that mutual coupling increases the channel gain on average under Rayleigh fading channels. Our theoretical analysis, confirmed by numerical simulations, shows that both fully- and tree-connected RISs with mutual coupling achieve the same channel gain upper bound when optimized with the proposed global optimal solutions. Furthermore, we observe that a mutual coupling-unaware optimization of RIS can cause a channel gain degradation of up to 5 dB.
... Accurate modeling of wireless channels involving RIS is crucial for designing and optimizing RIS-aided systems. To rigorously model wireless channels in the presence of a single RIS, multiport network analysis has been successfully utilized [9], [10]. Specifically, previous works derived physicscompliant RIS-aided channel models by using impedance parameters [9] and scattering parameters [10]. ...
... To rigorously model wireless channels in the presence of a single RIS, multiport network analysis has been successfully utilized [9], [10]. Specifically, previous works derived physicscompliant RIS-aided channel models by using impedance parameters [9] and scattering parameters [10]. The relationship between impedance and scattering parameters has been more recently analyzed in [11], [12], [13], [14], and a model based on the admittance parameters has been derived in [14]. ...
... II. MULTIPORT NETWORK THEORY Consider a communication system between a single-antenna transmitter and a single-antenna receiver aided by L RISs, each having N I elements, as represented in Fig. 1. Following previous literature [9], [10], [11], [12], [13], [14], we model the wireless channel as an N -port network, with N = 2+LN I . ...
Reconfigurable intelligent surface (RIS) is a revolutionary technology enabling the control of wireless channels and improving coverage in wireless networks. To further extend coverage, multi-RIS aided systems have been explored, where multiple RISs steer the signal toward the receiver via a multi-hop path. However, deriving a physics-compliant channel model for multi-RIS aided systems is still an open problem. In this study, we fill this gap by modeling multi-RIS aided systems through multiport network theory, and deriving the scaling law of the physics-compliant channel gain. The derived physics-compliant channel model differs from the widely used model, where the structural scattering of the RISs is neglected. Theoretical insights, validated by numerical results, show a significant discrepancy between the physics-compliant and the widely used models. This discrepancy increases with the number of RISs and decreases with the number of RIS elements, reaching 200% in a system with eight RISs with 128 elements each.
... One of the most pronounced issues is the mutual coupling (MC) effect. Initial investigations indicate that densifying the RIS layout will significantly strengthen the mutual coupling among adjacent RIS unit cells [17], [18]. Furthermore, increasing the RIS amplification coefficients can also substantially exacerbate the impact of MC on channel estimation and localization [19]. ...
... Typically, three equivalent representations can be used to analyze microwave networks: impedance, admittance, and scattering parameters [24]. An impedance matrix (Z-parameters) model of MC was first adopted in [17]. Subsequently, equivalent models based on the scattering matrix (S-parameters) have been developed [25]. ...
... ,ω MI ] ∈ C MB×MI . By applying a vectorization operation to (17) and substituting (15), we obtain ...
This work studies the problems of channel estimation and beamforming for active reconfigurable intelligent surface~(RIS)-assisted multiple-input multiple-output (MIMO) communication, incorporating the mutual coupling~(MC) effect through an electromagnetically consistent model based on scattering parameters. We first demonstrate that MC can be incorporated into a compressed sensing~(CS) estimation formulation, albeit with an increase in the dimensionality of the sensing matrix. To overcome this increased complexity, we propose a two-stage strategy. Initially, a low-complexity MC-unaware CS estimation is performed to obtain a coarse channel estimate, which is then used to implement a dictionary reduction (DR), effectively reducing the dimensionality of the sensing matrices. This method achieves low complexity comparable to the conventional MC-unaware approach while providing estimation accuracy close to that of the high-complexity MC-aware CS method. Furthermore, we consider the joint optimization of RIS configuration, base station precoding, and user combining in an single-user MIMO system. We employ an alternating optimization strategy to optimize these three beamformers. The primary challenge lies in optimizing the RIS configuration, as the MC effect renders the problem non-convex and intractable. To address this, we propose a novel algorithm based on the successive convex approximation (SCA) and the Neumann series expansion. Within the SCA framework, we propose a surrogate function that rigorously satisfies both convexity and equal-gradient conditions to update the iteration direction. Numerical results validate our proposal, demonstrating that the proposed channel estimation and beamforming methods effectively manage the MC in RIS, achieving higher spectral efficiency compared to state-of-the-art approaches.
... Currently, some of the published research results dedicated to bridging the gap between abstract system-level models of RIS and EM and physical implementations [10]- [15]. The authors of [11] and [12] introduced EM consistency into the model of RIS by utilizing the multiport network theory, where the former relies on impedance matrices (Z-parameter) while the latter is based on scattering matrices (S-parameter). The authors of [13] further investigated MIMO systems described by RIS model based on impedance matrices and designed an optimization algorithm aimed at maximizing the sum rate of the system. ...
... In particular, its S-parameter matrix containing MC and mismatch effects, ie., S AA , is applied to the optimization problem. With the analytical models presented in [11] and [35] as well as the full-wave simulator, the S-parameter matrix can be simulated and computed as shown in Table I. Specifically, S(1, 1) and S(2, 1) in the table can characterize the matching and MC terms , i.e., diagonal and non-diagonal elements, of S AA , respectively. ...
Reconfigurable Intelligent Surfaces (RIS) represent a transformative technology for sixth-generation (6G) wireless communications, but it suffers from a significant limitation, namely the double-fading attenuation. Active RIS has emerged as a promising solution, effectively mitigating the attenuation issues associated with conventional RIS-assisted systems. However, the current academic work on active RIS focuses on the system-level optimization of active RIS, often overlooking the development of models that are compatible with its electromagnetic (EM) and physical properties. The challenge of constructing realistic, EM-compliant models for active RIS-assisted communication, as well as understanding their implications on system-level optimization, remains an open research area. To tackle these problems, in this paper we develop a novel EM-compliant model with mutual coupling (MC) for active RIS-assisted wireless systems by integrating the developed scattering-parameter (S-parameter) based active RIS framework with multiport network theory, which facilitates system-level analysis and optimization. To evaluate the performance of the EM-compliant active RIS model, we design the joint optimization scheme based on the transmit beamforming at the transmitter and the reflection coefficient at the active RIS to maximize the achievable rate of EM-compliant active RIS-assisted MIMO system. To tackle the inherent non-convexity of this problem, we employ the Sherman-Morrison inversion and Neumann series (SMaN)-based alternating optimization (AO) algorithm. Simulation results verified that EM property (i.e., MC effect) is an indispensable factor in the optimization process of MIMO systems. Neglecting this effect introduces a substantial performance gap, highlighting its significance in the more pronounced the MC effect is, the greater the gap in achievable rates.
... In this paper, we propose EL model mismatch analysis using the analytical EM model [26]- [28] as the TM for direct and reconfigurable intelligent surface (RIS) [29] assisted localization. We analyze the EM propagation model features important for localization, select non-uniform array and RIS configurations and develop RIS profile optimization suitable for EM based localization. ...
