pith. machine review for the scientific record. sign in

arxiv: 2512.23246 · v2 · submitted 2025-12-29 · 📡 eess.SP

Recognition: 2 theorem links

· Lean Theorem

Ultra-Massive MIMO with Orthogonal Chirp Division Multiplexing for Near-Field Sensing and Communication Integration

Authors on Pith no claims yet

Pith reviewed 2026-05-16 19:49 UTC · model grok-4.3

classification 📡 eess.SP
keywords ultra-massive MIMOorthogonal chirp division multiplexingintegrated sensing and communicationnear-field sensingvirtual bistatic sensingfrequency-modulated continuous wavetarget positioningchannel estimation
0
0 comments X

The pith

Virtual bistatic sensing in UM-MIMO OCDM systems achieves high-accuracy near-field target positioning and three-dimensional velocity measurement.

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

The paper develops an integrated sensing and communication architecture that pairs ultra-massive MIMO transmit arrays with orthogonal chirp division multiplexing waveforms. A co-located sensing receiver applies frequency-modulated continuous wave processing to echoes from dedicated sensing subcarriers sent through selected antennas. These pairwise range and velocity estimates are fused via virtual bistatic sensing to locate targets and measure their full velocity vectors. The resulting method maintains accuracy even when channels exhibit spatial non-stationarity and uncorrelated multipath, conditions that degrade conventional monostatic approaches. Sensing outputs also refine the communication channel estimates for the same system.

Core claim

By allocating selected OCDM subcarriers to dedicated sensing antennas and processing their echoes with an optimized FMCW receiver, the architecture decouples signals from individual transmit-receive pairs. Virtual bistatic sensing then combines the pairwise estimates to deliver accurate three-dimensional target position and velocity. This remains effective in spatially non-stationary and uncorrelated multipath environments, while the extracted sensing data improves subsequent channel estimation for the communication link.

What carries the argument

Virtual bistatic sensing (VIBS), which aggregates range-velocity estimates from multiple dedicated-sensing-antenna pairs to determine target position and three-dimensional velocity.

If this is right

  • Sensing accuracy improves for near-field targets compared with single-antenna-pair methods.
  • Three-dimensional velocity vectors become measurable from the fused antenna-pair data.
  • Channel estimation for the communication link gains from the sensing-derived information.
  • Hardware complexity drops because the receiver uses standard FMCW processing rather than full MIMO radar chains.
  • Performance holds in spatially non-stationary and uncorrelated multipath channels.

Where Pith is reading between the lines

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

  • The architecture may lower deployment costs for integrated sensing and communication by using a simplified co-located receiver.
  • Dynamic adjustment of dedicated sensing subcarriers could extend robustness to time-varying target scenarios.
  • Scaling the array size further would increase angular resolution without added receiver hardware.
  • The approach points toward joint waveform optimization that simultaneously serves data rates and sensing precision in dense environments.

Load-bearing premise

That careful choice of dedicated sensing subcarriers and receiver parameters allows the FMCW receiver to separate echo signals from different dedicated sensing antennas.

What would settle it

A measurement showing that echoes from separate dedicated sensing antennas remain mixed at the receiver after the proposed subcarrier selection, producing large errors in range and velocity estimates.

Figures

Figures reproduced from arXiv: 2512.23246 by Christos Masouros, Fabien Heliot, Haiyang Zhang, Pei Xiao, Qu Luo, Sheng Chen, Yonina C. Eldar, Zhen Gao, Ziwei Wan.

Figure 1
Figure 1. Figure 1: OCDM signal representations. (a) The instantaneous frequencies. (b) [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The proposed ISAC scheme with UM-MIMO and OCDM-FMCW [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: An example of the IF signal (in-phase part) when [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The pre-processing of bistatic sensing with [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: The TMSE performance of (a) range-dependant parameter estimation [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: The MSE performance of VIBS regarding (a) position, and (b) velocity. [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 6
Figure 6. Figure 6: The convergence behaviour of (a) parameter estimation in Algorithm [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 10
Figure 10. Figure 10: Downlink communication BER performance evaluation for the [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
Figure 9
Figure 9. Figure 9: The NMSE performance of CE and its enhancement varying with (a) [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
read the original abstract

