Channel Estimation and Beamforming for Beyond Diagonal Reconfigurable Intelligent Surfaces

Beyond diagonal reconfigurable intelligent surface (BD-RIS) is a new advance and generalization of the RIS technique. BD-RIS breaks through the isolation between RIS elements by creatively introducing inter-element connections, thereby enabling smarter wave manipulation and enlarging coverage. However, exploring proper channel estimation schemes suitable for BD-RIS aided communication systems still remains an open problem. In this paper, we study channel estimation and beamforming design for BD-RIS aided multi-antenna systems. We first describe the channel estimation strategy based on the least square (LS) method, derive the mean square error (MSE) of the LS estimation, and formulate the joint pilot sequence and BD-RIS design problem with unique constraints induced by BD-RIS architectures. Specifically, we propose an efficient pilot sequence and BD-RIS design which theoretically guarantees to achieve the minimum MSE. With the estimated channel, we then consider two BD-RIS scenarios and propose beamforming design algorithms. Finally, we provide simulation results to verify the effectiveness of the proposed channel estimation scheme and beamforming design algorithms. We also show that more interelement connections in BD-RIS improves the performance while increasing the training overhead for channel estimation.

Wideband Modeling and Beamforming for Beyond Diagonal Reconfigurable Intelligent Surfaces

This work studies the wideband modeling and beamforming design of beyond diagonal reconfigurable intelligent surface (BD-RIS), which generalizes and goes beyond conventional RIS with diagonal phase shift matrices to achieve enhanced channel gain. Specifically, we investigate the response of BD-RIS in wideband systems by going back to its hardware circuit realizations. We propose a novel wideband model which has simple expressions while capturing the response variations of BD-RIS for signals with different frequencies. With this wideband model, we propose a BD-RIS design algorithm for an orthogonal frequency division multiplexing system to maximize the average rate over all subcarriers. Finally, we provide simulation results to evaluate the performance of the proposed design and show the importance of wideband modeling for BD-RIS.

Static Grouping Strategy Design for Beyond Diagonal Reconfigurable Intelligent Surfaces

Beyond diagonal reconfigurable intelligent surface (BD-RIS) extends conventional RIS through novel architectures, such as group-connected RIS, with scattering matrix not restricted to being diagonal. However, it remains unexplored how to optimally group the elements in group-connected RISs to maximize the performance while maintaining a low-complexity circuit. In this study, we propose and model BD-RIS with a static grouping strategy optimized based on the channel statistics. After formulating the corresponding problems, we design the grouping in single- and multi-user systems. Numerical results reveal the benefits of grouping optimization, i.e., up to 60% sum rate improvement, especially in highly correlated channels.

RISnet: A Domain-Knowledge Driven Neural Network Architecture for RIS Optimization with Mutual Coupling and Partial CSI

Multiple access techniques are cornerstones of wireless communications. Their performance depends on the channel properties, which can be improved by reconfigurable intelligent surfaces (RISs). In this work, we jointly optimize MA 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 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. In particular, we design a dedicated neural network (NN) architecture RISnet with good scalability and desired symmetry. Moreover, we combine ML-enabled RIS configuration and analytical precoding at BS since there exist analytical precoding schemes. Furthermore, we propose another variant of RISnet, which requires the channel state information (CSI) of a small portion of RIS elements (in this work, 16 out of 1296 elements) if the channel comprises a few specular propagation paths. 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 symmetry.

A Universal Framework for Multiport Network Analysis of Reconfigurable Intelligent Surfaces

Reconfigurable intelligent surface (RIS) is an emerging paradigm able to control the propagation environment in wireless systems. Most of the research on RIS has been dedicated to system-level optimization and, with the advent of beyond diagonal RIS (BD-RIS), to RIS architecture design. However, developing general and unified electromagnetic (EM)-compliant models for RIS-aided systems remains an open problem. In this study, we propose a universal framework for the multiport network analysis of RIS-aided systems. With our framework, we model RIS-aided systems and RIS architectures through impedance, admittance, and scattering parameter analysis. Based on these analyses, three equivalent models are derived accounting for the effects of impedance mismatching and mutual coupling. The three models are then simplified by assuming large transmission distances, perfect matching, and no mutual coupling to understand the role of the RIS in the communication model. The derived simplified models are consistent with the model used in related literature, although we show that an additional approximation is commonly considered in the literature. We discuss the benefits of each analysis in characterizing and optimizing the RIS and how to select the most suitable parameters according to the needs. Numerical results provide additional evidence of the equivalence of the three analyses.

Beyond Diagonal Reconfigurable Intelligent Surfaces with Mutual Coupling: Modeling and Optimization

This work studies the modeling and optimization of beyond diagonal reconfigurable intelligent surface (BD-RIS) aided wireless communication systems in the presence of mutual coupling among the RIS elements. Specifically, we first derive the mutual coupling aware BD-RIS aided communication model using scattering and impedance parameter analysis. Based on the obtained communication model, we propose a general BD-RIS optimization algorithm applicable to different architectures of BD-RIS to maximize the channel gain. Numerical results validate the effectiveness of the proposed design and demonstrate that the larger the mutual coupling the larger the gain offered by BD-RIS over conventional diagonal RIS.

