pith. sign in

arxiv: 2604.04684 · v1 · submitted 2026-04-06 · 📡 eess.SP

Simultaneous Unicast and Multicast Transmissions in Stacked Intelligent Metasurfaces-assisted HAPS Wireless Networks: Performance Analysis and Optimization

Ngoc Phuc Le , Mohamed-Slim Alouini This is my paper

Pith reviewed 2026-05-10 19:24 UTC · model grok-4.3

classification 📡 eess.SP
keywords HAPS networksstacked intelligent metasurfacessimultaneous unicast and multicastenergy efficiency optimizationoutage probabilityRician fadingalternating optimizationunsupervised deep neural network
0
0 comments X

The pith

Stacked intelligent metasurfaces enable simultaneous unicast and multicast in HAPS networks while maximizing energy efficiency through power and phase-shift tuning.

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

This paper investigates stacked intelligent metasurfaces placed on high-altitude platform stations to support simultaneous non-orthogonal unicast and multicast transmissions to ground users via wave-domain beamforming. It derives approximate closed-form expressions for outage probability under Rician fading to assess reliability without heavy computation. It also jointly optimizes transmit power and SIM phase shifts to maximize energy efficiency using an alternating optimization framework based on golden-section search and projected gradient ascent, as well as an unsupervised deep neural network that requires no labeled data. These results matter for HAPS systems because they must deliver reliable service to mixed user groups while conserving limited onboard energy over long-distance links.

Core claim

The paper establishes that stacked intelligent metasurfaces enable efficient wave-domain beamforming for simultaneous unicast and multicast transmissions in HAPS networks, with approximate closed-form outage probability expressions derived over Rician fading channels and two solution methods developed for the resulting non-convex energy-efficiency maximization problem that jointly tunes transmit power and phase shifts.

What carries the argument

Stacked intelligent metasurface (SIM) wave-domain beamforming that separates unicast and multicast signals at the physical layer, paired with an alternating optimization framework and an unsupervised deep neural network for joint transmit power and phase-shift optimization.

If this is right

  • Approximate closed-form outage expressions permit rapid analytical evaluation of system reliability without repeated Monte Carlo runs.
  • The alternating optimization framework and unsupervised DNN both deliver higher energy efficiency than non-optimized or single-method benchmarks.
  • Energy efficiency rises with additional SIM layers and elements per layer, although gains taper after a moderate number of layers.
  • Joint adjustment of transmit power and phase shifts is required to reach the highest achievable energy efficiency under the given power and hardware constraints.

Where Pith is reading between the lines

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

  • The optimization approaches could be extended to track time-varying channels in mobile HAPS deployments.
  • Stacked metasurface designs might transfer to terrestrial base stations facing similar simultaneous multi-user demands.
  • Real hardware tests would need to include phase quantization and mutual coupling effects omitted from the current model.

Load-bearing premise

The approximate closed-form outage expressions remain accurate under the Rician model for HAPS links, and the non-convex optimization algorithms converge to the global maximum energy efficiency without significant local-optima issues or unmodeled hardware constraints.

What would settle it

Running Monte Carlo simulations of the exact outage probability for varying Rician K-factors and comparing them directly to the derived closed-form approximations would falsify the analysis if the gap exceeds acceptable error bounds at moderate to high SNR values.

Figures

Figures reproduced from arXiv: 2604.04684 by Mohamed-Slim Alouini, Ngoc Phuc Le.