This paper integrates the emerging ultra-massive multiple-input multiple-output (UM-MIMO) technique with orthogonal chirp division multiplexing (OCDM) waveform to tackle the challenging near-field integrated sensing and communication (ISAC) problem. Specifically, we conceive a comprehensive ISAC architecture, where an UM-MIMO base station adopts OCDM waveform for communications and a co-located sensing receiver adopts the frequency-modulated continuous wave (FMCW) detection principle to simplify the associated hardware. For sensing tasks, several OCDM subcarriers, namely, dedicated sensing subcarriers (DSSs), are each transmitted through a dedicated sensing antenna (DSA) within the transmit antenna array. By judiciously designing the DSS selection scheme and optimizing receiver parameters, the FMCW-based sensing receiver can decouple the echo signals from different DSAs with significantly reduced hardware complexity. This setup enables the estimation of ranges and velocities of near-field targets in an antenna-pairwise manner. Moreover, by leveraging the spatial diversity of UM-MIMO, we introduce the concept of virtual bistatic sensing (VIBS), which incorporates the estimates from multiple antenna pairs to achieve high-accuracy target positioning and three-dimensional velocity measurement. The VIBS paradigm is immune to hostile channel environments characterized by spatial non-stationarity and uncorrelated multipath environment. Furthermore, the channel estimation of UM-MIMO OCDM systems enhanced by the sensing results is investigated. Simulation results demonstrate that the proposed ISAC scheme enhances sensing accuracy, and also benefits communication performance.

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 manuscript presents an integrated sensing and communication (ISAC) architecture combining ultra-massive MIMO (UM-MIMO) with orthogonal chirp division multiplexing (OCDM) waveforms for near-field applications. A co-located FMCW-based sensing receiver decouples echoes from dedicated sensing subcarriers (DSSs) transmitted via dedicated sensing antennas (DSAs), enabling antenna-pairwise range and velocity estimation. The virtual bistatic sensing (VIBS) concept fuses these estimates for high-accuracy 3D target positioning and velocity measurement, claimed to be robust to spatial non-stationarity and uncorrelated multipath. Sensing results are also used to enhance UM-MIMO channel estimation, with simulations demonstrating improved performance.

Significance. If the proposed decoupling mechanism and VIBS fusion prove robust, the work could offer a practical path to hardware-efficient near-field ISAC systems that maintain accuracy in challenging propagation environments. The integration of sensing with communication channel estimation is a notable strength, potentially leading to mutual benefits in UM-MIMO setups.

major comments (2)
  1. [Abstract] Abstract: The assertion that 'the VIBS paradigm is immune to hostile channel environments characterized by spatial non-stationarity and uncorrelated multipath environment' is load-bearing for the central contribution but is unsupported by any analytic bound on residual cross-DSA interference or Monte-Carlo results under spatially non-stationary channels, where round-trip delays vary continuously across the array.
  2. [Sensing Receiver Design] Sensing Receiver Design: The claim that 'judiciously designing the DSS selection scheme and optimizing receiver parameters' enables reliable decoupling with 'significantly reduced hardware complexity' lacks explicit selection algorithm, optimization criteria, or validation of zero residual interference, which is required for the subsequent pairwise estimation and VIBS fusion to hold.
minor comments (2)
  1. [Simulation Results] Simulation section: Error bars, number of Monte-Carlo trials, and explicit channel models for spatial non-stationarity are not reported, making it difficult to assess the statistical reliability of the claimed sensing accuracy gains.
  2. [VIBS Concept] Notation and figures: The VIBS fusion step and antenna-pairwise estimation process would benefit from an explicit block diagram or equations showing how range/velocity estimates are combined.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which help improve the clarity and rigor of our manuscript on UM-MIMO OCDM for near-field ISAC. We address each major comment point by point below, outlining the revisions we will incorporate.

read point-by-point responses
  1. Referee: [Abstract] Abstract: The assertion that 'the VIBS paradigm is immune to hostile channel environments characterized by spatial non-stationarity and uncorrelated multipath environment' is load-bearing for the central contribution but is unsupported by any analytic bound on residual cross-DSA interference or Monte-Carlo results under spatially non-stationary channels, where round-trip delays vary continuously across the array.

