Pith. sign in

REVIEW 3 major objections 5 minor 1 cited by

Near-Field Spatial non-Stationary Channel Estimation: Visibility-Region-HMM-Aided Polar-Domain Simultaneous OMP

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper proposes that interleaving HMM-based visibility-region estimation into polar-domain simultaneous OMP improves near-field, spatially non-stationary channel estimation in ELAA systems while keeping asymptotic complexity unchanged.

desk verdict A clean, incremental extension of P-SOMP with HMM-based VR estimation; the gains are real in simulation but the emission model is hand-tuned and the most relevant baselines are missing. read the letter →

arxiv 2508.04222 v1 pith:DYXAJQ2Z submitted 2025-08-06 eess.SP

Thibaut Ceulemans , Cel Thys , Robbert Beerten , Zhuangzhuang Cui , Sofie Pollin This is my paper · ORCID
classification eess.SP
keywords channelestimationextremelylargeaperturearraysnear-fieldspatialnon-stationarityvisibilityregionhiddenMarkovmodelorthogonalmatchingpursuit6G
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper is trying to establish that channel estimation for extremely large aperture arrays, where hundreds of antennas face near-field spherical wavefronts and different antennas see different propagation paths, can be made substantially more accurate by estimating, for each path, which antennas actually see it and masking the steering vectors accordingly. The proposed algorithm, VR-HMM-P-SOMP, does this by inserting a two-state hidden Markov model into the polar-domain simultaneous orthogonal matching pursuit loop: after each path is selected, the per-antenna reduction in the residual is converted into emission probabilities, Viterbi decoding yields the visibility-region mask, and the mask is applied before the next projection. In simulation the method beats the unmasked P-SOMP at every SNR tested and beats subarray-based estimators by about 6.5 dB at -5 dB SNR, while asymptotically keeping the same computational complexity. A reader should care because spatial non-stationarity and near-field propagation are two main obstacles to making ELAA systems work in 6G, and this is a low-complexity way to address both at once.

What carries the argument

A two-state hidden Markov model over the antenna array, with states 'in VR' and 'out of VR,' whose emission probabilities are a sigmoid (steepness $T=20$) of the per-antenna average residual reduction caused by adding the newly selected path. Viterbi decoding then returns the most likely binary VR mask, which is applied to the selected near-field polar-domain steering vector before the least-squares re-projection. The HMM's transition probabilities encode spatial continuity (probability $1-1/N$ of staying in the same state between adjacent antennas), which is what lets the mask estimation use neighboring-antenna context rather than treating antennas independently.

What would settle it

Run VR-HMM-P-SOMP on simulated channels where the true VR masks are known but the per-antenna residual reductions are deliberately decorrelated from VR membership, for example by adding two paths with overlapping support or strong noise correlation across antennas. If the Viterbi-decoded masks no longer match the true masks and the NMSE advantage over unmasked P-SOMP disappears, the central claim that residual reduction reveals visibility regions would be falsified. Alternatively, a measurement campaign with a controllable blocker could compare estimated masks against known blockage geometry.

Watch

Extended reading notes

Core claim

The central claim is that the visibility region of each propagation path can be recovered on the fly from the residual behavior of a greedy sparse-recovery algorithm, and that masking the near-field polar-domain steering vectors with that recovered mask yields a better channel estimate than either ignoring non-stationarity or partitioning the array into stationary subarrays. The paper models the channel with a physics-based hybrid model in which each path has a steering vector $b(\theta_l, r_l)$ depending on angle and distance, multiplied element-wise by a VR mask $s_{m,l}$; masks may be all-ones, binary, or non-binary, with the non-binary case following a Fresnel knife-edge diffraction gain

Load-bearing premise

The whole VR estimation rests on the assumption that the per-antenna average residual reduction is monotonically related to whether that antenna lies in the path's visibility region, with the relationship fixed as a sigmoid of steepness $T=20$; this mapping is introduced as a design choice and not derived from the channel statistics.