... where T is the number of snapshots, G is the M ×M diagonal matrix of signal power, S is the M ×T matrix of the unit power transmitted signals, P = [p 1 , ..., p M ] is the 3 × M matrix of source locations, and U is the N ×T matrix of additive thermal noise, where u t ∼ CN {0, σ 2 I N }, σ 2 is the noise power, and I N is the N × N unit matrix. As usually, for the EL and stochastic ML formulation, we assume s t ∼ CN {0, I M }. 2 Assuming that the array, RIS, and sources elements are vertical dipoles of l length and a radius, the true MIMO EM based model for the propagation channel H EM (P) is the N × M matrix defined according to the analytical EM model [26], [27]: ...
Accurate signal localization is critical for Internet of Things applications, but precise propagation models are often unavailable due to uncontrollable factors. Simplified models such as planar and spherical wavefront approximations are widely used but can cause model mismatches that reduce accuracy. To address this, we propose an expected likelihood ratio framework for model mismatch analysis and online model selection without requiring knowledge of the true propagation model. The framework leverages the scenario independent distribution of the likelihood ratio of the actual covariance matrix, enabling the detection of mismatches and outliers by comparing given models to a predefined distribution. When an accurate electromagnetic model is unavailable, the robustness of the framework is analyzed using data generated from a precise electromagnetic model and simplified models within positioning algorithms. Validation in direct localization and reconfigurable intelligent surface assisted scenarios demonstrates the ability to improve localization accuracy and reliably detect model mismatches in diverse Internet of Things environments.
... In the literature, a single-input single-output (SISO) RIS-assisted system was optimized [29]. A mutual impedance-based communication model considering mutual coupling was presented [30]. A mutual coupling aware characterization and performance analysis of the RIS was introduced [31]. ...
... In particular, if the RIS does not have mutual coupling, we have S II = 0 and (16) is reduced to (1). In this work, we apply the model from [30] to obtain the S II matrix. Remark 1. ...
Space-division multiple access (SDMA) plays an important role in modern wireless communications. Its performance depends on the channel properties, which can be improved by reconfigurable intelligent surfaces (RISs). In this work, we jointly optimize SDMA precoding at the base station (BS) and RIS configuration. We tackle difficulties of mutual coupling between RIS elements, scalability to more than 1000 RIS elements, and high requirement for channel estimation. We first derive an RIS-assisted channel model considering mutual coupling, then propose an unsupervised machine learning (ML) approach to optimize the RIS with a dedicated neural network (NN) architecture RISnet, which has good scalability, desired permutation-invariance, and a low requirement for channel estimation. Moreover, we leverage existing high-performance analytical precoding scheme to propose a hybrid solution of ML-enabled RIS configuration and analytical precoding at BS. More generally, this work is an early contribution to combine ML technique and domain knowledge in communication for NN architecture design. Compared to generic ML, the problem-specific ML can achieve higher performance, lower complexity and permutation-invariance.
... The result from Eq. (13) is widely used in the literature [34], [39], [40], [70]- [73]) and known as the "Redheffer star product" [74], which provides a compact notation to summarize Eqs. (13,14). Explicitly addressing the connection between ports C U and C V , we writẽ ...
... (7)] is smaller than the one of the Redheffer star product [Eq. (13)]. ...
The design of large complex wave systems (filters, networks, vacuum-electronic devices, metamaterials, smart radio environments, etc.) requires repeated evaluations of the scattering parameters resulting from complex connections between constituent subsystems. Instead of starting each new evaluation from scratch, we propose a computationally efficient method that updates the outcomes of previous evaluations using the Woodbury matrix identity. To enable this method, we begin by identifying a closed-form approach capable of evaluating arbitrarily complex connection schemes of multi-port networks. We pedagogically present unified equivalence principles for interpretations of system connections, as well as techniques to reduce the computational burden of the closed-form approach using these equivalence principles. Along the way, we also achieve the closed-form retrieval of the power waves traveling through connected ports. We illustrate our techniques considering a complex meta-network involving serial, parallel and cyclic connections between multi-port subsystems. We further validate all results with physics-compliant calculations considering graph-based subsystems, and we conduct exhaustive statistical analyses of computational benefits originating from the reducibility and updatability enabled by our approach. Finally, we find that working with scattering parameters (as opposed to impedance or admittance parameters) presents a fundamental advantage regarding an important class of connection schemes whose closed-form analysis requires the treatment of some connections as delayless, lossless, reflectionless and reciprocal two-port scattering systems. We expect our results to benefit the design (and characterization) of large composite (reconfigurable) wave systems.
... Note that (27) has dimensions of Ω −2 , consistent with the Z-parameter representation of the MP model, where S and t i in (2) denote impedance matrices with dimensions of Ω. The values of Z SS , Z RR , and Z T T can be analytically computed as demonstrated in [17], or determined using full-wave simulators as shown in [16]; nevertheless, they can be assumed to be known since they rely on the structural characteristics of the RIS, such as the length and spacing between dipoles (in the case of RIS composed of dipoles). ...
... The arrangement and type of antennas at Alice, Bob, and Willie are the same as those of the RIS described above. The parameters reported in the RIS model of (27) are set according to the analytical approach presented in [17]. ...
A novel framework for covert communications aided by Reconfigurable Intelligent Surfaces (RIS) is proposed. In this general framework, the use of multiport network theory for modelling the RIS consider various aspects that traditional RIS models in communication theory often overlook, including mutual coupling between elements and the impact of structural scattering. Moreover, the transmitter has only limited knowledge about the channels of the warden and the intended receiver. The proposed approach is validated through numerical results, demonstrating that communication with the legitimate user is successfully achieved while satisfying the covertness constraint.
... Physically, this implies that the IRS reflecting elements are independent of each other, i.e., no coupling exists between elements. However, as the investigation of hardware aspects of IRS has progressed, some authors proposed a nondiagonal structure for the phase shift matrix [84,85,86,87]. This is evident in two cases. ...
... This is evident in two cases. Firstly, non-diagonality occurs naturally due to electromagnetic effects that cause coupling between the elements [84]. Secondly, some researchers intentionally propose connecting some IRS elements, resulting in a non-diagonal phase shift matrix [86]. ...