    Authors: We appreciate this observation regarding the strength of the claim. The VIBS concept relies on spatial diversity across the UM-MIMO array and fusion of pairwise estimates to mitigate effects of non-stationarity and uncorrelated multipath, as illustrated through the system model and simulations in Sections III and V. However, we agree that targeted validation is warranted. In the revision, we will add Monte-Carlo results specifically under spatially non-stationary channels with continuously varying round-trip delays across the array, along with an analysis of residual cross-DSA interference to provide stronger support for the robustness claim. revision: yes

  2. Referee: [Sensing Receiver Design] Sensing Receiver Design: The claim that 'judiciously designing the DSS selection scheme and optimizing receiver parameters' enables reliable decoupling with 'significantly reduced hardware complexity' lacks explicit selection algorithm, optimization criteria, or validation of zero residual interference, which is required for the subsequent pairwise estimation and VIBS fusion to hold.

    Authors: We agree that the DSS selection and receiver optimization require explicit details for reproducibility and to validate the decoupling. The revised manuscript will include the specific DSS selection algorithm (based on subcarrier spacing and chirp rate to minimize overlap), the optimization criteria (e.g., minimizing inter-DSA interference while preserving communication performance), and simulation results confirming negligible residual interference. This will directly support the reliability of antenna-pairwise estimation and subsequent VIBS fusion. revision: yes

Circularity Check

0 steps flagged

No circularity: architecture and VIBS claims are simulation-validated proposals, not reductions to fitted inputs or self-citations

full rationale

The paper defines the UM-MIMO OCDM ISAC architecture, DSS selection, FMCW receiver decoupling, and VIBS fusion as new constructs whose performance is asserted via simulation results rather than any equation that reduces by construction to prior fitted parameters or self-cited uniqueness theorems. No load-bearing step equates a prediction to its own input (e.g., no parameter fitted on one subset then renamed as prediction on a related quantity). Self-citations, if present, are not invoked to justify the central immunity claim; the derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 2 invented entities

The architecture rests on standard near-field propagation assumptions and introduces new entities (DSS, DSA, VIBS) whose performance is demonstrated only via simulation; no free parameters are explicitly fitted in the abstract description.

axioms (1)
  • domain assumption Near-field channel model and spatial non-stationarity assumptions hold for the target scenarios
    Invoked to justify the need for antenna-pairwise estimation and VIBS immunity claims.
invented entities (2)
  • Virtual bistatic sensing (VIBS) no independent evidence
    purpose: Combine estimates from multiple antenna pairs to achieve high-accuracy 3D positioning and velocity measurement
    New concept introduced to leverage UM-MIMO spatial diversity; no independent evidence provided beyond simulation.
  • Dedicated sensing subcarriers (DSSs) and dedicated sensing antennas (DSAs) no independent evidence
    purpose: Transmit sensing signals that can be decoupled at the FMCW receiver
    New design elements for hardware simplification; performance depends on selection scheme not detailed here.

pith-pipeline@v0.9.0 · 5604 in / 1454 out tokens · 89231 ms · 2026-05-16T19:49:08.313077+00:00 · methodology

discussion (0)

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

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

45 extracted references · 45 canonical work pages

  1. [1]

    The itu vision and framework for 6G: Scenarios, capabilities, and enablers,

    R. Liuet al., “The itu vision and framework for 6G: Scenarios, capabilities, and enablers,”IEEE Veh. Technol. Mag., vol. 20, no. 2, pp. 114–122, Jun. 2025

  2. [2]

    Orthogonal chirp division multiplexing waveform design for 6G mmWave UA V integrated sensing and communication,

    Z. Wanet al., “Orthogonal chirp division multiplexing waveform design for 6G mmWave UA V integrated sensing and communication,” in 2024 International Wireless Communications and Mobile Computing (IWCMC), 2024, pp. 622–627

  3. [3]

    Joint radar and communication design: Applications, state- of-the-art, and the road ahead,

    F. Liuet al., “Joint radar and communication design: Applications, state- of-the-art, and the road ahead,”IEEE Trans. Commun., vol. 68, no. 6, pp. 3834–3862, Jun. 2020

  4. [4]

    Integrated sensing and communication with mmWave massive MIMO: A compressed sampling perspective,

