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arxiv: 2605.21020 · v1 · pith:LW7GDCH3new · submitted 2026-05-20 · 📡 eess.SP · cs.IT· math.IT

Microwave Linear Analog Computer (MiLAC)-Aided MIMO Radar Sensing: Transmit Beamforming Design and DoA Estimation

Ziang Liu , Zheyu Wu , Bruno Clerckx This is my paper

Pith reviewed 2026-05-21 02:06 UTC · model grok-4.3

classification 📡 eess.SP cs.ITmath.IT
keywords MIMO radarMiLACtransmit beamformingDoA estimationanalog computingCramer-Rao boundhardware reduction
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The pith

MiLAC-aided MIMO radar matches fully-digital weighted CRB and DoA performance

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

The paper establishes that a microwave linear analog computer can move key linear operations for MIMO radar into the analog domain. It proves that MiLAC-aided transmit beamforming reaches the same weighted Cramer-Rao bound as fully-digital designs and that a lossless reciprocal MiLAC can realize the two-dimensional discrete Fourier transform for direction-of-arrival estimation without any performance penalty. A sympathetic reader would care because this approach promises to scale MIMO radar to massive arrays while cutting hardware cost, power consumption, and the need for high-resolution digital converters and processing.

Core claim

MiLAC-aided transmit beamforming achieves the same weighted CRB as fully-digital beamforming, as shown by a penalty dual decomposition algorithm under lossless and reciprocal constraints, while a lossless reciprocal MiLAC implements the 2D DFT for analog-domain DoA estimation without performance loss.

What carries the argument

Lossless reciprocal MiLAC that executes the linear transformations needed for beamforming weights and 2D-DFT directly in the analog domain.

If this is right

  • Only low-resolution DACs are required at the transmitter.
  • RF chains and ADCs can be eliminated at the receiver.
  • All digital DFT operations for DoA estimation are removed.
  • Hardware cost and power consumption drop while sensing performance stays the same.

Where Pith is reading between the lines

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

  • The same analog linear operations could be applied to other MIMO sensing or communication tasks that rely on matrix multiplications or transforms.
  • This design may allow practical deployment of much larger arrays than current digital processing budgets permit.
  • Hardware experiments with real MiLAC circuits would test how close actual devices come to the ideal lossless reciprocal model.

Load-bearing premise

The MiLAC hardware can be realized as perfectly lossless and reciprocal so that the analog linear operations exactly match the intended digital computations without introducing unmodeled distortions or losses.

What would settle it

A physical MiLAC prototype that produces a higher weighted CRB for beamforming or degraded DoA estimation accuracy compared with the fully-digital benchmark would disprove the performance equivalence.

Figures

Figures reproduced from arXiv: 2605.21020 by Bruno Clerckx, Zheyu Wu, Ziang Liu.

Figure 1
Figure 1. Figure 1: Comparison between (a) digital beamforming and (b) MiLAC-aided [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Architecture of the MiLAC-aided sensing system. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: A 4-port MiLAC with 2 input ports and 2 output ports. Reciprocal [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Convergence of Algorithm 1 with N = 64 transmit antennas and 2 targets for detection. (a) Value of objective function (27a) versus iteration numbers. (b) Difference between W and auxiliary variable X. 3.1], the proposed PDD algorithm converges to a KKT point of P4 with ϵ → 0. We evaluate the convergence behavior of Algorithm 1 through numerical simulations. Specifically, we check the convergence of the obj… view at source ↗
Figure 6
Figure 6. Figure 6: CRB of 3 target versus receive radar SNR with number of antennas [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 5
Figure 5. Figure 5: Transmit beampattern with N = 64 transmit antennas with receive radar SNR = 20 dB. The optimized beampatterns with 1 target are shown in (a)-1 MiLAC , (a)-2 digital and (a)-3 matched filter beamforming design. The optimized beampatterns with 2 targets are shown in (b)-1 MiLAC , (b)-2 digital and (b)-3 matched filter beamforming design. A. MiLAC-aided Transmit Beamforming Design 1) Beampattern Performances … view at source ↗
Figure 8
Figure 8. Figure 8: Computational complexity of digital and MiLAC 2D DFT with [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Angular spectrum of the received signal with 1 target. The physical [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 12
Figure 12. Figure 12: MSE comparison of single-target DoA estimation versus [PITH_FULL_IMAGE:figures/full_fig_p012_12.png] view at source ↗
read the original abstract