Editorial extensions

If this is right

  • The algorithm improves NMSE over P-SOMP at all tested SNR levels, with roughly 2 dB gain at 5 dB SNR.
  • At low SNR, full-array VR masking beats subarray P-SOMP by up to 6.5 dB (at -5 dB SNR), because it avoids the reduced per-subarray aperture.
  • Adding HMM-based VR estimation does not change the asymptotic complexity order, $O(\hat{L} N S T M)$, relative to P-SOMP.
  • In denser scattering (larger $L$), the method still outperforms the benchmarks, indicating resilience to reduced sparsity.
  • The approach works with non-binary (diffraction) VR masks in the channel model even though it estimates binary masks, leaving explicit non-binary mask estimation as future work.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The residual-reduction observation is not tied to OMP; the same HMM-VR masking idea could be bolted onto other greedy or message-passing sparse-recovery schemes, potentially improving them where spatial non-stationarity is present.
  • Because the emission mapping is an assumed sigmoid rather than derived from channel statistics, the reported gains may be sensitive to the steepness $T=20$ and to the transition probabilities; tuning these from data or learning the mapping could change the margins.
  • The paper itself notes that explicit non-binary mask estimation is left for future research, so diffraction-shaped power variations are currently approximated by a hard binary mask; estimating quantized gain levels directly is a natural extension.
  • The flattening of the NMSE curve at high SNR suggests a floor set by VR estimation error; the genie-aided comparison already indicates this ceiling, making closure of that gap an open target.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper considers channel estimation for ELAA systems operating in the near field with spatial non-stationarity. It proposes a hybrid channel model that includes non-binary visibility-region (VR) masks generated by a knife-edge diffraction model. The main algorithmic contribution is VR-HMM-P-SOMP, which interleaves binary VR-mask estimation into the polar-domain simultaneous OMP framework. After each support selection, a two-state HMM over antennas is decoded via Viterbi to produce a VR mask; the mask is then applied to the selected steering vector before the next orthogonal projection. Simulations compare the proposed method with LS, P-SOMP, two subarray P-SOMP variants, and a genie-aided version, reporting NMSE gains particularly at low SNR and sparse settings. The paper claims the method preserves the asymptotic complexity of P-SOMP.

Significance. If the reported gains hold, the paper offers a low-complexity heuristic for incorporating spatial non-stationarity into greedy sparse channel estimation, an important problem for ELAA/6G. The paper is transparent about the oracle sparsity L_hat = 2L and about the heuristic nature of the HMM emission model, and it provides reproducible-looking algorithmic pseudocode and simulation details. However, the core advantage over P-SOMP depends entirely on the ad hoc sigmoid emission mapping with a fixed temperature T=20, and the validation is confined to the authors' own channel model with hand-set HMM parameters. The significance is therefore conditional on additional robustness and generalization evidence.

major comments (3)
  1. [Section III.C, Algorithm 1 Step 11 and Table I] The emission model in Step 11 is an ad hoc sigmoid mapping o -> sigma(o) with fixed steepness T=20. This mapping is not derived from the channel model in Eq. (3), and no sensitivity analysis is provided for T, the transition probabilities (1-1/N, 1/N), or the initial probabilities (0.55, 0.45). Since Step 13 multiplies the steering vector by the resulting binary mask, any miscalibration directly propagates into the support projection and the final NMSE. The claimed 2 dB gain over P-SOMP at 5 dB SNR rests on this untested calibration. I request either a derivation of the emission mapping from the channel statistics or a systematic robustness study varying T and the HMM parameters across SNR, pilot length, subcarrier number, and VR geometry.
  2. [Section III.A and Section IV] The simulations evaluate the algorithm only with the oracle stopping sparsity L_hat = 2L, as explicitly stated in Section III.A. This is a free parameter and is not available in practice. The performance comparison with P-SOMP and subarray methods could change materially when L_hat must be estimated from the data (e.g., via a threshold on residual energy or a sparsity penalty). The paper should either demonstrate that the reported gains persist with a realistic data-driven stopping rule or clearly state the sensitivity of the results to L_hat.
  3. [Section IV and channel model in Section II.B] The validation is entirely on the authors' synthetic channel model, including the non-binary VR masks generated by the knife-edge model in Eq. (5). The proposed algorithm estimates binary masks while the channel contains non-binary diffraction masks, so the benchmark comparison may be favorable because the competing methods are designed for stationary channels. To support the general claim of robustness, the paper should include at least one evaluation under a different or measurement-based channel model, or a model-mismatch analysis showing how performance degrades when the assumed VR statistics differ from the true ones.
minor comments (5)
  1. [Notation] The symbol T is used both for the pilot length in Eq. (1) and for the sigmoid temperature in Step 11 and Table I. This is confusing, especially in Step 10 where T appears in the averaging operation. Please rename one of them.
  2. [Table I] Table I lists 'Channel SNR 0 dB', but Fig. 3 sweeps SNR over -15 to 20 dB. This entry is inconsistent with the reported experiments and should be clarified or removed.
  3. [Section II.B] In the non-binary VR mask case, the mask depends on the subcarrier index m through lambda_m, but the model in Eq. (3) writes s_{m,l} without emphasizing this dependence in the notation. This makes the subsequent averaging in Step 10 over subcarriers less transparent. Please clarify.
  4. [Algorithm 1] The function freshape is described verbally but not defined precisely in the pseudocode or in the notation section. A concise definition would improve reproducibility.
  5. [Section V] The conclusion acknowledges that explicit non-binary mask estimation is left for future research. This is an honest limitation, but it should be reflected earlier in the paper and in the abstract, as the title and contribution list emphasize non-binary VR modeling.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the proposed algorithm's gains are evaluated against simulated ground truth, and its HMM/emission parameters are hand-set design choices, not fitted outputs renamed as predictions.

