Global Optimal Closed-Form Solutions for Intelligent Surfaces With Mutual Coupling: Is Mutual Coupling Detrimental or Beneficial?

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.

Non-Reciprocal Beyond Diagonal RIS: Multiport Network Models and Performance Benefits in Full-Duplex Systems

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.

Physics-Compliant Modeling and Scaling Laws of Multi-RIS Aided Systems

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.

Beyond Diagonal RIS: Passive Maximum Ratio Transmission and Interference Nulling Enabler

Beyond diagonal reconfigurable intelligent surfaces (BD-RIS) generalizes and goes beyond conventional diagonal reconfigurable intelligent surfaces (D-RIS) by interconnecting elements to generate beyond diagonal scattering matrices, which significantly strengthen the wireless channels. In this work, we use BD-RIS for passive multiuser beamforming in multiuser multiple-input-single-output (MU-MISO) systems. Specifically, we design the scattering matrix of BD-RIS to either maximize the sum received signal power at the users following maximum ratio transmission (MRT), or to nullify the interference at the users following zero forcing (ZF). Furthermore, we investigate uniform/optimized power allocation and ZF precoding at the base station (BS). Numerical results show that BD-RIS improves the interference nulling capability and sum rate with fewer reflecting elements (REs) compared to D-RIS. In addition, at moderate to high signal to noise ratios (SNRs), passive interference nulling reduces the complexity at the BS by relaxing the need for precoding or water-filling power allocation design. Furthermore, the passive MRT with ZF precoding achieves a tight sum rate performance to the joint design considering MU-MISO scenarios with many REs while maintaining low computational complexity and simplifying the channel estimation.

Enhancing Spatial Multiplexing and Interference Suppression for Near- and Far-Field Communications with Sparse MIMO

Multiple-input multiple-output has been a key technology for wireless systems for decades. For typical MIMO communication systems, antenna array elements are usually separated by half of the carrier wavelength, thus termed as conventional MIMO. In this paper, we investigate the performance of multi-user MIMO communication, with sparse arrays at both the transmitter and receiver side, i.e., the array elements are separated by more than half wavelength. Given the same number of array elements, the performance of sparse MIMO is compared with conventional MIMO. On one hand, sparse MIMO has a larger aperture, which can achieve narrower main lobe beams that make it easier to resolve densely located users. Besides, increased array aperture also enlarges the near-field communication region, which can enhance the spatial multiplexing gain, thanks to the spherical wavefront property in the near-field region. On the other hand, element spacing larger than half wavelength leads to undesired grating lobes, which, if left unattended, may cause severe inter-user interference. To gain further insights, we first study the spatial multiplexing gain of the basic single-user sparse MIMO communication system, where a closed-form expression of the near-field effective degree of freedom is derived. The result shows that the EDoF increases with the array sparsity for sparse MIMO before reaching its upper bound, which equals to the minimum value between the transmit and receive antenna numbers. Furthermore, the scaling law for the achievable data rate with varying array sparsity is analyzed and an array sparsity-selection strategy is proposed. We then consider the more general multi-user sparse MIMO communication system. It is shown that sparse MIMO is less likely to experience severe IUI than conventional MIMO.

Channel Estimation for Beyond Diagonal RIS via Tensor Decomposition

This paper addresses the channel estimation problem for beyond diagonal reconfigurable intelligent surface (BD-RIS) from a tensor decomposition perspective. We first show that the received pilot signals can be arranged as a three-way tensor, allowing us to recast the cascaded channel estimation problem as a block Tucker decomposition problem that yields decoupled estimates for the involved channel matrices while offering a substantial performance gain over the conventional (matrix-based) least squares (LS) estimation method. More specifically, we develop two solutions to solve the problem. The first one is a closed-form solution that extracts the channel estimates via a block Tucker Kronecker factorization (BTKF), which boils down to solving a set of parallel rank-one matrix approximation problems. Exploiting such a low-rank property yields a noise rejection gain compared to the standard LS estimation scheme while allowing the two involved channels to be estimated separately. The second solution is based on a block Tucker alternating least squares (BTALS) algorithm that directly estimates the involved channel matrices using an iterative estimation procedure. We discuss the uniqueness and identifiability issues and their implications for training design. We also propose a tensor-based design of the BD-RIS training tensor for each algorithm that ensures unique decoupled channel estimates under trivial scaling ambiguities. Our numerical results shed light on the tradeoffs offered by BTKF and BTALS methods. Specifically, while the first enjoys fast and parallel extraction of the channel estimates in closed form, the second has a more flexible training design, allowing for a significantly reduced training overhead compared to the state-of-the-art LS method.

