Capacity of MIMO Systems Aided by Microwave Linear Analog Computers (MiLACs)

Future wireless systems, known as gigantic multiple-input multiple-output (MIMO), are expected to enhance performance by significantly increasing the number of antennas, e.g., a few thousands. To enable gigantic MIMO overcoming the scalability limitations of digital architectures, microwave linear analog computers (MiLACs) have recently emerged. A MiLAC is a multiport microwave network that processes input microwave signals entirely in the analog domain, thereby reducing hardware costs and computational complexity of gigantic MIMO architectures. In this paper, we investigate the fundamental limits on the rate achievable in MiLAC-aided MIMO systems. We model a MIMO system employing MiLAC-aided beamforming at the transmitter and receiver, and formulate the rate maximization problem to optimize the microwave networks of the MiLACs, which are assumed lossless and reciprocal for practical reasons. Under the lossless and reciprocal constraints, we derive a global optimal solution for the microwave networks of the MiLACs in closed form. In addition, we also characterize in closed-form the capacity of MIMO systems operating MiLAC-aided beamforming. Our theoretical analysis, confirmed by numerical simulations, reveals that MiLAC-aided beamforming achieves the same capacity as digital beamforming, while significantly reducing the number of radio frequency (RF) chains, analog-to-digital converters (ADCs)/digital-to-analog converters (DACs) resolution requirements, and computational complexity.

A Tutorial on Beyond-Diagonal Reconfigurable Intelligent Surfaces: Modeling, Architectures, System Design and Optimization, and Applications

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 $\mathbf{\Theta}$ 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 $\mathbf{\Theta}$ 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.

Beyond-Diagonal RIS Prototype and Performance Evaluation

We present the first experimental prototype of a reflective beyond-diagonal reconfigurable intelligent surface (BD-RIS), i.e., a RIS with reconfigurable inter-element connections. Our BD-RIS consists of an antenna array whose ports are terminated by a tunable load network. The latter can terminate each antenna port with three distinct individual loads or connect it to an adjacent antenna port. Extensive performance evaluations in a rich-scattering environment validate that inter-element connections are beneficial. Moreover, we observe that our tunable load network's mentioned hardware constraints significantly influence, first, the achievable performance, second, the benefits of having inter-element connections, and, third, the importance of mutual-coupling awareness during optimization.

Enabling Gigantic MIMO Beamforming with Analog Computing

In our previous work, we have introduced a microwave linear analog computer (MiLAC) as an analog computer that processes microwave signals linearly, demonstrating its potential to reduce the computational complexity of specific signal processing tasks. In this paper, we extend these benefits to wireless communications, showcasing how MiLAC enables gigantic multiple-input multiple-output (MIMO) beamforming entirely in the analog domain. MiLAC-aided beamforming can implement regularized zero-forcing beamforming (R-ZFBF) at the transmitter and minimum mean square error (MMSE) detection at the receiver, while significantly reducing hardware costs by minimizing the number of radio-frequency (RF) chains and only relying on low-resolution analog-to-digital converters (ADCs) and digital-to-analog converters (DACs). In addition, it eliminates per-symbol operations by completely avoiding digital-domain processing and remarkably reduces the computational complexity of R-ZFBF, which scales quadratically with the number of antennas instead of cubically. Numerical results show that it can perform R-ZFBF with a computational complexity reduction of up to 7400 times compared to digital beamforming.

Analog Computing with Microwave Networks

Analog computing has been recently revived due to its potential for energy-efficient and highly parallel computations. In this paper, we investigate analog computers that linearly process microwave signals, named microwave linear analog computers (MiLACs), and their applications in signal processing for communications. We model a MiLAC as a multiport microwave network with tunable impedance components, which enables the execution of mathematical operations by reconfiguring the microwave network and applying input signals at its ports. We demonstrate that a MiLAC can efficiently compute the linear minimum mean square error (LMMSE) estimator, widely used in multiple-input multiple-output (MIMO) communications beamforming and detection, with remarkably low computational complexity, unachievable through digital computing. Specifically, the LMMSE estimator can be computed with complexity growing with the square of its input size, rather than the cube, with revolutionary applications to gigantic MIMO beamforming and detection.

T-Parameters Based Modeling for Stacked Intelligent Metasurfaces: Tractable and Physically Consistent Model

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.

Dual-Polarized Beyond Diagonal RIS

Beyond diagonal reconfigurable intelligent surface (BD-RIS) is a family of RIS architectures more flexible than conventional RIS. While BD-RIS has been primarily analyzed assuming uni-polarized systems, modern wireless deployments are dual-polarized. To address this gap, this paper investigates the fundamental limits of dual-polarized BD-RIS-aided systems. We derive the scaling laws governing the performance of BD-RIS and the Pareto frontier of the trade-off between performance and circuit complexity enabled by BD-RIS. Theoretical results show that the group-connected RIS with group size 2 provides remarkable gains over conventional RIS in both Rayleigh and line-of-sight (LoS) channels, while maintaining a reduced circuit complexity.

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.

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.