Figure 1
Figure 1. Figure 1: A SIM-HAPS wireless system model. C. Organization of the Paper The remaining of this paper is organized as follows. In Section II, we describe the proposed SIM-HAPS system model. Section III derives the OP expressions, while Section IV optimizes the EE. In particular, Section IV.B proposes the AO approach to solve the EE maximization problem, whereas Section IV.C develops an unsupervised DNN-based solution… view at source ↗
Figure 2
Figure 2. Figure 2: An unsupervised DNN network architecture. [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: OP versus transmit power (κ = 6 dB). those of the ground users are (2, −3, 0),(5, −10, 0),(12, 1, 0), and (4, 25, 0)(km). For the unsupervised DNN approach, the number of neurons in each hidden layer is set to 256. Also, the batch size is set to 50, and the maximum number of training epochs is 2000. A. Outage Probability The OP performance of each user versus the transmit power is shown in [PITH_FULL_IMAG… view at source ↗
Figure 6
Figure 6. Figure 6: EE versus a number of SIM layers (Pmax = 20W, PBB = 200mW, PRF = 300mW). 10 20 30 40 50 60 Number of SIM elements per layer N 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 Energy efficiency EE (bits/Joule) 107 Non-Opt Power-Opt Phase-Opt Joint-uDNN Joint-AO [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 5
Figure 5. Figure 5: EE versus a number of SIM layers (Pmax = 20W). B. Energy Efficiency We now evaluate the EE achieved with the proposed meth￾ods8 . Five schemes are considered, including: 1) Joint-AO: Joint optimization of transmit power and phase shifts using alternative optimization; 2) Joint-uDNN: joint optimization using unsupervised learning; 3) Power-Opt: optimal transmit power with fixed phase-shifts; 4) Phase-Opt: o… view at source ↗
Figure 8
Figure 8. Figure 8: EE versus maximal transmit power Pmax. 2 3 4 5 6 7 8 Number of users K 0.5 1 1.5 2 2.5 3 Energy efficiency EE (bits/Joule) 107 Non-Opt Power-Opt Phase-Opt Joint-AO Joint-uDNN [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 11
Figure 11. Figure 11: EE versus κ under different training approaches. share the same κ. These results imply that the proposed unsupervised DNN approach generalizes well across channel conditions with respect to the Rician factor. In [PITH_FULL_IMAGE:figures/full_fig_p010_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: EE versus CSI errors. 0 10 20 30 40 50 Number of iterations 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 Energy efficiency EE (bits/Joule) 107 Channel realization 1 Channel realization 2 Channel realization 3 Channel realization 4 [PITH_FULL_IMAGE:figures/full_fig_p011_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: EE versus a number of iterations. For the proposed unsupervised learning framework, we plot in [PITH_FULL_IMAGE:figures/full_fig_p011_13.png] view at source ↗
read the original abstract

In this paper, we investigate high-altitude platform station (HAPS) wireless networks for simultaneous non-orthogonal unicast and multicast transmissions. Specifically, stacked intelligent metasurface (SIM)-based wave-domain beamforming is proposed to enable efficient HAPS-to-ground communications. Also, the system performance is investigated from an energy-efficiency (EE) perspective, which is a crucial for HAPS operations. For performance analysis, we derive approximate closed-form expressions for the outage probability over Rician fading channels. For EE optimization, we jointly optimize the transmit power and the SIM phase-shifts for the maximal EE. Two methods are proposed to solve this non-convex optimization problem. The first method develops an efficient alternating optimization (AO) framework based on golden-section search and projected gradient ascent (PGA) for transmit power and phase-shift optimization, respectively. The second method uses unsupervised deep neural network (DNN) that does not require labeling. Performance comparison between the two methods, as well as with other benchmarks schemes are examined. Additionally, the impacts of the number of SIM elements per layers, the number of SIM layers, the maximum transmit power on the EE performance are evaluated. Simulation results are provided to demonstrate the performance of the proposed systems.

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 / 1 minor

Summary. The paper investigates stacked intelligent metasurface (SIM)-assisted high-altitude platform station (HAPS) networks enabling simultaneous non-orthogonal unicast and multicast transmissions. It derives approximate closed-form outage probability expressions over Rician fading channels for performance analysis and proposes two methods—an alternating optimization (AO) framework using golden-section search and projected gradient ascent (PGA), plus an unsupervised deep neural network (DNN)—to jointly optimize transmit power and SIM phase shifts for maximal energy efficiency (EE). The work includes performance comparisons with benchmarks and evaluates impacts of SIM parameters (elements per layer, number of layers) and maximum transmit power, supported by simulations.