    Z. Gaoet al., “Integrated sensing and communication with mmWave massive MIMO: A compressed sampling perspective,”IEEE Trans. Wireless Commun., vol. 22, no. 3, pp. 1745–1762, Mar. 2023

  5. [5]

    Integrated sensing and communication waveform design: A survey,

    W. Zhou, R. Zhang, G. Chen, and W. Wu, “Integrated sensing and communication waveform design: A survey,”IEEE Open J. Commun. Soc., vol. 3, pp. 1930–1949, 2022

  6. [6]

    Near-field MIMO communications for 6G: Fundamentals, challenges, potentials, and future directions,

    M. Cui, Z. Wu, Y . Lu, X. Wei, and L. Dai, “Near-field MIMO communications for 6G: Fundamentals, challenges, potentials, and future directions,”IEEE Commun. Mag., vol. 61, no. 1, pp. 40–46, Jan. 2023

  7. [7]

    Near-field integrated sensing and communication: Opportunities and challenges,

    J. Conget al., “Near-field integrated sensing and communication: Opportunities and challenges,”IEEE Wireless Communications, vol. 31, no. 6, pp. 162–169, 2024

  8. [8]

    Near-field integrated sensing and communications,

    Z. Wang, X. Mu, and Y . Liu, “Near-field integrated sensing and communications,”IEEE Commun. Lett., vol. 27, no. 8, pp. 2048–2052, Aug. 2023

  9. [9]

    Near- field ISAC: Beamforming for multi-target detection,

    D. Galappaththige, S. Zargari, C. Tellambura, and G. Y . Li, “Near- field ISAC: Beamforming for multi-target detection,”IEEE Wireless Commun. Lett., vol. 13, no. 7, pp. 1938–1942, Jul. 2024

  10. [10]

    Cram´er-rao bounds for near-field sens- ing with extremely large-scale MIMO,

    H. Wang, Z. Xiao, and Y . Zeng, “Cram´er-rao bounds for near-field sens- ing with extremely large-scale MIMO,”IEEE Trans. Signal Process., vol. 72, pp. 701–717, 2024

  11. [11]

    Rethinking integrated sensing and communication: When near field meets wideband,

    Z. Wang, X. Mu, and Y . Liu, “Rethinking integrated sensing and communication: When near field meets wideband,”IEEE Commun. Mag., vol. 62, no. 9, pp. 44–50, Sept. 2024

  12. [12]

    Wideband near-field integrated sensing and communica- tion with sparse transceiver design,

    X. Wanget al., “Wideband near-field integrated sensing and communica- tion with sparse transceiver design,”IEEE J. Sel. Topics Signal Process., vol. 18, no. 4, pp. 662–677, May 2024

  13. [13]

    Performance analysis of near-field sensing in wideband mimo systems,

    Z. Wang, X. Mu, and Y . Liu, “Performance analysis of near-field sensing in wideband mimo systems,”IEEE Trans. Wireless Commun., vol. 24, no. 10, pp. 8236–8251, Oct. 2025

  14. [14]

    Joint radar and communication: A survey,

    Z. Fenget al., “Joint radar and communication: A survey,”China Communications, vol. 17, no. 1, pp. 1–27, Jan. 2020

  15. [15]

    Waveform design and signal processing aspects for fusion of wireless communications and radar sensing,

    C. Sturm and W. Wiesbeck, “Waveform design and signal processing aspects for fusion of wireless communications and radar sensing,”Pro. IEEE, vol. 99, no. 7, pp. 1236–1259, Jul. 2011

  16. [16]

    Adaptive OFDM integrated radar and communications waveform design based on information theory,

    Y . Liuet al., “Adaptive OFDM integrated radar and communications waveform design based on information theory,”IEEE Commun. Lett., vol. 21, no. 10, pp. 2174–2177, Oct. 2017

  17. [17]

    Designing low-PAPR waveform for OFDM-based RadCom systems,

    Y . Huanget al., “Designing low-PAPR waveform for OFDM-based RadCom systems,”IEEE Trans. Wireless Commun., vol. 21, no. 9, pp. 6979–6993, Sept. 2022

  18. [18]

    Orthogonal time frequency space (OTFS) modulation for millimeter-wave communications systems,