The fifth-generation (5G) is in its business version, and researchers have started to look at the potential technologies to be employed in the next generation. In this context, intelligent reflecting surface (IRS) is a promising technology for the sixth-generation (6G) of wireless systems by introducing the smart radio environment concept. The promised gains of IRS-assisted communications depend on the accuracy of the channel state information. Using a tensor framework, particularly tensor decomposition, we propose different solutions to solve the channel estimation problem for different scenarios. We firstly address the receiver design for an IRS-assisted multiple-input multiple-output (MIMO) communication system via a tensor modeling approach to solve the channel estimation problem using supervised (pilot-assisted) methods. Considering a structured time-domain pattern of pilots and IRS phase shifts, we present two channel estimation methods that rely on a
parallel factors (PARAFAC) tensor modeling of the received signals. The first method has a closed-form solution based on a Khatri-Rao factorization of the cascaded MIMO channel by solving rank-1 matrix approximation problems, while the second is an iterative alternating estimation scheme. The common feature of both methods is the decoupling of the estimates of the involved MIMO channel matrices (base station (BS)-IRS and IRS-user terminal (UT)), which provides performance enhancements in comparison to competing methods that are based on unstructured least squares (LS) estimates of the cascaded channel. In this scenario, the numerical results show the effectiveness of the proposed receivers, highlight the involved trade-offs, and corroborate their superior performance compared to competing LS-based solutions. Second, we develop algorithms to jointly estimate the involved channel matrices and the transmitted symbols in a semi-blind fashion. This is achieved by introducing a simple space-time coding scheme at the transmitter, such that the received signal model can be advantageously built using the PARATUCK tensor model. As a result, a semi-blind receiver is derived by exploiting the algebraic structure of the PARATUCK tensor model. In this context, we first formulate a semi-blind receiver based on a trilinear alternating least squares method that iteratively estimates the two involved communication channels – IRS-BS and UT-IRS – and the transmitted symbol matrix. Second, we formulate an enhanced two-stage semi-blind receiver that efficiently exploits the direct link to refine the channel and symbol estimates iteratively. In addition, we discuss the impact of an imperfect IRS absorption (residual reflection) on the performance
of the proposed receiver. Finally, we formulate a tensor-based semi-blind receiver for an IRS-assisted uplink multi-user MIMO system where the proposed approach relies on a generalized PARATUCK tensor model of the signals reflected by the IRS, based on a two-stage closed-form semi-blind receiver using Khatri-Rao and Kronecker factorizations.
... The summary of each model is presented in Table 3 [45][46][47][48][49]. In the analysis of channel models utilizing Z, Y, and S parameters, several simplifications are applied under the assumptions of perfect matching and the absence of mutual coupling. ...
... Several other researchers have investigated mutual coupling-aware RIS-aided communications [48,73]. ...
The rapid development of reconfigurable intelligent surfaces (RISs) has sparked transformative advancements in wireless communication systems. These intelligent metasurfaces, adept at dynamically manipulating electromagnetic (EM) waves, hold vast potential for enhancing network capacity, coverage, and efficiency. However, effective optimization is crucial to fully unleashing RIS-aided communication systems' capabilities. This article provides a recent development of RIS-assisted communication from the viewpoint of physically consistent EM models. We delve into the realm of physically-consistent EM models, highlighting their pivotal role in achieving robust and efficient RIS designs.
Furthermore, this paper offers a survey of the optimization models utilized for RIS-assisted wireless communication systems, considering various physical aspects of RIS. We explore solution approaches to optimise different objectives, sum-rate/spectral efficiency, and energy efficiency, spanning traditional optimization models to machine learning-based methods. Additionally, we discuss some open research issues in this field.
... 图 2 (a)信息超表面单元的等效传输线模型 [43] ；(b)信息超表面单元的角度依赖相移器模型 [44] Fig.2 (a) Equivalent transmission line model for the unit cell of the RIS [43] ; (b) Angle-dependent phase shifter model for the unit cell of the RIS [44] 如图2(a)所示，第n个信息超表面单元对应的并 Fig.3 End-to-end mutual-coupling-aware communication model [45] 基于参考文献 [ ...
... 图 2 (a)信息超表面单元的等效传输线模型 [43] ；(b)信息超表面单元的角度依赖相移器模型 [44] Fig.2 (a) Equivalent transmission line model for the unit cell of the RIS [43] ; (b) Angle-dependent phase shifter model for the unit cell of the RIS [44] 如图2(a)所示，第n个信息超表面单元对应的并 Fig.3 End-to-end mutual-coupling-aware communication model [45] 基于参考文献 [ ...
... Notably, existing microwave network-based communication modeling can be categorized into two types: impedance matrix-based models and scattering matrix-based models. In the impedance matrix-based approach, the first effort can be found in [25], where an EMcompliant and mutual coupling-aware communication model is proposed by adopting the mutual impedance analysis among RIS unit cells. This model has proven effective in guiding RIS configuration, facilitating applications such as end-toend received power maximization in single-input-single-output (SISO) systems [26] and sum-rate optimization in multi-user interference multiple-input multiple-output (MIMO) channels [27]. ...
... To account for the mutual coupling effect in RIS-aided communication, several novel communication models have been recently proposed. These models can be categorized into two types: the impedance matrix (Z-parameters)-based model [25] and the scattering matrix (S-parameters)-based model [28]. It should be noted that based on microwave network theory, these two types of models are essentially equivalent and can be seamlessly converted to each other. ...
Mutual coupling is increasingly important in reconfigurable intelligent surface (RIS)-aided communications, particularly when RIS elements are densely integrated in applications such as holographic communications. This paper experimentally investigates the mutual coupling effect among RIS elements using a mutual coupling-aware communication model based on scattering matrices. Utilizing a fabricated 1-bit quasi-passive RIS prototype operating in the mmWave band, we propose a practical model training approach based on a single 3D full-wave simulation of the RIS radiation pattern, which enables the estimation of the scattering matrix among RIS unit cells. The formulated estimation problem is rigorously convex with a limited number of unknowns un-scaling with RIS size. The trained model is validated through both full-wave simulations and experimental measurements on the fabricated RIS prototype. Compared to the conventional communication model that does not account for mutual coupling in RIS, the mutual coupling-aware model incorporating trained scattering parameters demonstrates improved prediction accuracy. Benchmarked against the full-wave simulated RIS radiation pattern, the trained model can reduce prediction error by up to approximately 10.7%. Meanwhile, the S-parameter between the Tx and Rx antennas is measured, validating that the trained model exhibits closer alignment with the experimental measurements. These results affirm the accuracy of the adopted model and the effectiveness of the proposed model training method.
... RIS typically works as a passive array, which can reflect or redirect wireless signals that impinge on its surface, whereas antenna arrays can transmit signals directly. The practical RIS or array beam pattern is affected by several key factors [6], [7], including mutual coupling (MC) among elements, non-ideal radio frequency (RF) chains (e.g., the phase shift module connected to each element) and non-isotropic element patterns, where the reflection coefficients vary with the angle of departure. Moreover, fabrication errors further contribute to deviations from the idealized model. ...
High-accuracy localization is a key enabler for integrated sensing and communication (ISAC), playing an essential role in various applications such as autonomous driving. Antenna arrays and reconfigurable intelligent surface (RIS) are incorporated into these systems to achieve high angular resolution, assisting in the localization process. However, array and RIS beam patterns in practice often deviate from the idealized models used for algorithm design, leading to significant degradation in positioning accuracy. This mismatch highlights the need for beam calibration to bridge the gap between theoretical models and real-world hardware behavior. In this paper, we present and analyze three beam models considering several key non-idealities such as mutual coupling, non-ideal codebook, and measurement uncertainties. Based on the models, we then develop calibration algorithms to estimate the model parameters that can be used for future localization tasks. This work evaluates the effectiveness of the beam models and the calibration algorithms using both theoretical bounds and real-world beam pattern data from an RIS prototype. The simulation results show that the model incorporating combined impacts can accurately reconstruct measured beam patterns. This highlights the necessity of realistic beam modeling and calibration to achieve high-accuracy localization.
... • Investigation of RIS-Aided NF Localization with MC Effects: We address the challenge of NF RIS-assisted localization in the presence of MC by adopting a practical end-to-end EM communication model [15], [16]. The MC effects alter the RIS phase profiles, complicating the problem of joint localization and MC parameter estimation (JLMC). ...