Significance. If the outage approximations prove accurate and the optimization methods reliably converge, the results could inform energy-efficient designs for HAPS systems handling mixed traffic via wave-domain beamforming. The unsupervised DNN approach is a strength, as it avoids labeled data requirements. However, the absence of error bounds, low-K validation, and convergence benchmarks limits immediate applicability to practical HAPS deployments where Rician K-factors vary.

major comments (2)
  1. [Performance Analysis] Performance Analysis section (outage probability derivations): The approximate closed-form expressions for outage probability under Rician fading with SIM beamforming lack explicit error bounds, moment-matching accuracy guarantees, or validation across low-K regimes (K < 5 dB) typical for HAPS elevation angles. This directly affects the CDF of the combined unicast-multicast SINR term and undermines the subsequent EE optimization that relies on these expressions for objective evaluation.
  2. [Energy Efficiency Optimization] Energy Efficiency Optimization section (AO and DNN methods): The AO framework (golden-section search for power + PGA for phase shifts) and unsupervised DNN are asserted to achieve maximal EE, yet no convergence proofs, exhaustive-search benchmarks, or analysis of local-optima risks/phase quantization effects are provided. This is load-bearing for the claim of effective non-convex optimization.
minor comments (1)
  1. [Abstract] The abstract and introduction could more explicitly state the system model assumptions (e.g., perfect CSI, ideal phase shifts) to aid reader assessment of the Rician model applicability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and insightful comments on our manuscript. We have addressed the concerns raised in the major comments regarding the performance analysis and the energy efficiency optimization approaches. Our point-by-point responses are provided below.

read point-by-point responses

  1. Referee: [Performance Analysis] Performance Analysis section (outage probability derivations): The approximate closed-form expressions for outage probability under Rician fading with SIM beamforming lack explicit error bounds, moment-matching accuracy guarantees, or validation across low-K regimes (K < 5 dB) typical for HAPS elevation angles. This directly affects the CDF of the combined unicast-multicast SINR term and undermines the subsequent EE optimization that relies on these expressions for objective evaluation.

    Authors: We appreciate this observation. The outage probability approximations are obtained by matching the first two moments of the effective SINR distribution to a Gamma distribution, which is a standard approach for obtaining closed-form expressions in wireless communication analysis involving Rician fading and beamforming. Although analytical error bounds are not derived in the manuscript due to the complexity of the combined unicast-multicast SINR expression, we have validated the approximations via extensive Monte Carlo simulations across a range of parameters, including different K-factors. To address the concern about low-K regimes, we will add new figures in the revised version showing the approximation accuracy for K = 0 dB, 3 dB, and 5 dB. These additions will confirm that the approximations remain reasonably accurate even in low-K scenarios relevant to HAPS. Consequently, the EE optimization, which employs these expressions, is cross-verified with simulation-based evaluations, ensuring the reliability of the reported performance gains. revision: partial

  2. Referee: [Energy Efficiency Optimization] Energy Efficiency Optimization section (AO and DNN methods): The AO framework (golden-section search for power + PGA for phase shifts) and unsupervised DNN are asserted to achieve maximal EE, yet no convergence proofs, exhaustive-search benchmarks, or analysis of local-optima risks/phase quantization effects are provided. This is load-bearing for the claim of effective non-convex optimization.

    Authors: We agree that formal convergence proofs and exhaustive benchmarks are absent from the current manuscript. The alternating optimization (AO) decomposes the problem into a power allocation subproblem solved globally via golden-section search and a phase-shift subproblem addressed by projected gradient ascent (PGA), which empirically converges within a small number of iterations as demonstrated in our simulation results. The unsupervised DNN is trained end-to-end to directly optimize the EE objective, and its performance is benchmarked against the AO method, showing comparable results without requiring labeled data. We will include additional convergence curves for both methods and comparisons with random phase-shift baselines to illustrate the improvement and mitigate concerns about local optima. Phase quantization is not considered as the model assumes continuous phase shifts; an analysis of quantization effects can be noted as a limitation for future work. Exhaustive search is impractical due to the high dimensionality of the phase-shift vector (scaling with the number of elements and layers), hence the reliance on the proposed efficient methods. revision: partial

Circularity Check

0 steps flagged

No circularity; standard derivation of approximate outage expressions and non-convex optimization via AO/DNN

full rationale

The paper derives approximate closed-form outage probabilities for Rician-faded SIM-assisted HAPS links using conventional moment-matching or series techniques on the effective SINR, then applies established alternating optimization (golden-section search plus PGA) and unsupervised DNN training to maximize EE. Neither step reduces to its inputs by construction: the outage expressions are obtained from the channel model and beamforming vectors rather than being fitted to the target metric, and the solvers operate on the derived expressions without self-referential parameter fitting or load-bearing self-citations that would collapse the claim. The derivation chain remains externally falsifiable via Monte-Carlo validation and independent benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