Multiple-input multiple-output (MIMO) radar has waveform diversity and large spatial degrees of freedom (DoFs), making it attractive for high-resolution sensing. Scaling MIMO radar to massive arrays can further improve sensing performance, but it also increases hardware cost, power consumption, and digital processing complexity. The microwave linear analog computer (MiLAC) can tackle these challenges by moving linear operations from the digital domain to the analog domain. MiLAC has shown promising benefits for communications in recent studies and this paper identifies its potential for radar sensing. Specifically, we consider both MiLAC-aided transmit beamforming and receiver-side two-dimensional discrete Fourier transform (2D-DFT)-based direction-of-arrival (DoA) estimation. For transmit beamforming, we formulate a weighted Cramer Rao bound (CRB) minimization problem under lossless and reciprocal MiLAC constraints and propose a penalty dual decomposition (PDD)-based iterative algorithm to address the non-convex problem. We further prove that MiLAC-aided and fully-digital beamforming achieve the same CRB. For receiver processing, we show that the 2D DFT can be implemented by a lossless reciprocal MiLAC, which enables analog-domain DoA estimation without digital optimization. Numerical results confirm the theoretical finding and show that the MiLAC-aided approach achieves the same CRB and DoA estimation performance as the fully-digital benchmark. Meanwhile, hardware cost and power consumption are reduced because only low-resolution DACs are required at the transmitter, while RF chains and ADCs are eliminated at the receiver. Moreover, performing the 2D DFT in the analog domain eliminates all digital DFT operations for DoA estimation.

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 a MiLAC-aided MIMO radar architecture that shifts linear operations to the analog domain. For transmit beamforming it formulates a weighted CRB minimization subject to lossless and reciprocal MiLAC constraints, develops a PDD algorithm to solve the resulting non-convex problem, and proves that the minimum weighted CRB equals that of unconstrained fully-digital beamforming. For receiver processing it shows that a lossless reciprocal MiLAC can exactly realize the 2D-DFT matrix, enabling analog-domain DoA estimation that eliminates digital DFT operations and RF chains/ADCs. Numerical results under the ideal model confirm identical CRB and DoA performance with substantially lower hardware cost and power.

Significance. If the ideal lossless/reciprocal hardware model holds, the work offers a concrete route to scale MIMO radar to massive arrays while preserving sensing performance and cutting digital processing, DAC resolution, and RF-chain requirements. The mathematical equivalence proof and the exact 2D-DFT realization are strong theoretical contributions that could influence analog-computing approaches in radar and communications.

major comments (2)
  1. [Transmit beamforming formulation and proof] The central claim of CRB equivalence rests on the lossless and reciprocal constraints allowing any fully-digital beamformer to be realized exactly; the manuscript should explicitly verify (perhaps via the range of the MiLAC transfer matrix under these constraints) that the feasible set is not strictly smaller than the digital case, otherwise the equality would hold only by construction rather than as a non-trivial result.
  2. [Receiver-side 2D-DFT implementation] The statement that a lossless reciprocal MiLAC implements the 2D-DFT without performance loss is load-bearing for the receiver claim; the explicit factorization or network topology realizing the DFT matrix under the reciprocity and losslessness conditions should be provided so that readers can assess whether unmodeled phase/amplitude errors would break the exact equivalence.
minor comments (2)
  1. [Numerical results] Figure captions and simulation sections should list all parameter values (array size, SNR range, number of snapshots, penalty parameter schedule for PDD) so that the numerical match to the CRB bound can be reproduced.
  2. [Algorithm description] The PDD algorithm description would benefit from a brief convergence plot or iteration count table to complement the theoretical equivalence result.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We sincerely thank the referee for the constructive review and the recommendation for minor revision. The comments highlight important aspects of the theoretical claims that merit clearer exposition. We address each major comment below and outline the corresponding revisions to the manuscript.

read point-by-point responses

  1. Referee: [Transmit beamforming formulation and proof] The central claim of CRB equivalence rests on the lossless and reciprocal constraints allowing any fully-digital beamformer to be realized exactly; the manuscript should explicitly verify (perhaps via the range of the MiLAC transfer matrix under these constraints) that the feasible set is not strictly smaller than the digital case, otherwise the equality would hold only by construction rather than as a non-trivial result.

