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arxiv: 2604.13570 · v1 · submitted 2026-04-15 · 📡 eess.SP · cs.IT· math.IT

Active Beyond-Diagonal Reconfigurable Intelligent Surface with Hybrid Transmitting and Reflecting Mode

Fu Liu , Hongyu Li , Shanpu Shen This is my paper

Pith reviewed 2026-05-10 13:25 UTC · model grok-4.3

classification 📡 eess.SP cs.ITmath.IT
keywords beyond-diagonal reconfigurable intelligent surfaceactive RIShybrid transmitting and reflectingsum rate maximizationmulti-user communicationinter-element connectionswave manipulationfull-space coverage
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The pith

Active BD-RIS with hybrid transmit-reflect mode raises multi-user sum rates over passive and non-hybrid alternatives at equal power.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper sets out to show that active beyond-diagonal reconfigurable intelligent surfaces can operate in a hybrid transmitting and reflecting mode to deliver full-space coverage while amplifying signals. It derives a physics-compliant model, defines reciprocal and non-reciprocal architectures with varying inter-element connections, and supplies a single optimization routine that jointly tunes transmit precoding and the surface coefficients to maximize sum rate. A reader would care because the combination of amplification and flexible connections counters multiplicative fading more effectively than earlier RIS designs without raising the total power budget. Numerical comparisons confirm the resulting performance edge across multiple architectures.

Core claim

Active BD-RISs equipped with hybrid transmitting and reflecting capability, realized through cell-wise single, group, or full connections in reciprocal or non-reciprocal forms, produce synergy gains from inter-element connections, element arrangements, and active amplification. When the surface and transmit precoding are jointly optimized, these surfaces achieve substantially higher sum rates in multi-user systems than active or passive simultaneous transmitting and reflecting RISs and than passive BD-RISs with hybrid mode, all under the same total power constraint.

What carries the argument

Physics-compliant communication model of active BD-RIS in hybrid transmitting and reflecting mode that incorporates signal amplification and inter-element connections.

If this is right

  • Full-space coverage becomes available without leaving blind spots for users on either side of the surface.
  • The same unified optimization applies without modification to all listed connection architectures.
  • Sum-rate gains persist when the design is compared against both active and passive reference surfaces.
  • The combination of amplification and inter-element connections improves efficiency inside the fixed power budget.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Fewer surface elements may suffice to reach a target rate once hybrid active operation is used.
  • The framework could be reused for other active surfaces that combine amplification with programmable connections.
  • Dense multi-user deployments become more feasible because the same power yields higher aggregate throughput.

Load-bearing premise

The physics-compliant communication model accurately captures real-world active BD-RIS hybrid-mode behavior, including amplification and inter-element effects, without unmodeled losses, nonlinearities, or hardware imperfections.

What would settle it

A hardware prototype measurement that records whether the realized multi-user sum rate of the active hybrid BD-RIS exceeds the rates of the compared passive and non-hybrid designs by the margin predicted in the simulations under identical total power.

Figures

Figures reproduced from arXiv: 2604.13570 by Fu Liu, Hongyu Li, Shanpu Shen.

Figure 1
Figure 1. Figure 1: BD-RIS classification tree. that use active devices to amplify scattered signals has been proposed. In the family of active RISs, active D-RIS with a diagonal scattering matrix whose diagonal elements have con￾trollable phase shifts and amplitudes has been first proposed in [24]. Specifically, the amplitude of the scattered signals can be magnified by reflection-type amplifiers to compensate for the multip… view at source ↗
Figure 2
Figure 2. Figure 2: Diagram of an M-cell hybrid mode active BD-RIS aided communi￾cation system. where ΦIA = [Φ]1:2M;2M+1:4M ∈ C 2M×2M and ΦAI = [Φ]2M+1:4M;1:2M ∈ C 2M×2M are sub-matrices of Φ and are unitary when the passive reconfigurable network is lossless. According to [46], assuming that the multiple antennas at the transmitter/receiver and the elements at the hybrid mode active BD-RIS are perfectly matched with no mutua… view at source ↗
Figure 3
Figure 3. Figure 3: An M-cell hybrid mode active BD-RIS with 2M back to back placed uni-directional antennas. cover half of the space. Accordingly, we partition the overall channel matrix (2) and H¯ RI,kΘnI for user k, ∀k ∈ K, as Hk =HRT,k + [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Different cell-wise architectures of active BD-RIS [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: An illustration of the relative position among the BS [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Sum rate versus transmit power P tot T . G = 2 for group-connected architecture. of the scattered signals at the cost of higher circuit complexity. Third, the performance difference between reciprocal and non￾reciprocal active BD-RIS architectures is relatively small under the considered simulation settings. In particular, the reciprocal and non-reciprocal CWFC architectures achieve nearly iden￾tical sum r… view at source ↗
Figure 8
Figure 8. Figure 8: Sum rate versus the group size G of active BD-RIS. P tot T =20 dBm. MISO communication system versus the group size of the active BD-RIS with P tot T = 20 dBm. The group size G is selected from the set of divisors of the number of active BD￾RIS cells. In particular, G = 1 and G = M correspond to the cell-wise single-connected (STAR-RIS) and CWFC architec￾tures, respectively. From [PITH_FULL_IMAGE:figures/… view at source ↗
read the original abstract