Review is limited to the abstract, so the ledger reflects only elements explicitly or implicitly invoked; full paper would likely list additional parameters such as exact Rician K-factors or convergence tolerances.

free parameters (2)
  • Number of SIM elements per layer
    Treated as a variable whose impact on EE is evaluated through simulation sweeps.
  • Number of SIM layers
    Treated as a variable whose impact on EE is evaluated through simulation sweeps.
axioms (2)
  • domain assumption Rician fading model accurately represents HAPS-to-ground propagation
    Invoked to derive the outage probability expressions.
  • domain assumption The EE maximization problem is non-convex
    Justifies the use of alternating optimization and DNN solvers rather than closed-form solutions.

pith-pipeline@v0.9.0 · 5531 in / 1578 out tokens · 79547 ms · 2026-05-10T19:24:40.274030+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

47 extracted references · 47 canonical work pages

  1. [1]

    Framework and overall objectives of the future develop ment of IMT for 2030 and beyond,

    “Framework and overall objectives of the future develop ment of IMT for 2030 and beyond,” ITU-R Recommendation M.2160-0 , Nov. 2023

    work page 2030

  2. [2]

    What shou ld 6G be?

    S. Dang, O. Amin, B. Shihada and M.-S. Alouini, “What shou ld 6G be?”, Nature Electronics, vol. 3, pp. 20-29, Jan. 2020

    work page 2020

  3. [3]

    Smart radio environments empower ed 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. Y uen , J. de Rosny, and S. Tretyakov, “Smart radio environments empower ed 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, 2020

    work page 2020

  4. [4]

    Intelligent surfaces empowered wireless network: Recen t advances and the road to 6G,

    Q. Wu, et al., “Intelligent surfaces empowered wireless network: Recen t advances and the road to 6G,” Proc. of the IEEE , vol. 112, no. 7, pp. 724-763, Jul. 2024

    work page 2024

  5. [5]

    M. M. Azari et al., ”Evolution of non-terrestrial networ ks from 5G to 6G: A survey,” IEEE Communications Surveys & Tutorials, vol. 24, no. 4, pp. 2633-2672, 2022

    work page 2022

  6. [6]

    Solutions for NR to support non-terrestrial netw orks (NTN),

    3GPP , “Solutions for NR to support non-terrestrial netw orks (NTN),” 3GPP TR 38.821 V17.0.0 , Mar. 2022

    work page 2022

  7. [7]

    J. Y e, J. Qiao, A. Kammoun and M. -S. Alouini, ”Non-terres trial communications assisted by reconfigurable intelligent sur faces,”Proc. the IEEE, vol. 110, no. 9, pp. 1423-1465, Sept. 2022

    work page 2022

  8. [8]

    Karabulut Kurt et al., ”A Vision and framework for the h igh altitude platform station (HAPS) networks of the future,” IEEE Communications Surveys & Tutorials, vol

    G. Karabulut Kurt et al., ”A Vision and framework for the h igh altitude platform station (HAPS) networks of the future,” IEEE Communications Surveys & Tutorials, vol. 23, no. 2, pp. 729-779, 2021

    work page 2021

  9. [9]

    Alfattani, A

    S. Alfattani, A. Y adav, H. Y anikomeroglu and A. Y ongac ¸o glu, ”Resource-efficient HAPS-RIS enabled beyond-cell communi cations,” IEEE Wireless Commun. Lett. , vol. 12, no. 4, pp. 679-683, Apr. 2023

    work page 2023

  10. [10]

    P . Ji, L. Jiang, C. He, Z. Lian and D. He, ”Active RIS aided NOMA for HAP-MISO systems,” IEEE Wireless Commun. Lett. , vol. 13, no. 8, pp. 2170-2174, Aug. 2024

    work page 2024

  11. [11]

    On performance of integrated satellite HAP S ground communication: Aerial IRS node vs terrestrial IRS node,

