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A hybrid RIS with only a few active elements, optimized by deep-unfolded alternating optimization, yields substantially higher energy efficiency than fully passive or fully active surfaces.

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2026-07-11 11:53 UTC pith:2QOYBW27

load-bearing objection Solid hybrid-RIS EE methods paper: deep-unfolded PGD for joint active-set + 1-bit phases is the real increment, and the hybrid-vs-active/passive numbers are useful even if the surrogate softens the absolute claims. the 3 major comments →

arxiv 2607.04889 v1 pith:2QOYBW27 submitted 2026-07-06 eess.SP

Energy Efficiency Maximization for Hybrid RIS-Aided Communications via Deep Unfolding

Pouya Mobaraki , Abolfazl Zakeri , Marco Di Renzo , Markku Juntti , Nhan Thanh Nguyen This is my paper
classification eess.SP
keywords hybrid RISenergy efficiencydeep unfoldingalternating optimizationactive-element selectionbinary phase shiftsMU-MISO downlink
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper shows that a hybrid reconfigurable intelligent surface—where each element can be switched between amplifying (active) and purely reflecting (passive) modes—can deliver markedly higher energy efficiency than either a fully passive or a fully active surface in a multi-user downlink. The design jointly chooses which elements to activate, their amplification gains, their binary phases, and the base-station beamforming under realistic power budgets, amplifier limits, and noise. The authors solve the resulting mixed-integer problem by alternating zero-forcing power allocation at the base station with a model-driven deep-unfolding network that learns step sizes for the RIS subproblem. Simulations indicate roughly 30 percent higher energy efficiency than the same alternating procedure without unfolding, at least 10 percent better than a fully active RIS, and up to three times better than a fully passive RIS; most of the gain appears once only about 10 percent of the elements are active and only a small fraction of the dynamic power is given to the surface.

Core claim

Under practical hardware constraints, jointly optimizing active/passive mode selection together with beamforming and reflection coefficients via deep-unfolded alternating optimization yields energy-efficiency gains of about 30 percent over plain projected-gradient alternating optimization, at least 10 percent over a fully active RIS, and up to threefold over a fully passive RIS, with most of the gain captured by activating only a small fraction of elements and allocating only a small share of dynamic power to the RIS.

What carries the argument

Deep-unfolded projected gradient descent for the RIS subproblem: the iterations of projected gradient ascent are unrolled into trainable layers whose step sizes are learned, while binary phases and discrete active-set selection are handled by differentiable surrogates (tanh phase map and straight-through top-Na selection).

Load-bearing premise

The optimization uses a simplified energy-efficiency formula that drops the active-element noise from every user's signal quality and pretends the RIS always burns its entire power budget; if those terms are not small, the design optimized for the surrogate can diverge from true energy efficiency.

What would settle it

Re-optimize the same system geometries with the exact energy-efficiency expression that keeps active-RIS noise and the true dynamic amplifier power; if the reported 30 percent, 10 percent, and threefold gains largely disappear or reverse under the exact metric, the central claim fails.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Hybrid RIS hardware with only a modest number of amplifiers can outperform both fully passive and fully active surfaces on energy efficiency.
  • Most of the energy-efficiency benefit is already obtained once roughly 10 percent of the elements are active.
  • Allocating only a small fraction of the total dynamic power budget to the RIS is typically more energy-efficient than giving it a large share.
  • Learning the step sizes of a classical projected-gradient RIS update via deep unfolding accelerates convergence and improves the final energy efficiency relative to hand-tuned or fixed-step projected gradient.
  • Binary (one-bit) phase control remains compatible with substantial energy-efficiency gains when the active-set selection is optimized jointly.