Reconfigurable intelligent surfaces (RISs) have the potential to significantly enhance the performance of integrated sensing and communication (ISAC) systems, particularly in line-of-sight (LoS) blockage scenarios. However, as larger RISs are integrated into ISAC systems, mutual coupling (MC) effects between RIS elements become more pronounced, leading to a substantial degradation in performance, especially for localization applications. In this paper, we first conduct a misspecified and standard Cram\'er-Rao bound analysis to quantify the impact of MC on localization performance, demonstrating severe degradations in accuracy, especially when MC is ignored. Building on this, we propose a novel joint user equipment localization and RIS MC parameter estimation (JLMC) method in near-field wireless systems. Our two-stage MC-aware approach outperforms classical methods that neglect MC, significantly improving localization accuracy and overall system performance. Simulation results validate the effectiveness and advantages of the proposed method in realistic scenarios.
... Moreover, since the RIS unit cells are densely integrated on the finite-sized surface, the interactions between neighboring array elements may become non-negligible [54]. The practical manifestation of mutual interference depends on the material, deployment and manufacturing, and, thus, a simplified model- ing is adopted here merely for performance evaluation. ...
In this paper, we investigate the channel estimation and user localization problems for multi-user integrated sensing and communication (ISAC) systems empowered by the reconfigurable intelligent surface (RIS) technology. In order to perceive environmental information more deeply, we propose a spherical RIS architecture with spherically arranged unit cells. Based on the principle of phase mode excitation, we customize the design of RIS profiles and recover the equivalent channel parameters
via subspace estimation tools. By exploring the characteristics of RIS array manifold and free-space propagation, we develop a decoupling framework of three-dimensional channel parameters, which is not supported by conventional planar RIS topologies. Each user can achieve a self-localization by analyzing the signals
transmitted from other active users. Simulation results indicate that the spherical RIS can enable joint channel estimation, user localization and data transmission with remarkable performance that approaches the theoretical Cramer-Rao bounds.
... II-B. Unless otherwise stated, Z l is computed based on [12,Eq. (6)]. ...
This work develops a physically consistent model for stacked intelligent metasurfaces (SIM) using multiport network theory and transfer scattering parameters (T-parameters). Unlike the scattering parameters (S-parameters) model, which is highly complex and non-tractable due to its nested nature and excessive number of matrix inversions, the developed T-parameters model is less complex and more tractable due to its explicit and compact nature. This work further derives the constraints of T-parameters for a lossless reciprocal reconfigurable intelligent surfaces (RISs). A gradient descent algorithm (GDA) is proposed to maximize the sum rate in SIM-aided multiuser scenarios, and the results show that accounting for mutual coupling and feedback between consecutive layers can improve the sum rate. In addition, increasing the number of SIM layers with a fixed total number of elements degrades the sum rate when our exact and simplified channel models are used, unlike the simplified channel model with the Rayleigh-Sommerfeld diffraction coefficients which improves the sum rate.
... In [18], Babakhani et al. proposed a circuit-theorybased model for wireless communication systems with reconfigurable transceivers. In [39], Gradoni and Di Renzo proposed a general circuit-theory-based model for wireless communication systems with a reconfigurable channel. Further circuit-theory-based models for wireless systems with REMSs can be found in [40]- [47]. ...
Reconfigurable electromagnetic structures (REMSs), such as reconfigurable reflectarrays (RRAs) or reconfigurable intelligent surfaces (RISs), hold significant potential to improve the spectral efficiency of wireless communication systems and the accuracy of wireless sensing systems. Even though several REMS modeling approaches have been proposed in recent years, the literature lacks models that are both computationally efficient and physically consistent. As a result, algorithms that control the reconfigurable elements of REMSs (e.g., the phase shifts of a RIS) are often built on simplistic and thus inaccurate models. To enable physically accurate REMS-parameter tuning, we present a new framework for efficient and physically consistent modeling of general REMSs. Our modeling method combines a circuit-theoretic approach with a new formalism that describes a REMS’s interaction with the electromagnetic (EM) waves in its far-field region. Our modeling method enables efficient computation of the entire far-field radiation pattern for arbitrary configurations of the REMS reconfigurable elements once a single full-wave EM simulation of the non-reconfigurable parts of the REMS has been performed. The predictions made by our framework align with the physical laws of classical electrodynamics and model effects caused by inter-antenna coupling, non-reciprocal materials, polarization, ohmic losses, matching losses, influence of metallic housings, noise from low-noise amplifiers, and noise arising in or received by antennas. In order to validate the efficiency and accuracy of our modeling approach, we (i) compare our modeling method to EM simulations and (ii) conduct a case study involving an RRA that enables simultaneous multiuser beam-and null-forming using a new, computationally efficient, and physically accurate parameter tuning algorithm.
... Such a multi-port network model based on circuit theory can facilitate in-depth analysis of impedance matching, antenna mutual coupling, structural losses, and both intrinsic and extrinsic sources of noise [386]. For example, [387] proposed a circuit-based EM-compliant communication model for RIS assisted wireless communication systems, which characterizes the end-to-end mutual coupling in RIS elements based on mutual impedance. In [388], a universally EM-compliant framework was proposed for RIS-assisted wireless systems based on impedance, admittance, and scattering parameter analysis, revealing the effects of impedance mismatches and mutual coupling on RIS communication performance. ...
To accommodate new applications such as extended reality, fully autonomous vehicular networks and the metaverse, next generation wireless networks are going to be subject to much more stringent performance requirements than the fifth-generation (5G) in terms of data rates, reliability, latency, and connectivity. It is thus necessary to develop next generation advanced transceiver (NGAT) technologies for efficient signal transmission and reception. In this tutorial, we explore the evolution of NGAT from three different perspectives. Specifically, we first provide an overview of new-field NGAT technology, which shifts from conventional far-field channel models to new near-field channel models. Then, three new-form NGAT technologies and their design challenges are presented, including reconfigurable intelligent surfaces, flexible antennas, and holographic multi-input multi-output (MIMO) systems. Subsequently, we discuss recent advances in semantic-aware NGAT technologies, which can utilize new metrics for advanced transceiver designs. Finally, we point out other promising transceiver technologies for future research.
... The novel work by [162], [163] considers the mutual coupling gain that can be realized with ultra-small RIS unit cell sizes of λ/8 or even λ/16. Consequently, this forces a very tight spacing between unit cells, less than λ/2, and in this case, the effects of evanescent fields and mutual coupling between cells cannot be ignored. ...
Reconfigurable intelligent surfaces (RIS) are positioned as one of the key enabling technologies for 6G networks as they can provide ubiquitous coverage for areas with blocked line-of-sight (LOS) links. However, to be successfully integrated into functional networks such structures will require the addition of sensors and other radio network elements, thereby resulting in a multi-functional RIS (MF-RIS). These structures are expected to be deployed for integrated sensing and communications (ISAC) and radar and communication coexistence (RCC) in 6G, which will enhance the performance of radio communication and enable a smart wireless environment (SWE) that is programmable and self-reconfigurable. This survey provides an up-to-date summary of the state of the art. It considers applications for MF-RISs and the challenges associated with their deployment.