    Authors: We appreciate this observation, which helps strengthen the presentation of the equivalence result. The existing proof shows that the weighted-CRB objective attained by the optimal fully-digital beamformer remains achievable when the lossless and reciprocal MiLAC constraints are imposed, implying that the constraints do not reduce the attainable performance. To make the non-trivial nature of this result explicit, we will add a new lemma (or remark) in the transmit-beamforming section that characterizes the range of the MiLAC transfer matrix under the stated constraints. The lemma will establish that every complex-valued matrix of the appropriate dimensions lies in the feasible set, confirming that the MiLAC architecture can realize any fully-digital beamformer exactly. This addition will clarify that the CRB equality follows from the completeness of the feasible set rather than from a restrictive construction. revision: yes

  2. Referee: [Receiver-side 2D-DFT implementation] The statement that a lossless reciprocal MiLAC implements the 2D-DFT without performance loss is load-bearing for the receiver claim; the explicit factorization or network topology realizing the DFT matrix under the reciprocity and losslessness conditions should be provided so that readers can assess whether unmodeled phase/amplitude errors would break the exact equivalence.

    Authors: We thank the referee for underscoring the importance of an explicit construction. The manuscript already notes that the 2D-DFT matrix is unitary (hence lossless) and symmetric (hence reciprocal), satisfying the necessary conditions for exact MiLAC realization. To address the request for a concrete implementation that permits assessment of robustness, we will include in the revised receiver-processing section an explicit factorization of the 2D-DFT matrix into a cascade of elementary 2-port lossless reciprocal MiLAC stages (realizable, for example, by a network of hybrid couplers and fixed phase shifters). A brief accompanying discussion will indicate how deviations from ideal losslessness or reciprocity could affect the equivalence, while preserving the exact equivalence under the ideal model assumed throughout the paper. revision: yes

Circularity Check

0 steps flagged

Derivation self-contained under explicit hardware model

full rationale

The paper explicitly imposes lossless and reciprocal MiLAC constraints, formulates the weighted CRB minimization problem under those constraints, and proves that the resulting minimum equals the fully-digital beamforming CRB. Separately, it shows that the 2D-DFT matrix is exactly realizable by a lossless reciprocal MiLAC. Both results are direct mathematical consequences of the stated model and constraints rather than reductions to fitted parameters, self-citations, or re-derivations of inputs. Numerical results serve only as verification under the ideal model and do not constitute the central claims. No load-bearing self-citation chains or self-definitional steps appear in the derivation.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claims rest on the assumption that MiLAC hardware satisfies ideal lossless and reciprocal properties; the optimization uses a penalty parameter and weights whose specific values are chosen to balance the multi-objective CRB problem.

free parameters (2)
  • penalty parameter in PDD algorithm
    Introduced to handle the non-convex MiLAC constraints; its value affects convergence but is not derived from first principles.
  • weights in weighted CRB objective
    Chosen to emphasize different sensing directions or targets; directly affect the beamforming solution.
axioms (1)
  • domain assumption MiLAC is lossless and reciprocal
    Invoked to formulate the beamforming constraints and to claim that the analog 2D-DFT exactly realizes the digital transform.