Where Pith is reading between the lines

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

  • The same deep-unfolding template could be applied to multi-RIS or multi-cell settings where the combinatorial active-set decisions become even larger.
  • If real hardware measurements confirm that active-element noise and unused amplifier power remain small, the hybrid architecture becomes a practical low-cost upgrade path for existing passive RIS deployments.
  • The observed saturation of energy efficiency with active-element count suggests a natural design rule: provision only enough amplifiers to reach the knee of the curve rather than maximising amplification hardware.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper studies energy-efficiency (EE) maximization for a hybrid RIS-assisted MU-MISO downlink in which each RIS element can be switched between active (amplified) and passive modes. The design jointly optimizes BS beamforming, the active-element set, amplification gains, and binary phase shifts under BS/RIS power budgets, amplifier limits, amplification noise, and per-user SE QoS. An alternating-optimization (AO) framework is proposed: ZF beamforming with closed-form Dinkelbach power allocation for the BS subproblem, and a model-driven deep-unfolded projected gradient method (with differentiable relaxations for binary phases and Top-Na selection) for the RIS subproblem. A joint PGA baseline with barrier QoS penalties is also derived. Simulations under perfect CSI, blocked direct links, and Rician channels report faster convergence and higher EE than AO-PGD and PGA, roughly 30% EE gain over non-unfolded AO, at least 10% over fully-active RIS, up to threefold over fully-passive RIS, and that most of the gain is obtained with only a small active fraction (e.g., Na=10 of N=100) and a small share of the dynamic power budget allocated to the RIS.

Significance. If the numerical claims hold under the stated model, the work supplies a practical algorithmic route to hybrid-RIS EE design that jointly treats discrete mode selection and binary phases—constraints that conventional SCA/AO treatments often leave fixed or continuous. The explicit incorporation of amplifier noise, bias power, and power-budget sharing, together with the observation that sparse activation already captures most of the EE gain, is useful for hardware-aware RIS system design. Strengths include closed-form KKT power allocation (Algorithm 1), carefully derived gradients (Lemma 1 / Appendix A), and a transparent deep-unfolding construction that preserves the projected-gradient structure while learning only step sizes. The contribution is primarily algorithmic and empirical rather than theoretical optimality; its value therefore rests on the reliability of the reported EE rankings under the modeling approximations used for tractability.

major comments (3)
  1. §IV-A, eqs. (16)–(18) and the abstract claims: the designs are obtained by maximizing the surrogate fEE that (i) drops the active-RIS noise term σ_R²‖h_r,k^H Φ_a‖² from every SINR and (ii) replaces the state-dependent Pr(Φ_a,P) by its hard ceiling P_r^max in the EE denominator. Fig. 4 shows that the absolute gap between fEE and true EE (16) is modest in the paper’s geometry, yet the headline relative gains (≈30% vs AO-PGD, ≥10% vs fully-active, up to 3× vs fully-passive, and “most gain from Na≈10%”) are never re-evaluated under a true-EE objective or under the stronger RIS–user channel already considered in Fig. 4. Because the omitted noise term grows with |A| and with the amplitudes, the approximation error is systematically larger for the fully-active baseline than for a sparse hybrid design; consequently the hybrid-versus-active ranking (and, to a lesser extent, the DU-versus-PGD gap)
  2. §VI and Figs. 5–7: all quantitative claims rest on Monte Carlo simulations under perfect CSI, blocked direct links, ZF, fixed Rician factors, and a single geometry (BS–RIS–user cluster). No sensitivity study is provided for imperfect CSI, residual multiuser interference under non-ZF beamforming, or non-blocked direct links—settings that are standard stress tests for RIS EE papers and that can change both the absolute EE and the hybrid-versus-active ranking. While perfect CSI is stated as an assumption, the abstract presents the percentage gains without this caveat; at minimum the manuscript should quantify degradation under realistic CSI error or justify why the ranking is expected to be robust.
  3. §IV-B2 and Algorithm 2: the deep-unfolded PGD uses a straight-through estimator for Top-Na selection and a tanh relaxation for binary phases, with only the step sizes trained. The training protocol (400 channels, 100 epochs, J=5, Adam lr=0.01) is reported, but there is no ablation on the number of layers J, the sharpness β, or generalization to different (N,Na,P_r^max) than those used in training. Because the abstract’s “30% higher EE than the procedure without deep unfolding” is the central algorithmic claim, a short ablation confirming that the gain is not an artifact of a poorly tuned fixed-step AO-PGD baseline (or of a particular J) is needed for the claim to be load-bearing.
minor comments (6)
  1. Fig. 3 caption and text: the saw-tooth behavior of AO-DU/AO-PGD is attributed to alternating Dinkelbach re-solves; a short remark that the plotted EE is the true EE (16) evaluated after each outer iteration would remove ambiguity.
  2. Notation: the indicator vector is rendered as “/x31A_N” in several places (e.g., around (3)); this appears to be a LaTeX encoding artifact and should be corrected to the standard 1_A notation.
  3. §III-B1, power model: the claim that user power is omitted “similarly to [35]” is fine, but a one-sentence note that adding a constant user-circuit term would not change the optimizers would help readers who include it by default.
  4. Related work (§II): several recent hybrid-RIS EE papers that already optimize mode switching (e.g., [12], [14], [15]) are cited; a clearer one-sentence contrast of what is new (joint binary-phase + Top-Na deep unfolding under the exact power model) would sharpen the novelty statement.
  5. Algorithm 3 complexity: the O(S J K N²) claim is reasonable for large N, but a brief wall-clock comparison (or FLOPs count) against AO-PGD and PGA on the same hardware would make the “faster convergence” claim more concrete.
  6. Typos / polish: “efficiency” consistently uses a special f ligature that may break search; “amplified” vs “amplification” wording around (8)–(9) is slightly inconsistent; “nearly fourfold improvement over the PGA-based method” in the contributions list is stronger than the abstract’s wording and should be aligned with the actual figure values.