... Approaches based on impedance models are presented in [12,13], where the response of the RIS is no longer a linear term as in (1). They show, though, that this modified cascaded channel is valid if power conservation is ensured, although at the price of a significant reduction in the reflection phasecoverage. ...
Reconfigurable intelligent surfaces (RISs) are potential enablers of future wireless communications and sensing applications and use-cases. The RIS is envisioned as a dynamically controllable surface that is capable of transforming impinging electromagnetic waves in terms of angles and polarization. Many models has been proposed to predict the wave-transformation capabilities of potential RISs, where power conservation is ensured by enforcing that the scattered power equals the power impinging upon the aperture of the RIS, without considering whether the scattered field adds coherently of destructively with the source field. In effect, this means that power is not conserved, as elaborated in this paper. With the goal of investigating the implications of global and local power conservation in RISs, work considers a single-layer metasurface based RIS. A complete end-to-end communications channel is given through polarizability modeling and conditions for power conservation and channel reciprocity are derived. The implications of the power conservation conditions upon the end-to-end communications channel is analyzed.
... In [18], Babakhani et al. proposed a circuit-theory-based model for wireless communication systems containing reconfigurable transceivers. In [39], Gradoni and Di Renzo proposed a general circuit-theory-based model for wireless communication systems containing a reconfigurable channel. Further circuit-theorybased models for wireless systems containing REMS can also be found in [40]- [47]. ...
Reconfigurable electromagnetic structures (REMSs), such as reconfigurable reflectarrays (RRAs) or reconfigurable intelligent surfaces (RISs), hold significant potential to improve wireless communication and sensing systems. Even though several REMS modeling approaches have been proposed in recent years, the literature lacks models that are both computationally efficient and physically consistent. As a result, algorithms that control the reconfigurable elements of REMSs (e.g., the phase shifts of an RIS) are often built on simplistic models that are inaccurate. To enable physically accurate REMS-parameter tuning, we present a new framework for efficient and physically consistent modeling of general REMSs. Our modeling method combines a circuit-theoretic approach with a new formalism that describes a REMS's interaction with the electromagnetic (EM) waves in its far-field region. Our modeling method enables efficient computation of the entire far-field radiation pattern for arbitrary configurations of the REMS reconfigurable elements once a single full-wave EM simulation of the non-reconfigurable parts of the REMS has been performed. The predictions made by the proposed framework align with the physical laws of classical electrodynamics and model effects caused by inter-antenna coupling, non-reciprocal materials, polarization, ohmic losses, matching losses, influence of metallic housings, noise from low-noise amplifiers, and noise arising in or received by antennas. In order to validate the efficiency and accuracy of our modeling approach, we (i) compare our modeling method to EM simulations and (ii) conduct a case study involving a planar RRA that enables simultaneous multiuser beam- and null-forming using a new, computationally efficient, and physically accurate parameter tuning algorithm.
... Specifically, the fullduplex base station has N T B transmitting antennas and N R B receiving antennas; the RIS has N I elements; the uplink user has N T U transmitting antennas; and the downlink user has N R D receiving antennas. The whole system is regarded as an N = N T B + N T U + N I + N R B + N R D port network characterized by its scattering matrix S ∈ C N ×N [5], or, equivalently, its impedance matrix Z ∈ C N ×N [18], so that ...
Beyond diagonal reconfigurable intelligent surfaces (BD-RIS) is a new advance in RIS techniques that introduces reconfigurable inter-element connections to generate scattering matrices not limited to being diagonal. BD-RIS has been recently proposed and proven to have benefits in enhancing channel gain and enlarging coverage in wireless communications. Uniquely, BD-RIS enables reciprocal and non-reciprocal architectures characterized by symmetric and non-symmetric scattering matrices. However, the performance benefits and new use cases enabled by non-reciprocal BD-RIS for wireless systems remain unexplored. This work takes a first step toward closing this knowledge gap and studies the non-reciprocal BD-RIS in full-duplex systems and its performance benefits over reciprocal counterparts. We start by deriving a general RIS aided full-duplex system model using a multiport circuit theory, followed by a simplified channel model based on physically consistent assumptions. With the considered channel model, we investigate the effect of BD-RIS non-reciprocity and identify the theoretical conditions for reciprocal and non-reciprocal BD-RISs to simultaneously achieve the maximum received power of the signal of interest in the uplink and the downlink. Simulation results validate the theories and highlight the significant benefits offered by non-reciprocal BD-RIS in full-duplex systems. The significant gains are achieved because of the non-reciprocity principle which implies that if a wave hits the non-reciprocal BD-RIS from one direction, the surface behaves differently than if it hits from the opposite direction. This enables an uplink user and a downlink user at different locations to optimally communicate with the same full-duplex base station via a non-reciprocal BD-RIS, which would not be possible with reciprocal surfaces.
... The study of the mutual coupling in RIS-assisted communications has been deepened by some research groups by exploting circuit-based communication models. In [31] and [32] the authors exploit an end-to-end model for RIS-assisted wireless systems based on the mutual impedances between all the existing radiating elements. This model accounts for the mutual coupling among closely spaced scattering elements of the RIS, as well as the circuits of the electronic components that are used to make the RIS reconfigurable. ...
In the quest for sixth-generation wireless communication technology (6G), Terahertz waves represent a key technology due to their distinct advantages over microwaves and infrared radiation. Reconfigurable intelligent surfaces (RIS) emerge as a critical technology within this context. This paper presents a numerical investigation and the optimized design of a transparent graphene-based RIS operating in the THz spectrum. The aim of the paper is twofold: the former is to demonstrate the reconfigurability of the proposed RIS by exploiting two methods, referred to as “digital” and “analogical”. The latter is to demonstrate the effects of the losses and of the mutual coupling among unit cells on the power flow pattern. This aspect is crucial in the design of the RIS and cannot be overlooked, differently from other papers reported in the literature which analyze the RIS as an "ideal" structure evaluating only an analytical estimation of the array factor and neglecting the interaction among the unit cells. Our results hold significant promise for improving the development of a new class of smart devices crucial for 6G wireless communication systems.
... Building on a decade-old circuit theory of communication [22], [23], the literature contains by now many proposed formulations for physics-inspired models of D-RIS-parametrized channels based on multi-port network theory [7], [24]- [36], as well as three formulations for BD-RIS-parametrized channels [1], [16], [37]. These numerous formulations differ regarding the approximations and assumptions that they make, especially regarding the nature of the radio environment. ...
The parametrization of wireless channels by so-called "beyond-diagonal reconfigurable intelligent surfaces" (BD-RIS) is mathematically characterized by a matrix whose off-diagonal entries are partially or fully populated. Physically, this corresponds to tunable coupling mechanisms between the RIS elements that originate from the RIS control circuit. Here, we derive a physics-compliant diagonal representation for BD-RIS-parametrized channels. Recognizing that the RIS control circuit, irrespective of its detailed architecture, can always be represented as a multi-port network with auxiliary ports terminated by tunable individual loads, we physics-compliantly express the BD-RIS-parametrized channel as a multi-port chain cascade of i) radio environment, ii) static parts of the control circuit, and iii) individually tunable loads. Thus, the cascade of the former two systems is terminated by a system that is mathematically always characterized by a diagonal matrix. This physics-compliant diagonal representation implies that existing algorithms for channel estimation and optimization for conventional ("diagonal") RIS can be readily applied to BD-RIS scenarios. We demonstrate this in an experimentally grounded case study. Importantly, we highlight that, operationally, an ambiguous characterization of the cascade of radio environment and the static parts of the control circuit is required, but not the breakdown into the characteristics of its two constituent systems nor the lifting of the ambiguities. Nonetheless, we demonstrate how to derive or estimate the characteristics of the static parts of the control circuit for pedagogical purposes. The diagonal representation of BD-RIS-parametrized channels also enables their treatment with coupled-dipole-based models. We furthermore derive the assumptions under which the physics-compliant BD-RIS model simplifies to the widespread linear cascaded model.