full rationale

The paper's derivation chain is self-contained at the algorithmic level. The channel model (Eq. 3) is a physical simulator with non-binary VR masks from knife-edge diffraction [25],[30]; the proposed VR-HMM-P-SOMP estimates binary VR masks from residual reductions inside a standard P-SOMP loop (Algorithm 1, Steps 7-13). The HMM observation at Step 10 is computed from the current OMP residual, and Step 11's sigmoid emission mapping with T=20 is an explicitly empirical design choice, not a parameter fitted to the true VR mask and then reported as a prediction. The NMSE results (Figs. 3-4) compare the estimate against an independently generated channel realization, so the reported gains are not forced by construction. The cited prior work [24],[25],[26],[27],[28] is external; there is no load-bearing self-citation chain and no uniqueness argument imported from the authors' own prior results. The stated limitation that explicit non-binary mask estimation is left for future research (Section V) and the lack of sensitivity analysis for T are robustness/correctness concerns, but they do not make the central claim circular. No equation in the paper reduces to its own input by definition.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central claim relies on the sparse polar-domain representation, the elementwise VR mask model, and the ad hoc HMM emission; the algorithm's hand-set parameters (T=20, transition/initial probabilities, L_hat=2L) are free choices that affect the reported NMSE.

free parameters (5)
  • Stopping sparsity L_hat = 2L (twice true sparsity)
    Simulations run Algorithm 1 for L_hat = 2L, which requires knowledge of the true number of paths L; in practice a stopping rule is needed, and this oracle choice affects all NMSE results.
  • Sigmoid temperature T = 20
    Emission mapping steepness empirically set to 20 in Step 11 of Algorithm 1; no optimization or sensitivity analysis is provided.
  • HMM transition probability (stay in VR) = 1 - 1/N
    Transition matrix chosen by hand in Table I, not learned from data; assumes spatial continuity with a fixed switch probability.
  • HMM initial probabilities = (0.55, 0.45)
    Initial state distribution chosen in Table I, arbitrary and not estimated from channel statistics.
  • Polar dictionary size S = 2555
    Number of polar-domain steering vectors; based on the sampling strategy from [24] but a design parameter that trades resolution against complexity.
assumptions (6)
  • domain assumption Channel is sparse in the polar domain: each path can be represented by a near-field steering vector b(theta, r) and L << N.
    The P-SOMP dictionary W in Eq. 6 assumes exact sparse representation; introduced in Section III-A.
  • domain assumption VR mask multiplies the steering vector elementwise, and a binary mask suffices for estimation even when the true mask is non-binary.
    The channel model Eq. 3 uses element-wise multiplication; the HMM uses two states (in/out of VR), Section III-B.
  • domain assumption Spatial continuity of VR states follows a Markov chain with fixed transition probabilities.
    The HMM prior assumes adjacent antennas are likely to share VR state; transition probabilities set in Table I.
  • ad hoc to paper The emission likelihood: average residual reduction o is monotonically related to VR membership via sigmoid sigma(o).
    Introduced without derivation in Step 11; a design choice, not a consequence of the channel model.
  • domain assumption Near-field propagation uses spherical wavefronts.
    Steering vector b(theta, r) of Eq. 4 assumes spherical phase fronts; standard near-field model from [24].
  • standard math Viterbi decoding correctly infers the most likely HMM state sequence.
    Used in Step 12 to find the most likely VR mask; standard algorithm from [31].