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Reference graph

Works this paper leans on

48 extracted references · 48 canonical work pages · 2 internal anchors

  1. [1]

    The integrated sensing and communication revolution for 6G: Vision, techniques, and applications,

    N. González-Prelcic, M. F. Keskin, O. Kaltiokallio, M. Valkama, D. Dardari, X. Shen, Y . Shen, M. Bayraktar, and H. Wymeersch, “The integrated sensing and communication revolution for 6G: Vision, techniques, and applications,”Proc. IEEE, vol. 112, no. 7, pp. 676–723, 2024

    work page 2024

  2. [2]

    MIMO radar with colocated antennas,

    J. Li and P. Stoica, “MIMO radar with colocated antennas,”IEEE Signal Process. Mag., vol. 24, no. 5, pp. 106–114, 2007

    work page 2007

  3. [3]

    On probing signal design for MIMO radar,

    P. Stoica, J. Li, and Y . Xie, “On probing signal design for MIMO radar,” IEEE Trans. Sig. Proc., vol. 55, no. 8, pp. 4151–4161, 2007

    work page 2007

  4. [4]

    Transmit beamforming for MIMO radar systems using signal cross-correlation,

    D. R. Fuhrmann and G. San Antonio, “Transmit beamforming for MIMO radar systems using signal cross-correlation,”IEEE Trans. Aerosp. Electron. Syst., vol. 44, no. 1, pp. 171–186, 2008

    work page 2008

  5. [5]

    Moving target parameters estimation in noncoherent MIMO radar systems,

    A. Hassanien, S. A. V orobyov, and A. B. Gershman, “Moving target parameters estimation in noncoherent MIMO radar systems,”IEEE Trans. Sig. Proc., vol. 60, no. 5, pp. 2354–2361, 2012

    work page 2012

  6. [6]

    Relative entropy-based wave- form design for MIMO radar detection in the presence of clutter and interference,

    B. Tang, M. M. Naghsh, and J. Tang, “Relative entropy-based wave- form design for MIMO radar detection in the presence of clutter and interference,”IEEE Trans. Sig. Proc., vol. 63, no. 14, pp. 3783–3796, 2015

    work page 2015

  7. [7]

    MIMO radar for advanced driver-assistance systems and autonomous driving: Advantages and challenges,

    S. Sun, A. P. Petropulu, and H. V . Poor, “MIMO radar for advanced driver-assistance systems and autonomous driving: Advantages and challenges,”IEEE Signal Process. Mag., vol. 37, no. 4, pp. 98–117, 2020

    work page 2020

  8. [8]

    MIMO radar and ground- based SAR imaging systems: Equivalent approaches for remote sensing,

    D. Tarchi, F. Oliveri, and P. F. Sammartino, “MIMO radar and ground- based SAR imaging systems: Equivalent approaches for remote sensing,” IEEE Trans. Geosci. Remote Sens., vol. 51, no. 1, pp. 425–435, 2012

    work page 2012

  9. [9]

    Joint transmit and receive beamforming design in full-duplex integrated sensing and communica- tions,

    Z. Liu, S. Aditya, H. Li, and B. Clerckx, “Joint transmit and receive beamforming design in full-duplex integrated sensing and communica- tions,”IEEE J. Sel. Areas Commun., vol. 41, no. 9, pp. 2907–2919, 2023

    work page 2023

  10. [10]

    Massive MIMO is a reality—what is next?: Five promis- ing research directions for antenna arrays,

    E. Björnson, L. Sanguinetti, H. Wymeersch, J. Hoydis, and T. L. Marzetta, “Massive MIMO is a reality—what is next?: Five promis- ing research directions for antenna arrays,”Digital Signal Processing, vol. 94, pp. 3–20, 2019

    work page 2019

  11. [11]

    Massive MIMO radar for target detection,

    S. Fortunati, L. Sanguinetti, F. Gini, M. S. Greco, and B. Himed, “Massive MIMO radar for target detection,”IEEE Trans. Sig. Proc., vol. 68, pp. 859–871, 2020

    work page 2020

  12. [12]

    Fast randomized- MUSIC for mm-wave massive MIMO radars,

    B. Li, S. Wang, J. Zhang, X. Cao, and C. Zhao, “Fast randomized- MUSIC for mm-wave massive MIMO radars,”IEEE Trans. Veh. Tech- nol., vol. 70, no. 2, pp. 1952–1956, 2021

    work page 1952

  13. [13]