Circularity Check

0 steps flagged

No significant circularity: standard AO + deep-unrolling algorithm whose numerical EE gains are simulation outcomes, not quantities forced by definition or self-citation.

full rationale

This is a model-driven optimization paper. The EE objective (11)/(16), power model (7)–(10), ZF reformulation (12)–(15), Dinkelbach power allocation (Algorithm 1), and projected-gradient RIS update (27)–(28) are derived from first principles under stated assumptions; the only approximation is the explicit surrogate fEE (17) that drops the active-RIS noise term and replaces Pr by its budget ceiling. That surrogate is justified by a low-power argument and checked against true EE in Fig. 4; it is not used to redefine the reported metric. Deep unfolding (Algorithm 2) simply learns the step-size sequence of the same PGD map that is later run at inference; the training loss L = f(Φ^(J)) is the identical objective, which is ordinary supervised unrolling rather than a self-definitional prediction. Self-citations ([1], [8], [20], [22], [33]) supply prior hybrid-RIS architecture and unfolding context but do not underwrite uniqueness claims or force the numerical ranking of AO-DU versus AO-PGD / fully-active / fully-passive. Consequently the central quantitative claims remain independent simulation results, not tautologies of the inputs. Score 1 only for the minor presence of overlapping-author citations that are non-load-bearing.

Axiom & Free-Parameter Ledger

5 free parameters · 7 axioms · 0 invented entities

The central numerical claims rest on standard wireless modeling choices (perfect CSI, blocked direct links, ZF, Rician geometry), an ad-hoc EE surrogate that freezes RIS dynamic power at its budget and drops RIS noise from SINR, and several training/algorithm hyperparameters (unfolded depth, step-size init, STE/Top-Na, β). No new physical entity is postulated; hybrid RIS and deep unfolding are taken from prior work. Free parameters are algorithmic/training knobs and simulation scenario numbers, not fitted physical constants.

free parameters (5)
  • Unfolded layer count J and outer AO iterations S
    J=5 and S=20 (with I=2) are chosen by the authors; reported convergence and the 30% gain are measured at these depths and would change with different unrolling budgets.
  • Learnable PGD step sizes {η_Φ^(j)} and initial η_Φ=0.5
    Step sizes are trained (Adam lr 0.01, 400 channels, 100 epochs); the performance edge over AO-PGD is exactly the value of these fitted steps.
  • Phase-relaxation sharpness β and STE Top-Na
    β and the straight-through estimator for active-set selection are design knobs that make discrete variables differentiable; they are not derived from first principles.
  • Power-sharing coefficient τ and scenario budgets (P_t^max, P_r^max, Na, N, M, K)
    Default N=100, Na=60, P_t^max=30 dBm, P_r^max=-10 dBm, M=8, K=4 and the τ sweep define the operating point where the 10%/3×/80%-at-Na=10 claims are measured.
  • QoS barrier weights ω_k in the PGA baseline
    Penalty weights in (34) affect the PGA benchmark strength; values are not fully specified beyond positivity.
axioms (7)
  • domain assumption Perfect CSI of BS–RIS and RIS–user channels is available at the BS.
    Stated in §III-A and simulation setup; all beamforming and RIS designs use true channels. Practical CSI acquisition for RIS is acknowledged as challenging but not modeled.
  • domain assumption Direct BS–user links are fully blocked; communication is only via the hybrid RIS.
    §III-A system model; simplifies the cascaded channel and favors RIS-centric designs.
  • domain assumption Zero-forcing beamforming F = H† P^{1/2} is used, canceling multiuser interference.
    §IV before (12); reduces SINR to a power-over-noise form and enables closed-form Dinkelbach power allocation, at the cost of possible suboptimality vs. general beamforming.
  • ad hoc to paper Active-RIS noise in SINR is negligible and Pr may be replaced by P_r^max in the EE denominator (surrogate fEE).
    §IV-A, equations (16)–(17); justified by low-power RIS arguments and partially checked in Fig. 4, but is load-bearing for tractability of the AO split.
  • domain assumption Binary phase shifts θ_n ∈ {0,π} and fixed active cardinality |A|=Na.
    Hardware constraints (11f)–(11g); standard low-resolution RIS modeling, with continuous relaxation only inside training.
  • domain assumption Channels are quasi-static Rician with factor 4 and path-loss exponent 2; noise and circuit powers take the listed dBm values.
    §VI simulation setup; defines the numerical regime of all EE curves.
  • standard math Dinkelbach iteration and KKT conditions yield the global optimum of the convex power-allocation subproblem (20).
    Standard fractional programming / convex optimization; Algorithm 1.