how reviews work

0 comments
Cite this review

Pith. "Pith review of Near-Field Spatial non-Stationary Channel Estimation: Visibility-Region-HMM-Aided Polar-Domain Simultaneous OMP." pith.science (2026). https://pith.science/paper/DYXAJQ2Z

@misc{pith2026250804222,
  author       = {Pith},
  title        = {Pith review of: Near-Field Spatial non-Stationary Channel Estimation: Visibility-Region-HMM-Aided Polar-Domain Simultaneous OMP},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DYXAJQ2Z}},
  note         = {Machine review of arXiv:2508.04222}
}
read the original abstract

This work focuses on channel estimation in extremely large aperture array (ELAA) systems, where near-field propagation and spatial non-stationarity introduce complexities that hinder the effectiveness of traditional estimation techniques. A physics-based hybrid channel model is developed, incorporating non-binary visibility region (VR) masks to simulate diffraction-induced power variations across the antenna array. To address the estimation challenges posed by these channel conditions, a novel algorithm is proposed: Visibility-Region-HMM-Aided Polar-Domain Simultaneous Orthogonal Matching Pursuit (VR-HMM-P-SOMP). The method extends a greedy sparse recovery framework by integrating VR estimation through a hidden Markov model (HMM), using a novel emission formulation and Viterbi decoding. This allows the algorithm to adaptively mask steering vectors and account for spatial non-stationarity at the antenna level. Simulation results demonstrate that the proposed method enhances estimation accuracy compared to existing techniques, particularly in low-SNR and sparse scenarios, while maintaining a low computational complexity. The algorithm presents robustness across a range of design parameters and channel conditions, offering a practical solution for ELAA systems.

Figures

Figures reproduced from arXiv: 2508.04222 by the authors.

Figure 1
Figure 1. Diffraction gain Diffraction scatterer LOS blockage Reflection scatterer [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Illustration of SnS near-field scenario III. PROPOSED ALGORITHM A. P-SOMP The proposed algorithm builds upon the existing P￾SOMP [24] framework for channel estimation. In this frame￾work, the channel is transformed into a sparse representation in the polar domain as hm = WhP m, where h P denotes the sparse channel representation, and W is the polar-domain transformation matrix, defined as: W = [b(θ1, r1), b(θ2, r2),… view at source ↗
Figure 3
Figure 3. NMSE comparison for varying SNR. 1 2 3 4 5 6 7 8 9 10 L -16 -14 -12 -10 -8 -6 -4 -2 0 NMSE (dB) LS Genie aided VR-HMM-P-SOMP P-SOMP Subarray P-SOMP (i) Subarray P-SOMP (ii) VR-HMM-P-SOMP [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: NMSE comparison for varying number of dominant propagation paths. [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Parametric Diffraction-Based Object Sensing: Modeling, Estimation, and Fundamental Limits

    eess.SP 2026-07 conditional novelty 6.0 of 10

    Diffraction patterns of partially blocking objects carry enough information to jointly estimate blockage shape, range, and source directions, with ML estimation approaching the Cramér-Rao bound.

Reference graph

Works this paper leans on

31 extracted references · 31 canonical work pages · cited by 1 Pith paper

  1. [1]

    Future technology trends of terrestrial international mobile telecommu- nications systems towards 2030 and beyond,

    “Future technology trends of terrestrial international mobile telecommu- nications systems towards 2030 and beyond,” Geneva, Zwitserland, Rep. ITU-R M.2516-0

    work page

  2. [2]

    On the road to 6G: Visions, requirements, key technologies, and testbeds,

    C.-X. Wang, X. You, X. Gao, X. Zhu, Z. Li, C. Zhang, H. Wang, Y . Huang, Y . Chen, H. Haas, J. S. Thompson, E. G. Larsson, M. D. Renzo, W. Tong, P. Zhu, X. Shen, H. V . Poor, and L. Hanzo, “On the road to 6G: Visions, requirements, key technologies, and testbeds,” IEEE Communications Surveys & Tutorials , vol. 25, no. 2, pp. 905–974

    work page

  3. [3]