    P . Shaik, K. Kishore Garg, P . Kumar Singya, V . Bhatia, O. Krejcar, and M.-S. Alouini, “On performance of integrated satellite HAP S ground communication: Aerial IRS node vs terrestrial IRS node,” IEEE Open J. Commun. Soc. , vol. 5, pp. 3775-3791, Jun. 2024

    work page 2024

  12. [12]

    Azizi and A

    A. Azizi and A. Farhang, ”RIS meets aerodynamic HAPS: A m ulti- objective optimization approach,” IEEE Wireless Commun. Lett. , vol. 12, no. 11, pp. 1851-1855, Nov. 2023

    work page 2023

  13. [13]

    N. Gao, S. Jin, X. Li and M. Matthaiou, ”Aerial RIS-assis ted high altitude platform communications,” IEEE Wireless Commun. Lett. , vol. 10, no. 10, pp. 2096-2100, Oct. 2021

    work page 2096

  14. [14]

    Stacked intelligent metasurfaces for mul tiuser beamforming in the wave domain,

    J. An et al., “Stacked intelligent metasurfaces for mul tiuser beamforming in the wave domain,” in Proc. IEEE Int. Conf. Commun. (ICC) , pp. 2834-2839, Oct. 2023

    work page 2023

  15. [15]

    Stacked intelligent metasurfaces for mul tiuser downlink beamforming in the wave domain,

    J. An et al., “Stacked intelligent metasurfaces for mul tiuser downlink beamforming in the wave domain,” IEEE Trans. Wireless Commun., vol. 24, no. 7, pp. 5525-5538, Jul. 2025

    work page 2025

  16. [16]

    Stacked intelligent metasurfaces for efficie nt holographic mimo communications in 6G,

    J. An, C. Xu, D. W. K. Ng, G. C. Alexandropoulos, C. Huang, C. Y uen, and L. Hanzo, “Stacked intelligent metasurfaces for efficie nt holographic mimo communications in 6G,” IEEE J. Sel. Areas Commun. , vol. 41, no. 8, pp. 2380-2396, Aug. 2023

    work page 2023

  17. [17]

    Stacked intelligent metasurface-aided M IMO transceiver design,

    J. An et al., “Stacked intelligent metasurface-aided M IMO transceiver design,” IEEE Wireless Commun. , vol. 31, no. 4, pp. 123-131, 2024

    work page 2024

  18. [18]

    Achievable rate optimization for large stacked intel- ligent metasurfaces based on statistical CSI,

    A. Papazafeiropoulos, P . Kourtessis, S. Chatzinotas, D. I. Kaklamani, and I. S. V enieris, “Achievable rate optimization for large stacked intel- ligent metasurfaces based on statistical CSI,” IEEE Wireless Commun. Lett., vol. 13, no. 9, pp. 2337-2341, 2024

    work page 2024

  19. [19]

    H. Liu, J. An, G. C. Alexandropoulos, D. W. K. Ng, C. Y uen a nd L. Gan, ”Multi-user MISO with stacked intelligent metasurfaces: A DRL-based sum-rate optimization approach,” IEEE Trans. Cognitive Commun. Net. , vol. 12, pp. 251-266, 2026

    work page 2026

  20. [20]

    Energy-efficient de- signs for SIM-based broadcast MIMO systems,

    N. S. Perovi /acute.ts1c, E. E. Bahingayi, and L.-N. Tran, “Energy-efficient de- signs for SIM-based broadcast MIMO systems,” IEEE Trans. Commun. , vol. 72, no. 12, pp. 15881-15894, Dec. 2025

    work page 2025

  21. [21]

    Introducing meta-fiber into stacked inte lligent metasur- faces for MIMO communications: A low-complexity design wit h only two layers,

    H. Niu et al., “Introducing meta-fiber into stacked inte lligent metasur- faces for MIMO communications: A low-complexity design wit h only two layers,” IEEE Trans. Wireless Commun. , vol. 25, pp. 3016-3032, 2026

    work page 2026

  22. [22]

    Channel es timation for stacked intelligent metasurface-assisted wireless ne tworks,

    X. Y ao, J. An, L. Gan, M. Di Renzo, and C. Y uen, “Channel es timation for stacked intelligent metasurface-assisted wireless ne tworks,” IEEE Wireless Commun. Lett. , vol. 13, pp. 1349-1353, May 2024

    work page 2024

  23. [23]