pith-pipeline@v1.1.0-grok45 · 25882 in / 4233 out tokens · 34638 ms · 2026-07-11T11:53:12.290803+00:00 · methodology

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read the original abstract

We address energy-efficiency (EE) maximization in a multiuser (MU) multiple-input single-output (MISO) downlink system assisted by a hybrid reconfigurable intelligent surface(RIS), where each element can be dynamically configured to operate in either active or passive mode depending on whether its power amplifier is engaged. Practical hardware effects are explicitly incorporated, including base station (BS) and RIS power budgets, active-element amplifier gain limits, amplification noise, and binary phase control. To solve the problem, we develop an alternating-optimization framework in which the BS beamforming subproblem is handled via zero-forcing with closed-form power allocation, while the RIS subproblem is addressed using a model-driven deep unfolding approach. Numerical results show that the proposed method achieves faster convergence and higher EE than the considered benchmark schemes. In particular, it attains about 30% higher EE than the procedure without deep unfolding. Furthermore, our simulations demonstrate at least 10% EE improvement over the fully active RIS configuration and up to threefold EE gains compared with the fully passive RIS design. The results also show that most of the achievable EE gain can be captured by activating only a small fraction of RIS elements and allocating only a small portion of the dynamic power budget to the RIS.

Figures

Figures reproduced from arXiv: 2607.04889 by Abolfazl Zakeri, Marco Di Renzo, Markku Juntti, Nhan Thanh Nguyen, Pouya Mobaraki.

Figure 1
Figure 1. Figure 1: Considered hybrid RIS-assisted MU-MISO downlink system. of standard gradient-based deep unfolding steps due to their non-differentiability. This is the gap addressed in this work. III. System Model and Problem Formulation A. System Model We consider a hybrid RIS-assisted MU-MISO downlink system, as illustrated in [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Overall structure of the proposed algorithm. Algorithm 2 Proposed Deep Unfolded PGD for hybrid RIS Optimization Subproblem (26) Require: Ht, Hr, P, trained step sizes {η (j) Φ } J−1 j=0 1: for j = 0, . . . , J − 1 do 2: Compute gradient step: Φ˜ ← Φ (j) − η (j) Φ ∇Φf ( Φ (j) ) 3: Extract phases { ˜θn} and amplitudes {α˜n} from Φ˜ 4: Update each phase ˜θn according to (29), ∀n ∈ N 5: Select the set A (j+1) … view at source ↗
Figure 3
Figure 3. Figure 3: shows the convergence behavior of the solution algorithms for problem (11). It is observed that the proposed AO-DU method converges faster and achieves higher EE than AO-PGD and PGA. In particular, it yields a sharp increase in EE during the initial iterations and reaches a higher convergence point within fewer iterations. In contrast, the PGA method shows the slowest convergence and attains the lowest EE.… view at source ↗
Figure 4
Figure 4. Figure 4: compares the proposed approximation EEf in (17) with the exact EE in (16) for different values of the maxi￾mum RIS amplification power budget P max r . Here, the EE values are obtained based on the solution in Algorithm 3. It is seen that the approximate EE closely follows the exact EE over the whole considered range of P max r , confirming the tightness of the approximation. To further examine this, we al… view at source ↗
Figure 6
Figure 6. Figure 6: EE versus the power-sharing coefficient τ under a fixed total dynamic power budget (BS and RIS combined). scheme achieves the best performance in both figures over the whole considered transmit power range. The Fixed scheme performs worse, which highlights the importance of optimizing the active-element positions. The Fully-Active scheme is also inferior to the proposed AO-DU design, although it performs b… view at source ↗
Figure 7
Figure 7. Figure 7: EE and SE versus the BS transmit power budget for different RIS configurations with N = 100 elements. Appendix A Proof of Lemma 1 We first compute the gradient of EE by applying the chain rule, which gives ∇FEE = ∇FSE · Ptot − SE · ∇FPtot (Ptot) 2 (49) ∇ΦEE = ∇ΦSE · Ptot − SE · ∇ΦPtot (Ptot) 2 (50) To derive the gradient of SE, we first obtain the gradient of SEk and then sum the resulting per-user gradien… view at source ↗

