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Reconfigurable Intelligent Surfaces 2.0: Beyond Diagonal Phase Shift Matrices

Hongyu Li, Shanpu Shen, Matteo Nerini, Bruno Clerckx

arXiv:2301.03288v3eess.SPcs.IT

TL;DR

Conventional RIS 1.0 is limited by diagonal phase-shift matrices and restricted coverage, motivating beyond diagonal RIS with inter-element connections. The paper models and classifies BD-RIS, evaluates its modes and architectures, and reports performance, deployment, and coverage benefits while identifying implementation challenges.

  • Problem

    Conventional RIS 1.0 has limited passive-beamforming flexibility and same-side reflection because its elements are not interconnected.

  • Method

    The paper models BD-RIS using scattering parameter network analysis and classifies it by matrix characteristics, supported modes, and architectures.

  • Results

    BD-RIS group size 2 increases sum-rate by around 8% with half more impedance components and around 4 times the optimization complexity.

  • Takeaways & Limitations

    BD-RIS offers flexible wave manipulation, full-space coverage, deployment flexibility, and lower resolution-bit and element-number complexity.

  • Takeaways & Limitations

    Comprehensive hardware implementation of BD-RIS with different architectures remains unresolved, with only RIS using STAR-RIS/IOS currently implemented.

Abstract

from arXiv · show

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.

I. INTRODUCTION

Conventional RIS 1.0 uses diagonal phase-shift matrices and has limited beamforming flexibility and half-space coverage. The paper introduces BD-RIS, models and classifies it through scattering networks, and evaluates its modes and architectures.

  • I. INTRODUCTION: RIS 1.0 connects each element to its own impedance without inter-element connections, yielding a diagonal scattering matrix.This architecture controls phase but not magnitude and reflects signals toward the same side.
  • I. INTRODUCTION: BD-RIS introduces inter-element connections, producing beyond-diagonal scattering matrices at the expense of additional circuit complexity.The paper models BD-RIS using scattering parameter network analysis.
  • I. INTRODUCTION: The paper classifies BD-RIS by scattering-matrix characteristics, supported modes, and inter-cell architectures.The classification includes diagonal, block-diagonal, and permuted block-diagonal structures alongside different supported modes and architectures.
  • I. INTRODUCTION: BD-RIS designs use group-connected reconfigurable impedance networks together with different antenna-array arrangements.The paper illustrates reflective/group-connected, hybrid/cell-wise group-connected, and multi-sector/cell-wise single-connected combinations.
  • I. INTRODUCTION: For lossless networks, the scattering matrix is unitary, so reflected-wave power equals incident-wave power.This network property constrains the BD-RIS scattering model.

B. BD-RIS Classification

The BD-RIS classification tree first groups designs by scattering-matrix structure. Group-connected RIS uses block-diagonal unitary matrices, with fully-connected and conventional single-connected RIS as special cases.

  • B. BD-RIS Classification: Group-connected RIS partitions M antennas into G groups, connecting antennas within each group but not across groups.Its scattering matrix is block diagonal, with each block unitary.
  • B. BD-RIS Classification: Group-connected RIS can manipulate both phase and magnitude, enabling better performance than conventional RIS 1.0.Fully-connected RIS is the G = 1 case, while single-connected RIS is the M-group special case with a diagonal matrix.

2) Permuted Block Diagonal Matrix:

Dynamically group-connected RIS adapts antenna grouping to channel state information. This creates a permuted block-diagonal matrix with greater beam-control flexibility than fixed grouping.

  • 2) Permuted Block Diagonal Matrix:: Dynamically group-connected RIS adapts its antenna grouping strategy to channel state information.The resulting scattering matrix is permuted block diagonal.
  • 2) Permuted Block Diagonal Matrix:: The permuted block-diagonal structure provides higher beam-control flexibility than fixed group-connected RIS.

3) Non-Diagonal Matrix:

Non-diagonal BD-RIS structures support signal reflection, transmission, or scattering across multiple spatial regions. Hybrid and multi-sector modes extend coverage beyond the half-space reflective mode through specialized antenna and impedance-network arrangements.