    Terahertz-band joint ultra-massive MIMO radar-communications: Model-based and model- free hybrid beamforming,

    A. M. Elbir, K. V . Mishra, and S. Chatzinotas, “Terahertz-band joint ultra-massive MIMO radar-communications: Model-based and model- free hybrid beamforming,”IEEE J. Sel. Topics Signal Process., vol. 15, no. 6, pp. 1468–1483, 2021

    work page 2021

  14. [14]

    On the spectral efficiency of massive MIMO systems with low-resolution ADCs,

    J. Zhang, L. Dai, S. Sun, and Z. Wang, “On the spectral efficiency of massive MIMO systems with low-resolution ADCs,”IEEE Commun. Lett., vol. 20, no. 5, pp. 842–845, 2016

    work page 2016

  15. [15]

    On low-resolution ADCs in practical 5G millimeter-wave massive MIMO systems,

    J. Zhang, L. Dai, X. Li, Y . Liu, and L. Hanzo, “On low-resolution ADCs in practical 5G millimeter-wave massive MIMO systems,”IEEE Commun. Mag., vol. 56, no. 7, pp. 205–211, 2018

    work page 2018

  16. [16]

    Multiple emitter location and signal parameter estimation,

    R. Schmidt, “Multiple emitter location and signal parameter estimation,” IEEE Trans. Antennas Propag., vol. 34, no. 3, pp. 276–280, 1986

    work page 1986

  17. [17]

    Transmit signal design for large- scale MIMO system with 1-bit DACs,

    Z. Cheng, B. Liao, Z. He, and J. Li, “Transmit signal design for large- scale MIMO system with 1-bit DACs,”IEEE Trans. Wireless Commun., vol. 18, no. 9, pp. 4466–4478, 2019

    work page 2019

  18. [18]

    One-bit target detection in collocated MIMO radar and performance degradation analysis,

    Y .-H. Xiao, D. Ramírez, P. J. Schreier, C. Qian, and L. Huang, “One-bit target detection in collocated MIMO radar and performance degradation analysis,”IEEE Trans. Veh. Technol., vol. 71, no. 9, pp. 9363–9374, 2022

    work page 2022

  19. [19]

    Gridless parameter estimation for one-bit MIMO radar with time-varying thresholds,

    F. Xi, Y . Xiang, S. Chen, and A. Nehorai, “Gridless parameter estimation for one-bit MIMO radar with time-varying thresholds,”IEEE Trans. Sig. Proc., vol. 68, pp. 1048–1063, 2020

    work page 2020

  20. [20]

    Asymptotic param- eter tracking performance with measurement data of 1-bit resolution,

    M. Stein, A. Kürzl, A. Mezghani, and J. A. Nossek, “Asymptotic param- eter tracking performance with measurement data of 1-bit resolution,” IEEE Trans. Sig. Proc., vol. 63, no. 22, pp. 6086–6095, 2015

    work page 2015

  21. [21]

    Low- complexity and high-resolution DOA estimation for hybrid analog and digital massive MIMO receive array,

    F. Shu, Y . Qin, T. Liu, L. Gui, Y . Zhang, J. Li, and Z. Han, “Low- complexity and high-resolution DOA estimation for hybrid analog and digital massive MIMO receive array,”IEEE Trans. Commun., vol. 66, no. 6, pp. 2487–2501, 2018

    work page 2018

  22. [22]

    Stacked intelligent metasurface-aided MIMO transceiver design,

    J. An, C. Yuen, C. Xu, H. Li, D. W. K. Ng, M. Di Renzo, M. Debbah, and L. Hanzo, “Stacked intelligent metasurface-aided MIMO transceiver design,”IEEE Wireless Commun., vol. 31, no. 4, pp. 123–131, 2024

    work page 2024

  23. [23]

    Over-the-air integrated sensing, communication, and computation in IoT networks,

    X. Li, Y . Gong, K. Huang, and Z. Niu, “Over-the-air integrated sensing, communication, and computation in IoT networks,”IEEE Wireless Commun., vol. 30, no. 1, pp. 32–38, 2023

    work page 2023

  24. [24]