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Reference graph

Works this paper leans on

43 extracted references · 1 canonical work pages

  1. [1]

    Deep unfolding- empowered energy efficiency optimization in RIS-assisted wireless communications,

    P. Mobaraki, N. T. Nguyen, and M. Juntti, “Deep unfolding- empowered energy efficiency optimization in RIS-assisted wireless communications,” ser. IoT ’24, Oulu, Finland, 2025, p. 238–243. [Online]. A vailable: https://doi.org/10.1145/3703790. 3703830

    work page doi:10.1145/3703790 2025

  2. [2]

    Radio localization and mapping with reconfigurable intelligent surfaces: Challenges, opportunities, and research directions,

    H. Wymeersch, J. He, B. Denis, A. Clemente, and M. Juntti, “Radio localization and mapping with reconfigurable intelligent surfaces: Challenges, opportunities, and research directions,” IEEE Veh. Technol. Mag., vol. 15, no. 4, pp. 52–61, Dec. 2020

    2020

  3. [3]

    Reconfigurable intelligent surfaces in 6G radio localization: A survey of recent developments, opportunities, and challenges,

    A. Umer, I. Müürsepp, M. M. Alam, and H. Wymeersch, “Reconfigurable intelligent surfaces in 6G radio localization: A survey of recent developments, opportunities, and challenges,” IEEE Commun. Surveys Tuts., vol. 27, no. 6, pp. 3526–3560, Dec. 2025

    2025

  4. [4]

    Smart radio environments empowered by reconfigurable intelligent surfaces: How it works, state of research, and the road ahead,

    M. Di Renzo, A. Zappone, M. Debbah, M.-S. Alouini, C. Yuen, J. de Rosny, and S. Tretyakov, “Smart radio environments empowered by reconfigurable intelligent surfaces: How it works, state of research, and the road ahead,” IEEE J. Sel. Areas Commun., vol. 38, no. 11, pp. 2450–2525, Nov. 2020

    2020

  5. [5]

    Reconfigurable intelligent surfaces for energy efficiency in wireless communication,

    C. Huang, A. Zappone, G. C. Alexandropoulos, M. Debbah, and C. Yuen, “Reconfigurable intelligent surfaces for energy efficiency in wireless communication,” IEEE Trans. Wireless Commun., vol. 18, no. 8, pp. 4157–4170, Aug. 2019

    2019

  6. [6]

    Active RIS vs. passive RIS: Which will prevail in 6G?

    Z. Zhang, L. Dai, X. Chen, C. Liu, F. Yang, R. Schober, and H. V. Poor, “Active RIS vs. passive RIS: Which will prevail in 6G?” IEEE Trans. Commun., vol. 71, no. 3, pp. 1707–1725, Mar. 2023

    2023

  7. [7]

    Active reconfig- urable intelligent surface: Fully-connected or sub-connected?

    K. Liu, Z. Zhang, L. Dai, S. Xu, and F. Yang, “Active reconfig- urable intelligent surface: Fully-connected or sub-connected?” IEEE Commun. Lett., vol. 26, no. 1, pp. 167–171, Jan. 2022

    2022

  8. [8]

    Hybrid relay- reflecting intelligent surface-assisted wireless communications,

    N. T. Nguyen, Q.-D. Vu, K. Lee, and M. Juntti, “Hybrid relay- reflecting intelligent surface-assisted wireless communications,” IEEE Trans. Veh. Technol., vol. 71, no. 6, pp. 6228–6244, Jun. 2022

    2022

  9. [9]