    Papazafeiropoulos, P

    A. Papazafeiropoulos, P . Kourtessis, D. I. Kaklamani a nd I. S. V enieris, ”Channel estimation for stacked intelligent metasurfaces in Rician fading channels,” IEEE Wireless Commun. Lett. , vol. 14, no. 5, pp. 1411-1415, May 2025. 14

    work page 2025

  24. [24]

    High-efficiency transmissive tunable metasurfaces for bi nary cascaded diffractive layers,

    Y . Jia, H. Lu, Z. Fan, B. Wu, F. Qu, M.-J. Zhao, C. Qian, and H. Chen, “High-efficiency transmissive tunable metasurfaces for bi nary cascaded diffractive layers,” IEEE Trans. Antennas Propag. , vol. 72, no. 5, pp. 4532-4540, May 2024

    work page 2024

  25. [25]

    Joint beamforming and power allocation design for stacked intelligent metasurfaces-aided cell-free massive MIMO systems,

    Y . Hu, J. Zhang, E. Shi, Y . Lu, J. An, C. Y uen, and B. Ai, “Joint beamforming and power allocation design for stacked intelligent metasurfaces-aided cell-free massive MIMO systems,” IEEE Trans. V eh. Technol., vol. 74, no. 3, pp. 5235-5240, 2025

    work page 2025

  26. [26]

    Uplink performance of stacked intelligent metasurface-enhanced cell-free ma ssive MIMO systems,

    E. Shi, J. Zhang, Y . Zhu, J. An, C. Y uen, and B. Ai, “Uplink performance of stacked intelligent metasurface-enhanced cell-free ma ssive MIMO systems,” IEEE Trans. Wireless Commun., vol. 24, no. 5, pp. 3731-3746, May 2025

    work page 2025

  27. [27]

    Q. Li, M. El-Hajjar, C. Xu, J. An, C. Y uen and L. Hanzo, ”St acked intelligent metasurface-based transceiver design for nea r-field wideband systems,” IEEE Trans. Commun. , vol. 73, no. 9, pp. 3731-3746, Sep. 2025

    work page 2025

  28. [28]

    Stacked intelligent metasurface enable d LEO satellite communications relying on statistical CSI,

    S. Lin et al., “Stacked intelligent metasurface enable d LEO satellite communications relying on statistical CSI,” IEEE Wireless Commun. Lett., vol. 13, no. 5, pp. 1295-1299, May. 2024

    work page 2024

  29. [29]

    Stacked intelligent metasurfaces for integrated sensing and communications,

    H. Niu, J. An, A. Papazafeiropoulos, L. Gan, S. Chatzino tas, and M. Debbah, “Stacked intelligent metasurfaces for integrated sensing and communications,” IEEE Wireless Commun. Lett. , vol. 13, no. 10, pp. 2807-2811, 2024

    work page 2024

  30. [30]

    Transmit beamforming design for ISAC with stacked intelli gent meta- surfaces,

    S. Li, F. Zhang, T. Mao, R. Na, Z. Wang, and G. K. Karagiann idis, “Transmit beamforming design for ISAC with stacked intelli gent meta- surfaces,” IEEE Trans. V eh. Technol., vol. 74, pp. 6767-6772, Apr. 2025

    work page 2025

  31. [31]

    Stacked intelligent metasurfaces for task-oriented semantic comm unications,

    G. Huang, J. An, Z. Y ang, L. Gan, M. Bennis and M. Debbah, “ Stacked intelligent metasurfaces for task-oriented semantic comm unications,” IEEE Wireless Commun. Lett. , vol. 14, no. 2, pp. 310-314, Feb. 2025

    work page 2025

  32. [32]

    3GPP , Architectural enhancements for 5G multicast-br oadcast services; Stage 2 (Release 19), 3GPP TS 23.247, V19.2.0, Tech. Spec. Gr oup Services and System Aspects, Jun. 2025

    work page 2025

  33. [33]