    R. Hadaniet al., “Orthogonal time frequency space (OTFS) modulation for millimeter-wave communications systems,” in2017 IEEE MTT-S International Microwave Symposium (IMS), 2017, pp. 681–683

  19. [19]

    Orthogonal time-frequency space modulation: A promis- ing next-generation waveform,

    Z. Weiet al., “Orthogonal time-frequency space modulation: A promis- ing next-generation waveform,”IEEE Wireless Commun., vol. 28, no. 4, pp. 136–144, Aug. 2021

  20. [20]

    Orthogonal time frequency space (OTFS) modulation based radar system,

    P. Ravitejaet al., “Orthogonal time frequency space (OTFS) modulation based radar system,” in2019 IEEE Radar Conference (RadarConf), 2019, pp. 1–6

  21. [21]

    On the effectiveness of OTFS for joint radar parameter estimation and communication,

    L. Gaudioet al., “On the effectiveness of OTFS for joint radar parameter estimation and communication,”IEEE Trans. Wireless Commun., vol. 19, no. 9, pp. 5951–5965, Sept. 2020

  22. [22]

    OTFS-based joint communication and sensing for future industrial IoT,

    K. Wu, J. A. Zhang, X. Huang, and Y . J. Guo, “OTFS-based joint communication and sensing for future industrial IoT,”IEEE Internet Things J., vol. 10, no. 3, pp. 1973–1989, Feb. 2023

  23. [23]

    Integrated sensing and communication-assisted orthog- onal time frequency space transmission for vehicular networks,

    W. Yuanet al., “Integrated sensing and communication-assisted orthog- onal time frequency space transmission for vehicular networks,”IEEE J. Sel. Topics Signal Process., vol. 15, no. 6, pp. 1515–1528, Nov. 2021

  24. [24]

    Orthogonal chirp division multiplexing,

    X. Ouyang and J. Zhao, “Orthogonal chirp division multiplexing,”IEEE Trans. Commun., vol. 64, no. 9, pp. 3946–3957, Sept. 2016

  25. [25]

    Performance analysis of OCDM for wireless communications,

    M. S. Omar and X. Ma, “Performance analysis of OCDM for wireless communications,”IEEE Trans. Wireless Commun., vol. 20, no. 7, pp. 4032–4043, Jul. 2021

  26. [26]

    Channel estimation for OCDM transmissions with carrier frequency offset,

    R. Zhang, Y . Wang, and X. Ma, “Channel estimation for OCDM transmissions with carrier frequency offset,”IEEE Wireless Commun. Lett., vol. 11, no. 3, pp. 483–487, Mar. 2022

  27. [27]

    Channel estimation for multiple-input multiple-output orthogonal chirp-division multiplexing systems,

    X. Ouyanget al., “Channel estimation for multiple-input multiple-output orthogonal chirp-division multiplexing systems,”IEEE Trans. Wireless Commun., vol. 23, no. 1, pp. 436–449, Jan. 2024

  28. [28]

    Underwater acoustic com- munications based on OCDM for internet of underwater things,

    B. Wang, Y . Wang, Y . Li, and X. Guan, “Underwater acoustic com- munications based on OCDM for internet of underwater things,”IEEE Internet Things J., vol. 10, no. 24, pp. 22 128–22 142, Dec. 2023

  29. [29]

    OCDM with index modula- tion for autonomous underwater vehicles communication,

    Z. Jia, R. Zhang, Z. Chen, and F. Yuan, “OCDM with index modula- tion for autonomous underwater vehicles communication,”IEEE Trans. Intell. Veh., vol. 10, no. 4, pp. 2765–2780, Apr. 2025

  30. [30]

    Evaluation of orthogonal chirp division mul- tiplexing for automotive integrated sensing and communications,

    S. Bhattacharjeeet al., “Evaluation of orthogonal chirp division mul- tiplexing for automotive integrated sensing and communications,” in ICASSP 2022-2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2022, pp. 8742–8746

  31. [31]

    Joint radar-communication systems: Modula- tion schemes and system design,

    L. G. De Oliveiraet al., “Joint radar-communication systems: Modula- tion schemes and system design,”IEEE Trans. Microw. Theory Techn., vol. 70, no. 3, pp. 1521–1551, Mar. 2022

  32. [32]

    THz-over-fiber system with orthogonal chirp division multiplexing for integrated sensing and communication,