    Efficient power allocation strategies in hybrid active-passive reconfigurable intelligent surfaces,

    D. V. Q. Rodrigues and T. Singh, “Efficient power allocation strategies in hybrid active-passive reconfigurable intelligent surfaces,” IEEE Commun. Lett., vol. 28, no. 1, pp. 113–117, Jan. 2024

    2024

  10. [10]

    Energy- efficient cell-free network assisted by hybrid RISs,

    W. Lyu, Y. Xiu, S. Yang, C. Yuen, and Z. Zhang, “Energy- efficient cell-free network assisted by hybrid RISs,” IEEE Wire- less Commun. Lett., vol. 12, no. 4, pp. 718–722, Apr. 2023

    2023

  11. [11]

    Energy-efficient beamforming optimization for hybrid-RIS-aided massive MIMO networks,

    D. Choudhury and A. K. Sah, “Energy-efficient beamforming optimization for hybrid-RIS-aided massive MIMO networks,” IEEE Trans. Veh. Technol., pp. 1–13, 2026

    2026

  12. [12]

    Hybrid active-passive RIS transmitter-enabled energy-efficient multi-user communi- cations,

    A. Huang, X. Mu, L. Guo, and G. Zhu, “Hybrid active-passive RIS transmitter-enabled energy-efficient multi-user communi- cations,” IEEE Trans. Wireless Commun., vol. 23, no. 9, pp. 10 653–10 666, Sep. 2024

    2024

  13. [13]

    Distributed hybrid active-passive RIS-assisted THz wireless systems: Performance analysis and optimization,

    N. P. Le and M.-S. Alouini, “Distributed hybrid active-passive RIS-assisted THz wireless systems: Performance analysis and optimization,” IEEE Trans. Commun., vol. 73, no. 2, pp. 1399– 1414, Feb. 2025

    2025

  14. [14]

    Energy efficiency optimization for hybrid active-passive RIS-aided com- munications: A novel dynamic subarray-based architecture,

    S. Xie, S. Gong, H. Liu, T. Yu, N. Zhao, and C. Xing, “Energy efficiency optimization for hybrid active-passive RIS-aided com- munications: A novel dynamic subarray-based architecture,” IEEE Trans. Wireless Commun., vol. 25, pp. 8228–8245, 2025

    2025

  15. [15]

    Hybrid active-passive IRS-assisted energy-efficient wireless communica- tion,

    Q. Peng, Q. Wu, G. Chen, R. Liu, S. Ma, and W. Chen, “Hybrid active-passive IRS-assisted energy-efficient wireless communica- tion,” IEEE Commun. Lett., vol. 27, no. 8, pp. 2202–2206, Aug. 2023

    2023

  16. [16]

    Deep unfolding: Model-based inspiration of novel deep architectures,

    J. R. Hershey, J. Le Roux, and F. Weninger, “Deep unfolding: Model-based inspiration of novel deep architectures,” arXiv preprint arXiv:1409.2574, Sep. 2014

    Pith/arXiv arXiv 2014

  17. [17]

    Deep unfolding: Recent developments, theory, and design guidelines,

    N. Shlezinger, S. Segarra, Y. Zhang, D. A vrahami, Z. Davidov, T. Routtenberg, and Y. C. Eldar, “Deep unfolding: Recent developments, theory, and design guidelines,” arXiv preprint arXiv:2512.03768, Mar. 2025

    arXiv 2025

  18. [18]

    Beamform- ing optimization for hybrid active-passive RIS-assisted wire- less communications: A rate-maximization perspective,

    Y. Ju, S. Gong, H. Liu, C. Xing, J. An, and Y. Li, “Beamform- ing optimization for hybrid active-passive RIS-assisted wire- less communications: A rate-maximization perspective,” IEEE Trans. Commun., vol. 72, no. 9, pp. 5428–5442, Sep. 2024

    2024

  19. [19]

    Active-passive IRS-aided wire- less communication: New hybrid architecture and elements allo- cation optimization,

    Z. Kang, C. You, and R. Zhang, “Active-passive IRS-aided wire- less communication: New hybrid architecture and elements allo- cation optimization,” IEEE Trans. Wireless Commun., vol. 23, no. 4, pp. 3450–3464, Apr. 2024

    2024

  20. [20]