  • 3) Non-Diagonal Matrix:: Hybrid mode partially reflects signals to the incident side and partially transmits them to the opposite side, providing whole-space coverage.Each cell uses two back-to-back antennas connected to a 2-port fully-connected impedance network.
  • 3) Non-Diagonal Matrix:: Multi-sector mode divides full space into L sectors and scatters signals between the incident sector and the other L−1 sectors.Each cell uses L polygon-arranged antennas connected to an L-port fully-connected network.
  • 3) Non-Diagonal Matrix:: The figure pairs reflective, hybrid, and multi-sector modes with group-connected, cell-wise group-connected, and cell-wise single-connected architectures.
  • 3) Non-Diagonal Matrix:: Multi-sector mode covers full space like hybrid mode while providing higher performance gains through narrower-beamwidth, higher-gain antennas.
  • 3) Non-Diagonal Matrix:: Cell-wise single, group, and fully-connected architectures produce diagonal, block-diagonal, and full scattering matrices, respectively.The architectures apply to hybrid and multi-sector BD-RIS.

C. Unified Architectures and Modes

BD-RIS implementations combine group-connected impedance networks with antenna arrangements tailored to reflective, hybrid, or multi-sector operation.

  • C. Unified Architectures and Modes: Three examples pair reflective mode with group-connected architecture, hybrid mode with cell-wise group-connected architecture, and multi-sector mode with cell-wise single-connected architecture.These examples illustrate how modes and architectures are realized together.

III. PERFORMANCE EVALUATION FOR BD-RIS

The evaluation studies BD-RIS sum-rate in a four-user MU-MISO system across modes and architectures, showing performance–complexity trade-offs and benefits from multi-sector and fully connected designs.

  • III. PERFORMANCE EVALUATION FOR BD-RIS: The paper evaluates BD-RIS across nine modes and architectures while summarizing their circuit complexity.The supplied table caption identifies the scope but does not provide individual complexity values.
  • III. PERFORMANCE EVALUATION FOR BD-RIS: The MU-MISO evaluation jointly optimizes the transmitter precoder and BD-RIS to maximize sum-rate for four users distributed across the supported sectors.Fig. 3 reports sum-rate versus the number of BD-RIS antennas for reflective and hybrid/multi-sector modes.
  • III. PERFORMANCE EVALUATION FOR BD-RIS: BD-RIS with group size 2 increases sum-rate by around 8% with half more impedance components and around 4 times the optimization complexity.This configuration is identified as a trade-off between performance and complexity under reflective mode.
  • III. PERFORMANCE EVALUATION FOR BD-RIS: Multi-sector BD-RIS with cell-wise single-connected architecture outperforms hybrid BD-RIS with inter-cell single/group-connected architectures while retaining full-space coverage.The result is attributed to narrower beamwidth and higher antenna gains in multi-sector operation.
  • III. PERFORMANCE EVALUATION FOR BD-RIS: For all three modes, fully connected architectures produce sum-rates that grow faster with M than single-connected architectures.The added flexibility comes with circuit complexity growing quadratically rather than linearly with M.

A. Benefits of BD-RIS

BD-RIS extends RIS 1.0 by controlling diagonal and off-diagonal scattering terms, enabling stronger wave manipulation, full-space coverage, and more flexible deployment.

  • 1) High Flexibility in Wave Manipulation:: BD-RIS manipulates both diagonal and off-diagonal scattering-matrix entries, increasing wave-manipulation flexibility over RIS 1.0.Reported results include up to 62% higher received power and a 2 dB SNR gain in specified architectures.
  • 4) Potential Applications:: BD-RIS is presented for applications including power-grid wireless-power relaying, wireless backhaul and access, mmWave/THz communications, wireless sensing, and integrated sensing and communication.The figure also lists simultaneous wireless information and power transfer among its potential applications.
  • 2) Full Space Coverage:: BD-RIS with suitable group-connected networks and antenna arrangements supports hybrid and multi-sector modes for full-space coverage.Multi-sector operation can extend communication range through narrower beamwidth and higher antenna gain.
  • 3) Flexible Deployment:: Hybrid and multi-sector modes make BD-RIS locations more flexible than conventional RIS 1.0, facilitating practical deployment.This deployment benefit follows from the availability of full-space coverage.