Beyond-diagonal reconfigurable intelligent surfaces (BD-RISs), originally in the passive form, have attracted attention due to their benefits in enhanced wave manipulating through flexible inter-element connections and element arrangements. To mitigate the severe multiplicative fading, the concept of active BD-RISs with signal amplification capability has recently been proposed. Inspired by this, we investigate the hybrid transmitting and reflecting mode of active BD-RISs to achieve full-space coverage. We start by deriving a physics compliant communication model applying active BD-RIS with hybrid mode. We further propose novel architectures including reciprocal and non-reciprocal implementations with cell-wise single, group, and fully connections. We also develop a unified optimization framework for the joint transmit precoding and hybrid mode active BD-RIS design to maximize the sum rate of multi-user communication systems, which is applicable to all considered architectures. Numerical results demonstrate that, under the same total power budget, the proposed active BD-RIS with hybrid mode substantially outperforms active and passive simultaneous transmitting and reflecting RISs as well as passive BD-RISs with hybrid mode. This shows the synergy gain from inter-element connection, element arrangements, and active amplification.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes active beyond-diagonal reconfigurable intelligent surfaces (BD-RIS) operating in hybrid transmitting and reflecting mode for full-space coverage. It derives a physics-compliant communication model for active BD-RIS with hybrid mode, introduces reciprocal and non-reciprocal architectures with cell-wise single/group/fully connected inter-element links, develops a unified optimization framework for joint transmit precoding and RIS parameter design to maximize sum rate in multi-user MIMO systems, and reports numerical results claiming substantial outperformance over active/passive STAR-RIS and passive BD-RIS schemes under an identical total power budget, attributing gains to the synergy of inter-element connections, element arrangements, and active amplification.

Significance. If the performance claims hold under consistent power accounting, the work advances RIS research by combining active amplification with BD-RIS flexibility and hybrid-mode operation, offering a pathway to improved coverage and spectral efficiency. The physics-compliant model derivation and the unified optimization framework applicable across multiple architectures represent clear strengths that could be adopted in subsequent studies.

major comments (2)
  1. [unified optimization framework (sum-rate maximization problem)] The central numerical claim (abstract) of outperformance 'under the same total power budget' is load-bearing and requires explicit verification that the power constraint in the unified optimization framework accounts for DC/amplification power consumption in the proposed active BD-RIS and active baselines while using only transmit power for passive baselines. If the constraint is formulated solely on transmit power without including active-element consumption (as is common in such papers), the reported gains become incomparable and the synergy conclusion does not follow.
  2. [communication model derivation] The physics-compliant communication model must be shown to incorporate the power consumed by active amplification without unmodeled losses or nonlinearities; the hybrid-mode channel matrix derivation should explicitly relate the amplification gain, inter-element connections, and element arrangements to the effective end-to-end channel, with the total power budget constraint written in terms of these quantities.
minor comments (2)
  1. [architectures section] Notation for the hybrid-mode scattering matrix and connection types (reciprocal vs. non-reciprocal) should be introduced with a clear table or diagram early in the manuscript to aid readability across the architectures.
  2. [numerical results] Numerical results section would benefit from an explicit statement of the total power budget value used for all schemes and a sensitivity plot varying the amplification power fraction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and the opportunity to clarify key aspects of our work. We address each major comment below with explanations and indicate the revisions that will be made to strengthen the manuscript's rigor and transparency.

read point-by-point responses

  1. Referee: [unified optimization framework (sum-rate maximization problem)] The central numerical claim (abstract) of outperformance 'under the same total power budget' is load-bearing and requires explicit verification that the power constraint in the unified optimization framework accounts for DC/amplification power consumption in the proposed active BD-RIS and active baselines while using only transmit power for passive baselines. If the constraint is formulated solely on transmit power without including active-element consumption (as is common in such papers), the reported gains become incomparable and the synergy conclusion does not follow.

    Authors: We agree that explicit verification of consistent power accounting is necessary to support the performance claims. In the unified optimization framework, the total power budget constraint is defined to encompass both the base-station transmit power and the DC plus amplification power consumed by active BD-RIS elements. The amplification power is computed from the element-wise gains and the network matrix arising from inter-element connections. Passive baselines are constrained only on transmit power, as they incur no additional consumption. To address the referee's concern directly, we will revise the manuscript to include the explicit power-consumption equations, re-state the optimization problem with the total-power constraint written out, and confirm that all numerical comparisons respect this accounting. This will substantiate the reported synergy gains. revision: yes

  2. Referee: [communication model derivation] The physics-compliant communication model must be shown to incorporate the power consumed by active amplification without unmodeled losses or nonlinearities; the hybrid-mode channel matrix derivation should explicitly relate the amplification gain, inter-element connections, and element arrangements to the effective end-to-end channel, with the total power budget constraint written in terms of these quantities.

    Authors: We thank the referee for emphasizing the need for a fully transparent derivation. The physics-compliant model begins from the scattering parameters of active elements, treating amplification as a linear gain whose associated power is P_amp = f(gain, incident power) with no additional unmodeled losses assumed within the linear regime. The hybrid-mode channel matrix is obtained by composing the transmitting/reflecting coefficients with the inter-element connection matrix (single/group/fully connected) and the element-arrangement geometry, yielding the effective end-to-end channel. The total power budget is expressed directly as a function of these gains and the connection topology. We will augment Section II with the missing explicit relations between gain, connections, arrangements, and both the channel matrix and the power constraint, thereby eliminating any ambiguity. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper derives a physics-compliant communication model for active BD-RIS with hybrid mode from first principles, proposes reciprocal/non-reciprocal architectures with varying connection types, and develops a unified optimization framework for joint precoding and RIS design to maximize sum rate. These steps rely on standard optimization techniques and the derived model rather than reducing any prediction or claim to fitted parameters, self-referential definitions, or load-bearing self-citations. Numerical comparisons under a total power budget follow directly from the framework without evidence of the result being forced by construction or renaming of known patterns. The central performance claims rest on independent model derivation and optimization, making the chain self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available, so specific free parameters, axioms, and invented entities cannot be extracted. The central claim rests on an unspecified physics-compliant model and optimization framework whose assumptions are not detailed.

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Reference graph

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