    Fairness enhancement of UA V systems with hybrid active-passive RIS,

    N. T. Nguyen, V.-D. Nguyen, H. Van Nguyen, Q. Wu, A. Tölli, S. Chatzinotas, and M. Juntti, “Fairness enhancement of UA V systems with hybrid active-passive RIS,” IEEE Trans. Wireless Commun., vol. 23, no. 5, pp. 4379–4396, May 2024

    2024

  21. [21]

    Exploring hybrid active-passive RIS- aided MEC systems: From the mode-switching perspective,

    H. Xie, D. Li, and B. Gu, “Exploring hybrid active-passive RIS- aided MEC systems: From the mode-switching perspective,” IEEE Trans. Wireless Commun., vol. 23, no. 9, pp. 11 291– 11 308, Sep. 2024

    2024

  22. [22]

    Hybrid active-passive reconfigurable intelli- gent surface-assisted multi-user MISO systems,

    N. T. Nguyen, V.-D. Nguyen, Q. Wu, A. Tölli, S. Chatzinotas, and M. Juntti, “Hybrid active-passive reconfigurable intelli- gent surface-assisted multi-user MISO systems,” in Proc. IEEE Works. on Sign. Proc. Adv. in Wirel. Comms., Oulu, Finland, Jul. 2022, pp. 1–5

    2022

  23. [23]

    Spectral–energy efficiency tradeoff of nearly- passive RIS in mimo urllc downlink: Diagonal versus beyond diagonal,

    M. Soleymani, A. Zappone, E. Jorswieck, M. Di Renzo, and I. Santamaria, “Spectral–energy efficiency tradeoff of nearly- passive RIS in mimo urllc downlink: Diagonal versus beyond diagonal,” IEEE Wireless Commun. Lett., vol. 15, pp. 890–894, Dec. 2025

    2025

  24. [24]

    Energy efficiency optimization in RIS-aided wireless networks: Active versus nearly-passive RIS with global reflection constraints,

    R. K. Fotock, A. Zappone, and M. Di Renzo, “Energy efficiency optimization in RIS-aided wireless networks: Active versus nearly-passive RIS with global reflection constraints,” IEEE Trans. Commun., vol. 72, no. 1, pp. 257–272, Jan. 2024

    2024

  25. [25]

    Online RIS configuration learning for arbitrary large numbers of 1-bit phase resolution elements,

    K. Stylianopoulos and G. C. Alexandropoulos, “Online RIS configuration learning for arbitrary large numbers of 1-bit phase resolution elements,” in Proc. IEEE Works. on Sign. Proc. Adv. in Wirel. Comms., Oulu, Finland, Jul. 2022, pp. 1–5

    2022

  26. [26]

    Quantized phase alignment by discrete phase shifts for reconfigurable intelligent surface-assisted communication systems,

    J. Sang, J. Lan, M. Zhou, B. Gao, W. Tang, X. Li, X. Yi, and S. Jin, “Quantized phase alignment by discrete phase shifts for reconfigurable intelligent surface-assisted communication systems,” IEEE Trans. Veh. Technol., vol. 73, no. 4, pp. 5259– 5275, Apr. 2024

    2024

  27. [27]

    On the optimal number of reflecting elements for reconfigurable intelligent surfaces,

    A. Zappone, M. Di Renzo, X. Xi, and M. Debbah, “On the optimal number of reflecting elements for reconfigurable intelligent surfaces,” IEEE Wireless Communications Letters, vol. 10, no. 3, pp. 464–468, Mar. 2021

    2021

  28. [28]

    Hybrid active- passive RIS-empowered secure communications: Joint archi- tecture design and beamforming optimization,

    S. Gong, Y. Ju, H. Liu, L. Liu, and C. Xing, “Hybrid active- passive RIS-empowered secure communications: Joint archi- tecture design and beamforming optimization,” IEEE Trans. Commun., vol. 73, no. 7, pp. 5094–5110, Jul. 2025

    2025

  29. [29]

    AI-empowered RIS-assisted NOMA networks: Deep learning or reinforcement learning?