Channel Shaping Using Beyond Diagonal Reconfigurable Intelligent Surface: Analysis, Optimization, and Enhanced Flexibility

This paper investigates the capability of a passive Reconfigurable Intelligent Surface (RIS) to redistribute the singular values of point-to-point Multiple-Input Multiple-Output (MIMO) channels for achieving power and rate gains. We depart from the conventional Diagonal (D)-RIS with diagonal phase shift matrix and adopt a Beyond Diagonal (BD) architecture that offers greater wave manipulation flexibility through element-wise connections. Specifically, we first provide shaping insights by characterizing the channel singular value regions attainable by D-RIS and BD-RIS via a novel geodesic optimization. Analytical singular value bounds are then derived to explore their shaping limits in typical deployment scenarios. As a side product, we tackle BD-RIS-aided MIMO rate maximization problem by a local-optimal Alternating Optimization (AO) and a shaping-inspired low-complexity approach. Results show that compared to D-RIS, BD-RIS significantly improves the dynamic range of all channel singular values, the trade-off in manipulating them, and thus the channel power and achievable rate. Those observations become more pronounced when the number of RIS elements and MIMO dimensions increase. Of particular interest, BD-RIS is shown to activate multi-stream transmission at lower transmit power than D-RIS, hence achieving the asymptotic Degrees of Freedom (DoF) at low Signal-to-Noise Ratio (SNR) thanks to its higher flexibility of shaping the distribution of channel singular values.

Stacked Intelligent Metasurfaces for Wireless Sensing and Communication: Applications and Challenges

The rapid advancement of wireless communication technologies has precipitated an unprecedented demand for high data rates, extremely low latency, and ubiquitous connectivity. In order to achieve these goals, stacked intelligent metasurfaces (SIM) has been developed as a novel solution to perform advanced signal processing tasks directly in the electromagnetic wave domain, thus achieving ultra-fast computing speed and reducing hardware complexity. This article provides an overview of the SIM technology by discussing its hardware architectures, advantages, and potential applications for wireless sensing and communication. Specifically, we explore the utilization of SIMs in enabling wave-domain beamforming, channel modeling and estimation in SIM-assisted communication systems. Furthermore, we elaborate on the potential of utilizing a SIM to build a hybrid optical-electronic neural network (HOENN) and demonstrate its efficacy by examining two case studies: disaster monitoring and direction-of-arrival estimation. Finally, we identify key implementation challenges, including practical hardware imperfections, efficient SIM configuration for realizing wave-domain signal processing, and performance analysis to motivate future research on this important and far-reaching topic.

Meta-Learning Based Optimization for Large Scale Wireless Systems

Optimization algorithms for wireless systems play a fundamental role in improving their performance and efficiency. However, it is known that the complexity of conventional optimization algorithms in the literature often exponentially increases with the number of transmit antennas and communication users in the wireless system. Therefore, in the large scale regime, the astronomically large complexity of these optimization algorithms prohibits their use and prevents assessing large scale wireless systems performance under optimized conditions. To overcome this limitation, this work proposes instead the use of an unsupervised meta-learning based approach to directly perform non-convex optimization at significantly reduced complexity. To demonstrate the effectiveness of the proposed meta-learning based solution, the sum-rate (SR) maximization problem for the following three emerging 6G technologies is contemplated: hierarchical rate-splitting multiple access (H-RSMA), integrated sensing and communication (ISAC), and beyond-diagonal reconfigurable intelligent surfaces (BD-RIS). Through numerical results, it is demonstrated that the proposed meta-learning based optimization framework is able to successfully optimize the performance and also reveal unknown aspects of the operation in the large scale regime for the considered three 6G technologies.

Full-Space Wireless Sensing Enabled by Multi-Sector Intelligent Surfaces

The multi-sector intelligent surface (IS), benefiting from a smarter wave manipulation capability, has been shown to enhance channel gain and offer full-space coverage in communications. However, the benefits of multi-sector IS in wireless sensing remain unexplored. This paper introduces the application of multi-sector IS for wireless sensing/localization. Specifically, we propose a new self-sensing system, where an active source controller uses the multi-sector IS geometry to reflect/scatter the emitted signals towards the entire space, thereby achieving full-space coverage for wireless sensing. Additionally, dedicated sensors are installed aligned with the IS elements at each sector, which collect echo signals from the target and cooperate to sense the target angle. In this context, we develop a maximum likelihood estimator of the target angle for the proposed multi-sector IS self-sensing system, along with the corresponding theoretical limits defined by the Cram\'er-Rao Bound. The analysis reveals that the advantages of the multi-sector IS self-sensing system stem from two aspects: enhancing the probing power on targets (thereby improving power efficiency) and increasing the rate of target angle (thereby enhancing the transceiver's sensitivity to target angles). Finally, our analysis and simulations confirm that the multi-sector IS self-sensing system, particularly the 4-sector architecture, achieves full-space sensing capability beyond the single-sector IS configuration. Furthermore, similarly to communications, employing directive antenna patterns on each sector's IS elements and sensors significantly enhances sensing capabilities. This enhancement originates from both aspects of improved power efficiency and target angle sensitivity, with the former also being observed in communications while the latter being unique in sensing.