    L. Liet al., “THz-over-fiber system with orthogonal chirp division multiplexing for integrated sensing and communication,”Journal of Lightwave Technology, vol. 42, no. 1, pp. 176–183, Jan. 2024

  33. [33]

    Orthogonal chirp division multiplexing assisted dual- function radar communication in IoT networks,

    S. Liet al., “Orthogonal chirp division multiplexing assisted dual- function radar communication in IoT networks,”IEEE Internet Things J., vol. 11, no. 13, pp. 23 752–23 764, Jul. 2024

  34. [34]

    Automotive radars: A review of signal processing techniques,

    S. M. Patole, M. Torlak, D. Wang, and M. Ali, “Automotive radars: A review of signal processing techniques,”IEEE Signal Process. Mag., vol. 34, no. 2, pp. 22–35, Mar. 2017

  35. [35]

    Channel estimation for extremely large-scale MIMO: Far-field or near-field?

    M. Cui and L. Dai, “Channel estimation for extremely large-scale MIMO: Far-field or near-field?”IEEE Trans. Commun., vol. 70, no. 4, pp. 2663–2677, Apr. 2022

  36. [36]

    Non-stationarities in extra-large-scale massive MIMO,

    E. De Carvalhoet al., “Non-stationarities in extra-large-scale massive MIMO,”IEEE Wireless Commun., vol. 27, no. 4, pp. 74–80, Aug. 2020

  37. [37]

    Super resolution DOA based on relative motion for FMCW automotive radar,

    W. Zhang, P. Wang, N. He, and Z. He, “Super resolution DOA based on relative motion for FMCW automotive radar,”IEEE Trans. Veh. Technol., vol. 69, no. 8, pp. 8698–8709, Aug. 2020

  38. [38]

    Closed-loop sparse channel estimation for wideband millimeter-wave full-dimensional MIMO systems,

    A. Liaoet al., “Closed-loop sparse channel estimation for wideband millimeter-wave full-dimensional MIMO systems,”IEEE Trans. Com- mun., vol. 67, no. 12, pp. 8329–8345, Dec. 2019

  39. [39]

    Two-point step size gradient methods,

    J. Barzilai and J. M. Borwein, “Two-point step size gradient methods,” IMA J. Numer. Anal., vol. 8, no. 1, pp. 141–148, 1988

  40. [40]

    MUSIC, maximum likelihood, and Cramer- Rao bound,

    P. Stoica and A. Nehorai, “MUSIC, maximum likelihood, and Cramer- Rao bound,”IEEE Trans. Acoust., Speech, Signal Process., vol. 37, no. 5, pp. 720–741, May 1989

  41. [41]

    K-means clustering-aided non- coherent detection for molecular communications,

    X. Qian, M. Di Renzo, and A. Eckford, “K-means clustering-aided non- coherent detection for molecular communications,”IEEE Transactions on Communications, vol. 69, no. 8, pp. 5456–5470, Aug. 2021

  42. [42]

    Circulant matrices and their application to vibration analysis,

    B. J. Olsonet al., “Circulant matrices and their application to vibration analysis,”Appl. Mech. Rev., vol. 66, no. 4, p. 040803, 2014

  43. [43]

    Spatially common sparsity based adaptive channel estimation and feedback for FDD massive MIMO,

    Z. Gao, L. Dai, Z. Wang, and S. Chen, “Spatially common sparsity based adaptive channel estimation and feedback for FDD massive MIMO,” IEEE Trans. Signal Process., vol. 63, no. 23, pp. 6169–6183, Dec. 2015

  44. [44]

    Broadband channel estimation for intelligent reflecting surface aided mmwave massive mimo systems,

    Z. Wan, Z. Gao, and M.-S. Alouini, “Broadband channel estimation for intelligent reflecting surface aided mmwave massive mimo systems,” inICC 2020-2020 IEEE International Conference on Communications (ICC), 2020, pp. 1–6

  45. [45]

    Estimation of multipath parameters in wireless communications,

    M. C. Vanderveen, A.-J. Van der Veen, and A. Paulraj, “Estimation of multipath parameters in wireless communications,”IEEE Trans. Signal Process., vol. 46, no. 3, pp. 682–690, Mar. 1998