The vision for 6th-generation (6G) wireless communication systems emphasizes the need for robust and reliable communication in extremely high-mobility scenarios, while also addressing critical demands for energy and spectral efficiency. Under such scenarios, doubly time-frequency selective fading channels often significantly degrade the performance of orthogonal frequency-division multiplexing (OFDM) based systems due to the impact of large delay and Doppler shifts. Recently, orthogonal time frequency space (OTFS) modulation has emerged as a promising alternative. By processing signals in the delay-Doppler (DD) domain, OTFS offers several advantages, including quasi-static channel characteristics, full-time-frequency diversity, and low peak-to-average power ratio (PAPR), making it a promising candidate for high-mobility communications. Reconfigurable intelligent surfaces (RIS) are being further integrated to enhance the performance of OTFS systems cost-effectively. With their ability to dynamically reconfigure the wireless environment, the integration of RIS can offer significant performance improvements for OTFS systems. This survey offers a comprehensive review of RIS-assisted OTFS systems, including the fundamental principles, recent advances, and future research directions. Specifically, we first introduce the background of RIS-assisted OTFS systems, outlining the opportunities and challenges of their integration. To ensure the survey is self-contained, we provide a brief overview of the fundamental principles of OTFS and RIS technologies. Building on these foundations, we present a general input-output relationship and capacity characterization for RIS-assited MIMO-OTFS systems. Then, this survey further explores cutting-edge research in areas such as input-output analysis, RIS phase shift design, channel estimation, detection techniques, RIS-assisted integrated sensing and communication (ISAC), and other novel technologies. Finally, we outline some future research directions.
This paper investigates the fundamental problem of cascaded channel estimation in reconfigurable intelligent surface (RIS) aided multi-user (MU) multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. To address the high pilot overhead required by existing methods, we introduce appropriate auxiliary variables to decompose the received signal model into a subcarrier-wise bilinear sub-model and two linear sub-models with respect to the MU-to-RIS and RIS-to-base-station (BS) cascaded channels. The proposed model decomposition maintains the matrix factorization structure of the two cascaded channels and avoids the problem of parameter expansion in exiting methods. In the two linear sub-models, in addition, the cascaded channels are transformed into the delay-angle domain to leverage the joint sparsity. Based on the established models, we consider the problem of simultaneously estimating the MU-to-RIS and RIS-to-BS channel matrices as a bilinear estimation problem. To tackle this problem, we formulate a Bayesian inference framework and develop a hybrid message-passing (HVMP) algorithm to achieve approximate Bayesian inference by leveraging the Bethe method. Notably, the HVMP algorithm infers the two cascaded channels iteratively, where the covariance of each cascaded channel matrix is estimated to characterize the correlation of the matrix elements. Simulation results show that the proposed algorithm achieves accurate channel estimation with low pilot overhead while state-of-the-art baseline schemes exhibit poor performance. Furthermore, the proposed algorithm can approach the estimation oracle bound of the MU-to-RIS (or RIS-to-BS) channel which assumes perfect knowledge of the RIS-to-BS (or MU-to-RIS) channel.
The cell-to-cell coupling in a reconfigurable intelligent surface (RIS) is very different from a periodic structure, where coupling effects can be precisely evaluated via full-wave analysis with periodic boundary conditions. We propose a novel method based on convolutional neural networks (CNNs), to predict the contribution of mutual coupling on the near-zone tangential electric field of every RIS unit cell that characterizes its scattering. Our CNN model incorporates an attention mechanism based on the squeeze-and-excitation block module, enhancing its capability to discern and quantify coupling effects, especially from neighboring cells surrounding the unit cell of interest. The predictions of the model enable the computation of RIS scattered fields, fully accounting for the aperiodic nature of an RIS. Comparisons to finite-element analysis confirm that our computed fields are accurate at any point and for any RIS configuration. Furthermore, our machine learning model generalizes well to different incident waves and RIS dimensions. Therefore, the proposed method is a valuable tool for various practical applications, such as synthesizing RIS scattered field patterns and evaluating the performance of RIS-enabled channels.
Reconfigurable Intelligent Surfaces (RIS) are transformative technologies for next-generation wireless communication, offering advanced control over electromagnetic wave propagation. While RIS have been extensively studied, Stacked Intelligent Metasurfaces (SIM), which extend the RIS concept to multi-layered systems, present significant modeling and optimization challenges. This work addresses these challenges by introducing a new optimization framework for heterogeneous SIM architectures that, compared to previous approaches, is based on a comprehensive model without relying on specific assumptions, allowing for a broader applicability of the results. To this end, we first present a model based on multi-port network theory for characterizing a general electromagnetic collaborative object (ECO) and derive a general framework for ECO optimization. We then introduce the SIM as an ECO with a specific architecture and provide insights into SIM optimization for various architectures, discussing the complexity in each case. Next, we analyze the impact of commonly used assumptions, and as a further contribution, we propose a backpropagation algorithm for implementing the gradient descent method for a simplified SIM configuration.
In this chapter, we will introduce promising techniques that may be used for implementing STARSs and hardware models for characterizing the tuning capability of STARSs at different levels of accuracy. We will also discuss the advantages and disadvantages of different channel models that can used for STARSs. Moreover, two STARS variants, namely the dual-sided STARS and the active STARS, will be discussed.
Reconfigurable intelligent surface (RIS)-aided millimeter wave (mmWave) wireless systems offer robustness to blockage and enhanced coverage. In this paper, we develop an algorithmic solution that shows how RISs can also enhance the positioning performance in a joint localization and communication setting, even when hardware impairments are considered. We propose a realistic system architecture that considers the clock offset between the transmitter and the receiver, impairments at transmit and receive arrays, and mutual coupling between the RIS elements. We formulate the estimation of the composite channel in a RIS-aided mmWave system as a multidimensional orthogonal matching pursuit problem, which can be solved with high accuracy and low complexity, even when operating with large antenna arrays as required at mmWave. In addition, we introduce a dictionary learning stage to calibrate the hardware impairments at the user array. To complete our design, we devise a localization scheme that exploits the estimated composite channel while accounting for the clock offset between the transmitter and the receiver. Numerical results show how RIS-aided mmWave systems can significantly improve the localization accuracy in a realistic 3D indoor scenario simulated by ray tracing.