4) Low Complexity in Resolution Bit Number:

BD-RIS reduces implementation complexity by achieving satisfactory performance with fewer resolution bits and fewer elements, while supporting flexible wireless deployments.

  • One resolution bit is sufficient for fully-connected reflective BD-RIS, compared with four bits for conventional RIS 1.0 near continuous-value performance.
  • A 6-sector BD-RIS maintains the same sum-rate as a 3-sector BD-RIS with 20% fewer elements.This reduction lowers RIS complexity, cost, and form factor.
  • BD-RIS can aid wireless power transfer to all receivers with suitable power levels, deployments, and locations, whereas conventional RIS 1.0 serves specific directions.
  • BD-RIS supports indoor and outdoor communications by combining full-space coverage with highly directional beams that help bypass obstacles and compensate for path loss.

3) Wireless Sensing:

BD-RIS extends wireless sensing across line-of-sight and obstructed environments, while supporting broader integrated wireless systems with simpler deployments than conventional RIS 1.0.

  • BD-RIS improves target detection accuracy and reduces parameter estimation error for targets with line-of-sight links.
  • In environments without radar-target line of sight, BD-RIS enables sensing and enlarges coverage by creating effective line-of-sight links.Vehicle networks are given as an example of such complicated propagation environments.
  • BD-RIS can support integrated sensing and communication and simultaneous wireless information and power transfer with reasonable numbers of surfaces and simple deployments.The paper contrasts this with networks that would be very complicated or impractical using only conventional RIS 1.0.
  • The paper identifies practical BD-RIS challenges in hardware implementation, architecture design, RF impairments, channel estimation, and wideband modeling.

A. Hardware Implementation

BD-RIS hardware uses interconnected impedance networks and mode-specific antenna arrangements, but practical implementations face rising complexity, cost, and unresolved RF-impairment challenges.

  • A. Hardware Implementation: Only STAR-RIS/IOS has been implemented so far, leaving comprehensive hardware implementation across BD-RIS architectures unresolved.The model supports antenna arrays connected to reconfigurable impedance networks, but broader physical implementation remains ongoing.
  • A. Hardware Implementation: Reflective, hybrid, and multi-sector modes require different antenna layouts, including back-to-back directional antennas or polygon-edge cells.The layouts are specified for uniform arrays and mode-specific cell construction.
  • A. Hardware Implementation: Group-connected impedance networks implement continuous or discrete BD-RIS using varactors or PIN diodes, respectively.Larger group sizes increase circuit complexity and cost because of inter-element connections.
  • A. Hardware Implementation: Practical mismatching and mutual coupling make the channel model nonlinear in Θ, complicating beamforming design.This issue has not been investigated in existing works cited by the passage.
  • A. Hardware Implementation: PIN-diode BD-RIS cannot use simple elementwise quantization because its matrix entries depend on one another.Discrete-value design for hybrid and multi-sector modes with different architectures remains open.

C. Channel Estimation

BD-RIS channel estimation and modeling remain constrained by topology-dependent cascaded channels and narrowband assumptions, motivating lower-power estimation and simpler wideband designs.

  • C. Channel Estimation: BD-RIS requires accurate CSI for its pronounced performance gain, while conventional passive cascaded-channel estimation does not directly transfer.The cascaded-channel dimension depends on the reconfigurable impedance-network topology.
  • C. Channel Estimation: Semi-passive estimation remains available but adds power consumption through extra RF chains.Developing lower-power BD-RIS channel-estimation strategies is identified as important.
  • D. Wideband BD-RIS Modeling: The current BD-RIS model is narrowband, so wideband modeling must include frequency-dependent impedance responses and inter-element relationships.These dependencies prevent element-by-element design as in conventional RIS 1.0.
  • C. Channel Estimation: The paper presents BD-RIS modeling, classification, benefits, applications, challenges, and future research directions.Its scope includes different modes and architectures rather than a single implementation setting.
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