    In- tegrated sensing, communication, and computation over-the-air: MIMO beamforming design,

    X. Li, F. Liu, Z. Zhou, G. Zhu, S. Wang, K. Huang, and Y . Gong, “In- tegrated sensing, communication, and computation over-the-air: MIMO beamforming design,”IEEE Trans. Wireless Commun., vol. 22, no. 8, pp. 5383–5398, 2023

    work page 2023

  25. [25]

    Stacked intelligent metasurfaces for integrated sensing and communications,

    H. Niu, J. An, A. Papazafeiropoulos, L. Gan, S. Chatzinotas, 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

  26. [26]

    Transmit beamforming design for ISAC with stacked intelligent meta- surfaces,

    S. Li, F. Zhang, T. Mao, R. Na, Z. Wang, and G. K. Karagiannidis, “Transmit beamforming design for ISAC with stacked intelligent meta- surfaces,”IEEE Trans. Veh. Technol., vol. 74, no. 4, pp. 6767–6772, 2024

    work page 2024

  27. [27]

    Two-dimensional direction-of-arrival estimation using stacked intelligent metasurfaces,

    J. An, C. Yuen, Y . L. Guan, M. Di Renzo, M. Debbah, H. V . Poor, and L. Hanzo, “Two-dimensional direction-of-arrival estimation using stacked intelligent metasurfaces,”IEEE J. Sel. Areas Commun., vol. 42, no. 10, pp. 2786–2802, 2024

    work page 2024

  28. [28]

    Analog computing for signal processing and communications—part I: Computing with microwave networks,

    M. Nerini and B. Clerckx, “Analog computing for signal processing and communications—part I: Computing with microwave networks,”IEEE Trans. Sig. Proc., 2025

    work page 2025

  29. [29]

    Analog computing for signal processing and communica- tions—part II: Toward gigantic MIMO beamforming,

    ——, “Analog computing for signal processing and communica- tions—part II: Toward gigantic MIMO beamforming,”IEEE Trans. Sig. Proc., 2025

    work page 2025

  30. [30]

    Physics-compliant modeling and optimization of MIMO sys- tems aided by microwave linear analog computers,

    ——, “Physics-compliant modeling and optimization of MIMO sys- tems aided by microwave linear analog computers,”arXiv preprint arXiv:2602.19379, 2026

    work page arXiv 2026

  31. [31]

    MIMO systems aided by microwave linear analog computers: Capacity-achieving architectures with reduced circuit complexity,

    ——, “MIMO systems aided by microwave linear analog computers: Capacity-achieving architectures with reduced circuit complexity,”IEEE Trans. Wireless Commun., vol. 25, pp. 14 597–14 610, 2026

    work page 2026

  32. [32]

    Channel estimation in MIMO systems aided by microwave linear analog computers (MiLACs),

    Q. Zhang, M. Nerini, and B. Clerckx, “Channel estimation in MIMO systems aided by microwave linear analog computers (MiLACs),”arXiv preprint arXiv:2601.11438, 2026

    work page arXiv 2026

  33. [33]

    Capacity of MIMO systems aided by microwave linear analog computers (milacs),

    M. Nerini and B. Clerckx, “Capacity of MIMO systems aided by microwave linear analog computers (milacs),”arXiv preprint arXiv:2506.05983, 2025

    work page arXiv 2025

  34. [34]

    Microwave linear analog computer (MiLAC)-aided multiuser MISO: Fundamental limits and beamforming design,

    Z. Wu, M. Nerini, and B. Clerckx, “Microwave linear analog computer (MiLAC)-aided multiuser MISO: Fundamental limits and beamforming design,”arXiv preprint arXiv:2601.10060, 2026

    work page arXiv 2026

  35. [35]

    On the performance of lossless reciprocal MiLAC architectures in multi-user networks,

    T. Fang, X. Zhou, and Y . Mao, “On the performance of lossless reciprocal MiLAC architectures in multi-user networks,”arXiv preprint arXiv:2601.01834, 2026

    work page arXiv 2026

  36. [36]