Reconfigurable Intelligent Surfaces (RIS) are one of the emerging technologies aimed at meeting the expectations of next-generations wireless systems. In this field, the use of multi-port network models for the characterization and optimization of RIS has emerged in recent years. These models take into account aspects traditionally not considered in communication theory, such as mutual coupling of RIS elements and the presence of structural scattering. In this work, we refer to this model and focus on the problem of maximizing the average achievable rate in a multi-user uplink scenario by leveraging statistical Channel State Information (CSI). This approach significantly reduces the computational burden and communication overhead in CSI estimation compared to schemes requiring instantaneous CSI estimation. These benefits are achieved with performance that, in many cases, is reasonably close to that of the perfect CSI scenario. This is one of the outcomes achievable with the proposed optimization scheme. Moreover, it is shown how in multi-user scenarios, namely in the presence of interference, the use of inadequate models to characterize RIS can lead to very poor performances. For example, models that do not consider structural scattering may fail to account for interference caused by RIS.
Multiport network theory has been proved to be a suitable abstraction model for analyzing and optimizing reconfigurable intelligent surfaces (RISs) in an electromagnetically consistent manner, especially for studying the impact of the electromagnetic mutual coupling among radiating elements that are spaced less than half of the wavelength apart and for considering the interrelation between the amplitude and phase of the reflection coefficients. Both representations in terms of
Z
-parameter (impedance) and
S
-parameter (scattering) matrices are widely utilized. In this paper, we embrace multiport network theory for analyzing and optimizing the reradiation properties of RIS-aided channels, and provide four new contributions. (i) First, we offer a thorough comparison between the
Z
-parameter and
S
-parameter representations. This comparison allows us to unveil that typical scattering models utilized for RIS-aided channels ignore the structural scattering from an RIS, which is well documented in antenna theory. We show that the structural scattering results in an unwanted specular reflection. (ii) Then, we develop an iterative algorithm for optimizing, in the presence of electromagnetic mutual coupling, the tunable loads of an RIS based on the
S
-parameters representation. We prove that small perturbations of the step size of the algorithm result in larger variations of the
S
-parameter matrix compared with the
Z
-parameter matrix, resulting in a faster convergence rate. (iii) Subsequently, we generalize the proposed algorithm to suppress the specular reflection due to the structural scattering, while maximizing the received power towards the direction of interest, and analyze the effectiveness and tradeoffs of the proposed approach. (iv) Finally, we validate the theoretical findings and algorithms with numerical simulations and a commercial full-wave electromagnetic simulator based on the method of moments.
Clustering protocols are potential solutions to address the severe energy constraints faced by cognitive radio sensor networks (CRSNs). To further exploit the potential of clustering protocols in reducing node energy consumption, active reconfigurable intelligent surface (RIS) is for the first time incorporated into clustered CRSNs to assist the uplink data transmission towards the sink. To minimize the total node energy consumed by uplink data transmission, we formulate the problem of maximizing the normalized energy efficiency improvement ratio for all nodes in active RIS-assisted clustered CRSNs compared to conventional clustered CRSNs and solve it by jointly optimizing the active RIS beamforming and transmit power of CRSNs nodes. Specifically, by considering the physical and electromagnetic properties of the active RIS, we redefine the conditions for successful information transmission under deterministic channels. Analytical expressions for the optimal reflection coefficients of the active reflecting elements (REs), as well as semiclosed-form solutions for the transmit power of CRSNs nodes are derived. Moreover, the optimal configurations of key parameters, such as the number of active REs, total power budget for the active RIS, wavelength of transmitted signal, and physical dimensions of REs are theoretically derived and validated through numerical simulations, thereby offering design guidance for future active RIS-assisted clustered CRSNs. Simulation results indicate that the proposed mechanism significantly outperforms its baseline counterparts and is suitable for CRSNs nodes with severe computational and energy constraints.
This paper presents a theoretical and mathematical framework for the design of a conformal reconfigurable intelligent surface (RIS) that adapts to non-planar geometries, which is a critical advancement for the deployment of RIS on non-planar and irregular surfaces as envisioned in smart radio environments. Previous research focused mainly on the optimization of RISs assuming a predetermined shape, while neglecting the intricate interplay between shape optimization, phase optimization, and mutual coupling effects. Our contribution, the Tailored 3D RIS (T3DRIS) framework, addresses this fundamental problem by integrating the configuration and shape optimization of RISs into a unified model and design framework, thus facilitating the application of RIS technology to a wider spectrum of environmental objects. The mathematical core of T3DRIS is rooted in optimizing the 3D deployment of the unit cells and tuning circuits, aiming at maximizing the communication performance. Through rigorous full-wave simulations and a comprehensive set of numerical analyses, we validate the proposed approach and demonstrate its superior performance and applicability over contemporary designs. This study—the first of its kind—paves the way for a new direction in RIS research, emphasizing the importance of a theoretical and mathematical perspective in tackling the challenges of conformal RISs.
We introduce algorithms for optimizing a single-input single-output reconfigurable intelligent surface (RIS) assisted system. The RIS is modeled by using an electromagnetic-compliant framework based on mutual impedances and its reconfigurability is realized through tunable lumped impedances. In the absence of mutual coupling among the scattering elements of the RIS, we derive a closed-form expression for the optimal tunable impedances, which accounts for the interplay between the amplitude and phase of the lumped loads of the RIS. In the presence of mutual coupling, we introduce an iterative algorithm for optimizing the tunable impedances of the RIS. The algorithm is proved to be convergent by showing that the objective function is non-decreasing and upper bounded. Numerical results reveal that the mutual coupling significantly affects the end-to-end received power. If the RIS is optimized by taking the mutual coupling into account, the received power can be increased.
Reconfigurable intelligent surfaces (RISs) comprised of tunable unit cells have recently drawn significant attention due to their superior capability in manipulating electromagnetic waves. In particular, RIS-assisted wireless communications have the great potential to achieve significant performance improvement and coverage enhancement in a cost-effective and energy-efficient manner, by properly programming the reflection coefficients of the unit cells of RISs. In this paper, free-space path loss models for RIS-assisted wireless communications are developed for different scenarios by studying the physics and electromagnetic nature of RISs. The proposed models, which are first validated through extensive simulation results, reveal the relationships between the free-space path loss of RIS-assisted wireless communications and the distances from the transmitter/receiver to the RIS, the size of the RIS, the near-field/far-field effects of the RIS, and the radiation patterns of antennas and unit cells. In addition, three fabricated RISs (metasurfaces) are utilized to further corroborate the theoretical findings through experimental measurements conducted in a microwave anechoic chamber. The measurement results match well with the modeling results, thus validating the proposed free-space path loss models for RIS, which may pave the way for further theoretical studies and practical applications in this field.
Reconfigurable intelligent surfaces (RISs) have the potential of realizing the emerging concept of smart radio environments by leveraging the unique properties of metamaterials and large arrays of inexpensive antennas. In this article, we discuss the potential applications of RISs in wireless networks that operate at high-frequency bands, e.g., millimeter wave (30-100 GHz) and sub-millimeter wave (greater than 100 GHz) frequencies. When used in wireless networks, RISs may operate in a manner similar to relays. The present paper, therefore, elaborates on the key differences and similarities between RISs that are configured to operate as anomalous reflectors and relays. In particular, we illustrate numerical results that highlight the spectral efficiency gains of RISs when their size is sufficiently large as compared with the wavelength of the radio waves. In addition, we discuss key open issues that need to be addressed for unlocking the potential benefits of RISs for application to wireless communications and networks.