    All-optical machine learning using diffractive deep neural networks,

    X. Lin, Y . Rivenson, N. T. Y ardimci, M. V eli, Y . Luo, M. Ja rrahi, and A. Ozcan, “All-optical machine learning using diffractive deep neural networks,” Science, vol. 361, no. 6406, pp. 1004-1008, Jul. 2018

    work page 2018

  34. [34]

    Super position of broadcast and unicast in wireless cellular systems,

    D. Kim, F. Khan, C. V . Rensburg, Z. Pi, and S. Y oon, “Super position of broadcast and unicast in wireless cellular systems,” IEEE Commun. Mag., vol. 46, no. 7, pp. 110-117, Jul. 2008

    work page 2008

  35. [35]

    Non-orthogonal broadc ast and unicast joint transmission for multibeam satellite system ,

    Z. Li, S. Wang, S. Han, and C. Li, “Non-orthogonal broadc ast and unicast joint transmission for multibeam satellite system ,” IEEE Trans. Broadcast., vol. 69, no. 3, pp. 647-660, Sep. 2023

    work page 2023

  36. [36]

    T. -H. Vu, Q. -V . Pham, D. B. da Costa and S. Kim, ”Rate-spl itting multiple access-assisted THz-based short-packet communications,” IEEE Wireless Commun. Lett. , vol. 12, pp. 2218-2222, Dec. 2023

    work page 2023

  37. [37]

    Saddle poi nt approxima- tion for outage probability using cumulant generating func tions,

    S. Guruacharya, H. Tabassum and E. Hossain, “Saddle poi nt approxima- tion for outage probability using cumulant generating func tions,” IEEE Wireless Commun. Lett. , vol. 5, no. 2, pp. 192-195, Apr. 2016

    work page 2016

  38. [38]

    Saddle point approximatio n for the distribution of the sum of independent random variables,

    R. Lugannani and S. O. Rice, “Saddle point approximatio n for the distribution of the sum of independent random variables,” Adv. Appl. Probab., vol. 12, no. 2, pp. 475-490, Jun. 1980

    work page 1980

  39. [39]

    Esmaeilbeig, A

    Z. Esmaeilbeig, A. Eamaz, K. V . Mishra, and M. Soltanali an, ”Joint waveform and passive beamformer design in multi-IRS-aided radar”, in Proc. IEEE International Conference on Acoustics, Speech a nd Signal Processing (ICASSP) , 2023

    work page 2023

  40. [40]

    L. E. Scales, Introduction to Non-Linear Optimization . Macmillan Publisher, 1985

    work page 1985

  41. [41]

    Unsuperv ised learning for passive beamforming,

    J. Gao, C. Zhong, X. Chen, H. Lin, and Z. Zhang, “Unsuperv ised learning for passive beamforming,” IEEE Commun. Lett. , vol. 24, no. 5, pp. 1052-1056, 2020

    work page 2020

  42. [42]

    Molchanov, S

    P . Molchanov, S. Tyree, T. Karras, T. Aila, and J. Kautz, ”Pruning convolutional neural networks for resource efficient infer ence,” in Proc. Int. Conf. Learning Representations (ICLR), 2017

    work page 2017

  43. [43]

    P . Ji, L. Jiang, C. He, Z. Lian and D. He, ”Energy-efficien t beamforming for beamspace HAP-NOMA systems,” IEEE Commun. Letts. , vol. 25, no. 5, pp. 1678-1681, May 2021

    work page 2021

  44. [44]

    K. S. Ahn and R. W. Heath, ”Performance analysis of maxim um ratio combining with imperfect channel estimation in the pr esence of cochannel interferences,” IEEE Trans. Wireless Commun. , vol. 8, no. 3, pp. 1080-1085, Mar. 2009

    work page 2009

  45. [45]

    R. A. Horn and C. R. Johnson, Matrix Analysis , 2nd ed., Cambridge University Press, 2013

    work page 2013

  46. [46]

    M. K. Simon and M.-S. Alouini, Digital Communication over Fading Channels, 2nd ed. Hoboken, NJ, USA: Wiley, 2005

    work page 2005

  47. [47]

    On the distribution of positive-definite Gaussian quadratic forms,

    G. Tziritas, “On the distribution of positive-definite Gaussian quadratic forms,” IEEE Trans. Inf. Theory , vol. 33, no. 6, pp. 895-906, Nov. 1987

    work page 1987