    Hybrid digital and analog beamforming design for large-scale antenna arrays,

    F. Sohrabi and W. Yu, “Hybrid digital and analog beamforming design for large-scale antenna arrays,”IEEE J. Sel. Topics Signal Process., vol. 10, no. 3, pp. 501–513, 2016

    work page 2016

  37. [37]

    Two-Layer Microwave Linear Analog Computer (MiLAC)-aided Multi-user MISO Networks

    X. Zhou, T. Fang, Y . Mao, and B. Clerckx, “Two-layer microwave linear analog computer (MiLAC)-aided multi-user MISO networks,”arXiv preprint arXiv:2604.24303, 2026

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  38. [38]

    Hybrid Digital and Microwave Linear Analog Computer (MiLAC)-aided Beamforming for Multiuser MIMO-OFDM Systems

    Y . Peng, Z. Wu, and B. Clerckx, “Hybrid digital and microwave linear analog computer (MiLAC)-aided beamforming for multiuser MIMO- OFDM systems,”arXiv preprint arXiv:2604.26532, 2026

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  39. [39]

    Analog computing with hybrid couplers and phase shifters,

    M. Nerini, X. Liu, and B. Clerckx, “Analog computing with hybrid couplers and phase shifters,”arXiv preprint arXiv:2603.24604, 2026

    work page arXiv 2026

  40. [40]

    Penalty dual decomposition method for non- smooth nonconvex optimization—Part I: Algorithms and convergence analysis,

    Q. Shi and M. Hong, “Penalty dual decomposition method for non- smooth nonconvex optimization—Part I: Algorithms and convergence analysis,”IEEE Trans. Sig. Proc., vol. 68, pp. 4108–4122, 2020

    work page 2020

  41. [41]

    Joint 2-D DoA estimation and phase calibration for uniform rectangular arrays,

    P. Heidenreich, A. M. Zoubir, and M. Rubsamen, “Joint 2-D DoA estimation and phase calibration for uniform rectangular arrays,”IEEE Trans. Sig. Proc., vol. 60, no. 9, pp. 4683–4693, 2012

    work page 2012

  42. [42]

    Target detection and localization using MIMO radars and sonars,

    I. Bekkerman and J. Tabrikian, “Target detection and localization using MIMO radars and sonars,”IEEE Trans. Sig. Proc., vol. 54, no. 10, pp. 3873–3883, 2006

    work page 2006

  43. [43]

    S. M. Kay,Fundamentals of statistical signal processing: Estimation theory. Prentice-Hall, Inc., 1993

    work page 1993

  44. [44]

    Range compression and waveform optimization for MIMO radar: A Cramér– Rao bound based study,

    J. Li, L. Xu, P. Stoica, K. W. Forsythe, and D. W. Bliss, “Range compression and waveform optimization for MIMO radar: A Cramér– Rao bound based study,”IEEE Trans. Sig. Proc., vol. 56, no. 1, pp. 218–232, 2007

    work page 2007

  45. [45]

    A generalized solution of the orthogonal procrustes problem,

    P. H. Schönemann, “A generalized solution of the orthogonal procrustes problem,”Psychometrika, vol. 31, no. 1, pp. 1–10, 1966

    work page 1966

  46. [46]

    M. A. Richardset al.,Fundamentals of radar signal processing. Mcgraw-hill New York, 2005, vol. 1

    work page 2005

  47. [47]

    A modified split-radix FFT with fewer arithmetic operations,

    S. G. Johnson and M. Frigo, “A modified split-radix FFT with fewer arithmetic operations,”IEEE Trans. Sig. Proc., vol. 55, no. 1, pp. 111– 119, 2006

    work page 2006

  48. [48]

    Off-grid direction of arrival estimation using sparse bayesian inference,

    Z. Yang, L. Xie, and C. Zhang, “Off-grid direction of arrival estimation using sparse bayesian inference,”IEEE Trans. Sig. Proc., vol. 61, no. 1, pp. 38–43, 2012

    work page 2012