    R. Zhong, Y. Liu, X. Mu, Y. Chen, and L. Song, “AI-empowered RIS-assisted NOMA networks: Deep learning or reinforcement learning?” IEEE J. Sel. Areas Commun., vol. 40, no. 1, pp. 182–196, Jan. 2022

    2022

  30. [30]

    Deep learning-based rate-splitting multiple access for reconfigurable intelligent surface-aided tera-hertz massive MIMO,

    M. Wu, Z. Gao, Y. Huang, Z. Xiao, D. W. K. Ng, and Z. Zhang, “Deep learning-based rate-splitting multiple access for reconfigurable intelligent surface-aided tera-hertz massive MIMO,” IEEE J. Sel. Areas Commun., vol. 41, no. 5, pp. 1431– 1451, May 2023

    2023

  31. [31]

    Deep unfolding for communications systems: A survey and some new directions,

    A. Balatsoukas-Stimming and C. Studer, “Deep unfolding for communications systems: A survey and some new directions,” in Proc. IEEE Workshop Signal Process. Syst. (SiPS), Nanjing, China, Oct. 2019, pp. 266–271

    2019

  32. [32]

    Joint design for RIS-aided ISAC via deep unfolding learning,

    J. Zhang, M. Liu, J. Tang, N. Zhao, D. Niyato, and X. Wang, “Joint design for RIS-aided ISAC via deep unfolding learning,” IEEE Trans. on Cogn. Commun. Netw., vol. 11, no. 1, pp. 349– 361, Feb. 2025

    2025

  33. [33]

    Joint communications and sensing hybrid beamforming design via deep unfolding,

    N. T. Nguyen, L. V. Nguyen, N. Shlezinger, Y. C. Eldar, A. L. Swindlehurst, and M. Juntti, “Joint communications and sensing hybrid beamforming design via deep unfolding,” IEEE J. Sel. Topics Signal Process., vol. 18, no. 5, pp. 901–916, Jul. 2024

    2024

  34. [34]

    Active RIS versus passive RIS: Which is superior with the same power budget?

    K. Zhi, C. Pan, H. Ren, K. K. Chai, and M. Elkashlan, “Active RIS versus passive RIS: Which is superior with the same power budget?” IEEE Commun. Lett., vol. 26, no. 5, pp. 1150–1154, May 2022

    2022

  35. [35]

    Hybrid RIS with sub-connected active partitions: Performance analysis and transmission design,

    K. Ntougias, S. Chatzinotas, and I. Krikidis, “Hybrid RIS with sub-connected active partitions: Performance analysis and transmission design,” IEEE Trans. Wireless Commun., vol. 24, no. 8, pp. 6705–6721, Aug. 2025

    2025

  36. [36]

    On nonlinear fractional programming,

    W. Dinkelbach, “On nonlinear fractional programming,” Man- agement Science, vol. 13, no. 7, pp. 492–498, 1967

    1967

  37. [37]

    The matrix cookbook,

    K. B. Petersen, M. S. Pedersen et al., “The matrix cookbook,” Technical University of Denmark, p. 510, 2008

    2008

  38. [38]

    S. P. Boyd and L. Vandenberghe, Convex optimization. Cam- bridge University Press, 2004

    2004

  39. [39]

    Comprehensive review of deep unfolding tech- 14 niques for next-generation wireless communication systems,

    S. Deka, K. Deka, N. T. Nguyen, S. Sharma, V. Bhatia, and N. Rajatheva, “Comprehensive review of deep unfolding tech- 14 niques for next-generation wireless communication systems,” arXiv preprint arXiv:2502.05952, Feb. 2025

    arXiv 2025

  40. [40]

    Understanding top- k sparsification in distributed deep learning,

    S. Shi, X. Chu, K. C. Cheung, and S. See, “Understanding top- k sparsification in distributed deep learning,” arXiv preprint arXiv:1911.08772, Nov. 2019

    Pith/arXiv arXiv 1911

  41. [41]

    Estimating or prop- agating gradients through stochastic neurons for conditional computation,

    Y. Bengio, N. Léonard, and A. Courville, “Estimating or prop- agating gradients through stochastic neurons for conditional computation,” arXiv preprint arXiv:1308.3432, Aug. 2013

    Pith/arXiv arXiv 2013

  42. [42]

    Un- derstanding straight-through estimator in training activation- quantized neural nets,

    P. Yin, J. Lyu, S. Zhang, S. Osher, Y. Qi, and J. Xin, “Un- derstanding straight-through estimator in training activation- quantized neural nets,” arXiv preprint arXiv:1903.05662, Mar. 2019

    Pith/arXiv arXiv 1903

  43. [43]

    Hjørungnes, Complex-valued matrix derivatives: With appli- cations in signal processing and communications

    A. Hjørungnes, Complex-valued matrix derivatives: With appli- cations in signal processing and communications. Cambridge University Press, 2011

    2011