Intelligent reflecting surface (IRS) that enables the control of wireless propagation environment has recently emerged as a promising cost-effective technology for boosting the spectral and energy efficiency of future wireless communication systems. Prior works on IRS are mainly based on the ideal phase shift model assuming full signal reflection by each of its elements regardless of the phase shift, which, however, is practically difficult to realize. In contrast, we propose in this paper a practical phase shift model that captures the phase-dependent amplitude variation in the element-wise reflection design. Based on the proposed model and considering an IRS-aided multiuser system with one IRS deployed to assist in the downlink communications from a multi-antenna access point (AP) to multiple single-antenna users, we formulate an optimization problem to minimize the total transmit power at the AP by jointly designing the AP transmit beamforming and the IRS reflect beamforming, subject to the users’ individual signal-to-interference-plus-noise ratio (SINR) constraints. Iterative algorithms are proposed to find suboptimal solutions to this problem efficiently by utilizing the alternating optimization (AO) as well as penalty-based optimization techniques. Moreover, to draw essential insight, we analyze the asymptotic performance loss of the IRS-aided system that employs practical phase shifters but assumes the ideal phase shift model for beamforming optimization, as the number of IRS elements goes to infinity. Simulation results unveil substantial performance gains achieved by the proposed beamforming optimization based on the practical phase shift model as compared to the conventional ideal model.
Future wireless networks are expected to constitute a distributed intelligent wireless communications, sensing, and computing platform, which will have the challenging requirement of interconnecting the physical and digital worlds in a seamless and sustainable manner. Currently, two main factors prevent wireless network operators from building such networks: (1) the lack of control of the wireless environment, whose impact on the radio waves cannot be customized, and (2) the current operation of wireless radios, which consume a lot of power because new signals are generated whenever data has to be transmitted. In this paper, we challenge the usual “more data needs more power and emission of radio waves” status quo, and motivate that future wireless networks necessitate a smart radio environment: a transformative wireless concept, where the environmental objects are coated with artificial thin films of electromagnetic and reconfigurable material (that are referred to as reconfigurable intelligent meta-surfaces), which are capable of sensing the environment and of applying customized transformations to the radio waves. Smart radio environments have the potential to provide future wireless networks with uninterrupted wireless connectivity, and with the capability of transmitting data without generating new signals but recycling existing radio waves. We will discuss, in particular, two major types of reconfigurable intelligent meta-surfaces applied to wireless networks. The first type of meta-surfaces will be embedded into, e.g., walls, and will be directly controlled by the wireless network operators via a software controller in order to shape the radio waves for, e.g., improving the network coverage. The second type of meta-surfaces will be embedded into objects, e.g., smart t-shirts with sensors for health monitoring, and will backscatter the radio waves generated by cellular base stations in order to report their sensed data to mobile phones. These functionalities will enable wireless network operators to offer new services without the emission of additional radio waves, but by recycling those already existing for other purposes. This paper overviews the current research efforts on smart radio environments, the enabling technologies to realize them in practice, the need of new communication-theoretic models for their analysis and design, and the long-term and open research issues to be solved towards their massive deployment. In a nutshell, this paper is focused on discussing how the availability of reconfigurable intelligent meta-surfaces will allow wireless network operators to redesign common and well-known network communication paradigms.
A procedure to achieve near-field multiple input multiple output (MIMO) communication with equally strong channels is demonstrated in this paper. This has applications in near-field wireless communications, such as Chip-to-Chip (C2C) communication or wireless links between printed circuit boards. Designing the architecture of these wireless C2C networks is, however, based on standard engineering design tools. To attain this goal, a network optimization procedure is proposed, which introduces decoupling and matching networks. As a demonstration, this optimization procedure is applied to a 2-by-2 MIMO with dipole antennas. The potential benefits and design trade-offs are discussed for implementation of wireless radio-frequency interconnects in chip-to-chip or device-to-device communication such as in an Internet-of-Things scenario.
In this paper, we introduce a physics-consistent analytical characterization of the free-space path-loss of a wireless link in the presence of a reconfigurable intelligent surface. The proposed approach is based on the vector generalization of Green’s theorem. The obtained path-loss model can be applied to two-dimensional homogenized metasurfaces, which are made of sub-wavelength scattering elements and that operate either in reflection or transmission mode. The path-loss is formulated in terms of a computable integral that depends on the transmission distances, the polarization of the radio waves, the size of the surface, and the desired surface transformation. Closed-form expressions are obtained in two asymptotic regimes that are representative of far-field and near-field deployments. Based on the proposed approach, the impact of several design parameters and operating regimes is unveiled.
We consider a fading channel in which a multi-antenna transmitter communicates with a multi-antenna receiver through a reconfigurable intelligent surface (RIS) that is made of N reconfigurable passive scatterers impaired by phase noise. The beamforming vector at the transmitter, the combining vector at the receiver, and the phase shifts of the N scatterers are optimized in order to maximize the signal-to-noise-ratio (SNR) at the receiver. By assuming Rayleigh fading (or line-of-sight propagation) on the transmitter-RIS link and Rayleigh fading on the RIS-receiver link, we prove that the SNR is a random variable that is equivalent in distribution to the product of three (or two) independent random variables whose distributions are approximated by two (or one) gamma random variables and the sum of two scaled non-central chi-square random variables. The proposed analytical framework allows us to quantify the robustness of RIS-aided transmission to fading channels. For example, we prove that the amount of fading experienced on the transmitter-RIS-receiver channel linearly decreases with N1. This proves that RISs of large size can be effectively employed to make fading less severe and wireless channels more reliable.
Reconfigurable intelligent surfaces (RISs) are an emerging transmission technology for application to wireless communications. RISs can be realized in different ways, which include (i) large arrays of inexpensive antennas that are usually spaced half of the wavelength apart; and (ii) metamaterial-based planar or conformal large surfaces whose scattering elements have sizes and inter-distances much smaller than the wavelength. Compared with other transmission technologies, e.g., phased arrays, multi-antenna transmitters, and relays, RISs require the largest number of scattering elements, but each of them needs to be backed by the fewest and least costly components. Also, no power amplifiers are usually needed. For these reasons, RISs constitute a promising software-defined architecture that can be realized at reduced cost, size, weight, and power (C-SWaP design), and are regarded as an enabling technology for realizing the emerging concept of smart radio environments (SREs). In this paper, we (i) introduce the emerging research field of RIS-empowered SREs; (ii) overview the most suitable applications of RISs in wireless networks; (iii) present an electromagnetic-based communication-theoretic framework for analyzing and optimizing metamaterial-based RISs; (iv) provide a comprehensive overview of the current state of research; and (v) discuss the most important research issues to tackle. Owing to the interdisciplinary essence of RIS-empowered SREs, finally, we put forth the need of reconciling and reuniting C. E. Shannon’s mathematical theory of communication with G. Green’s and J. C. Maxwell’s mathematical theories of electromagnetism for appropriately modeling, analyzing, optimizing, and deploying future wireless networks empowered by RISs.
A communication model for large intelligent surfaces
- R J Williams
R. J. Williams et al., "A communication model for large intelligent
surfaces", IEEE Int. Conf. Commun., Jun. 2020.