Beyond Diagonal Reconfigurable Intelligent Surfaces Utilizing Graph Theory: Modeling, Architecture Design, and Optimization

Recently, beyond diagonal reconfigurable intelligent surface (BD-RIS) has been proposed to generalize conventional RIS. BD-RIS has a scattering matrix that is not restricted to being diagonal and thus brings a performance improvement over conventional RIS. While different BD-RIS architectures have been proposed, it still remains an open problem to develop a systematic approach to design BD-RIS architectures achieving the optimal trade-off between performance and circuit complexity. In this work, we propose novel modeling, architecture design, and optimization for BD-RIS based on graph theory. This graph theoretical modeling allows us to develop two new efficient BD-RIS architectures, denoted as tree-connected and forest-connected RIS. Tree-connected RIS, whose corresponding graph is a tree, is proven to be the least complex BD-RIS architecture able to achieve the performance upper bound in multiple-input single-output (MISO) systems. Besides, forest-connected RIS allows us to strike a balance between performance and complexity, further decreasing the complexity over tree-connected RIS. To optimize tree-connected RIS, we derive a closed-form global optimal solution, while forest-connected RIS is optimized through a low-complexity iterative algorithm. Numerical results confirm that tree-connected (resp. forest-connected) RIS achieves the same performance as fully-connected (resp. group-connected) RIS, while reducing the complexity by up to 16.4 times.

Synergizing Beyond Diagonal Reconfigurable Intelligent Surface and Rate-Splitting Multiple Access

This work focuses on the synergy of rate-splitting multiple access (RSMA) and beyond diagonal reconfigurable intelligent surface (BD-RIS) to enlarge the coverage, improve the performance, and save on antennas. Specifically, we employ a multi-sector BD-RIS modeled as a prism, which can achieve highly directional full-space coverage, in a multiuser multiple input single output communication system. With the multi-sector BD-RIS aided RSMA model, we jointly design the transmit precoder and BD-RIS matrix under the imperfect channel state information (CSI) conditions. The robust design is performed by solving a stochastic average sum-rate maximization problem. With sample average approximation and weighted minimum mean square error-rate relationship, the stochastic problem is transformed into a deterministic one with multiple blocks, each of which is iteratively designed. Simulation results show that multi-sector BD-RIS aided RSMA outperforms space division multiple access schemes. More importantly, synergizing multi-sector BD-RIS with RSMA is an efficient strategy to reduce the number of active antennas at the transmitter and the number of passive antennas in BD-RIS.

Reconfigurable Intelligent Surfaces 2.0: Beyond Diagonal Phase Shift Matrices

Reconfigurable intelligent surface (RIS) has been envisioned as a promising technique to enable and enhance future wireless communications due to its potential to engineer the wireless channels in a cost-effective manner. Extensive research attention has been drawn to the use of conventional RIS 1.0 with diagonal phase shift matrices, where each RIS element is connected to its own load to ground but not connected to other elements. However, the simple architecture of RIS 1.0 limits its flexibility of manipulating passive beamforming. To fully exploit the benefits of RIS, in this paper, we introduce RIS 2.0 beyond diagonal phase shift matrices, namely beyond diagonal RIS (BD-RIS). We first explain the modeling of BD-RIS based on the scattering parameter network analysis and classify BD-RIS by the mathematical characteristics of the scattering matrix, supported modes, and architectures. Then, we provide simulations to evaluate the sum-rate performance with different modes/architectures of BD-RIS. We summarize the benefits of BD-RIS in providing high flexibility in wave manipulation, enlarging coverage, facilitating the deployment, and requiring low complexity in resolution bit and element numbers. Inspired by the benefits of BD-RIS, we also discuss potential applications of BD-RIS in various wireless systems. Finally, we list key challenges in modeling, designing, and implementing BD-RIS in practice and point to possible future research directions for BD-RIS.

A Dual-Function Radar-Communication System Empowered by Beyond Diagonal Reconfigurable Intelligent Surface

This work focuses on the use of reconfigurable intelligent surface (RIS) in dual-function radar-communication (DFRC) systems to improve communication capacity and sensing precision, and enhance coverage for both functions. In contrast to most of the existing RIS aided DFRC works where the RIS is modeled as a diagonal phase shift matrix and can only reflect signals to half space, we propose a novel beyond diagonal RIS (BD-RIS) aided DFRC system. Specifically, the proposed BD-RIS supports the hybrid reflecting and transmitting mode, and is compatible with flexible single/group/fully-connected architectures, enabling the system to realize full-space coverage. To achieve the expected benefits, we jointly optimize the transmit waveform, the BD-RIS coefficients, and sensing receive filters, by maximizing the minimum signal-to-clutter-plus-noise ratio for fair target detection, subject to the constraints of the communication quality of service, different BD-RIS architectures and power budget. To solve the non-convex and non-smooth max-min problem, a general solution based on the alternating direction method of multipliers is provided for all considered BD-RIS architectures. Numerical simulations validate the efficacy of the proposed algorithm and show the superiority of the BD-RIS aided DFRC system in terms of both communication and sensing compared to conventional RIS aided DFRC.