    A tutorial on near-field XL- MIMO communications towards 6G,

    H. Lu, Y . Zeng, C. You, Y . Han, J. Zhang, Z. Wang, Z. Dong, S. Jin, C.- X. Wang, T. Jiang, X. You, and R. Zhang, “A tutorial on near-field XL- MIMO communications towards 6G,” IEEE Communications Surveys & Tutorials, pp. 1–1

    work page

  4. [4]

    Spherical wave channel and analysis for large linear array in LoS conditions,

    Z. Zhou, X. Gao, J. Fang, and Z. Chen, “Spherical wave channel and analysis for large linear array in LoS conditions,” in 2015 IEEE Globecom Workshops (GC Wkshps) . IEEE, pp. 1–6

    work page 2015

  5. [5]

    Near-field communications: A tutorial review,

    Y . Liu, Z. Wang, J. Xu, C. Ouyang, X. Mu, and R. Schober, “Near-field communications: A tutorial review,” pp. 1999–2049, 2023

    work page 1999

  6. [6]

    Towards very large aperture massive MIMO: A measurement based study,

    A. O. Martinez, E. De Carvalho, and J. Ø. Nielsen, “Towards very large aperture massive MIMO: A measurement based study,” in 2014 IEEE Globecom Workshops (GC Wkshps) . IEEE, 2014, pp. 281–286

    work page 2014

  7. [7]

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

    E. De Carvalho, A. Ali, A. Amiri, M. Angjelichinoski, and R. W. Heath, “Non-stationarities in extra-large-scale massive MIMO,” IEEE Wireless Communications, vol. 27, no. 4, pp. 74–80, 2020

    work page 2020

  8. [8]

    Scaling up MIMO: Opportunities and challenges with very large arrays,

    F. Rusek, D. Persson, B. K. Lau, E. G. Larsson, T. L. Marzetta, O. Edfors, and F. Tufvesson, “Scaling up MIMO: Opportunities and challenges with very large arrays,” IEEE Signal Processing Magazine , vol. 30, no. 1, pp. 40–60, 2013

    work page 2013

Show all 31 references
  1. [9]

    Measurement-based analysis of millimeter-wave channel sparsity,

    W. Sloane, C. Gentile, M. Shafi, J. Senic, P. A. Martin, and G. K. Woodward, “Measurement-based analysis of millimeter-wave channel sparsity,” IEEE Antennas and Wireless Propagation Letters , vol. 22, no. 4, pp. 784–788, 2023

    2023

  2. [10]

    Wireless channel sparsity: Measurement, analysis, and exploitation in estimation,

    R. He, B. Ai, G. Wang, M. Yang, C. Huang, and Z. Zhong, “Wireless channel sparsity: Measurement, analysis, and exploitation in estimation,” IEEE Wireless Communications , vol. 28, no. 4, pp. 113–119, 2021

    2021

  3. [11]

    Deterministic ray tracing: A promising approach to THz channel modeling in 6G deployment scenarios,

    J. Zhang, J. Lin, P. Tang, W. Fan, Z. Yuan, X. Liu, H. Xu, Y . Lyu, L. Tian, and P. Zhang, “Deterministic ray tracing: A promising approach to THz channel modeling in 6G deployment scenarios,” IEEE Communications Magazine, vol. 62, no. 2, pp. 48–54, 2024

    2024

  4. [12]

    Channel sparsity variation and model-based analysis on 6, 26, and 105 GHz measurements,

    X. Liu, J. Zhang, P. Tang, L. Tian, H. Tataria, S. Sun, and M. Shafi, “Channel sparsity variation and model-based analysis on 6, 26, and 105 GHz measurements,” IEEE Transactions on V ehicular Technology , vol. 73, no. 7, pp. 9387–9397, 2024

    2024

  5. [13]

    Compressed channel sensing: A new approach to estimating sparse multipath chan- nels,

    W. U. Bajwa, J. Haupt, A. M. Sayeed, and R. Nowak, “Compressed channel sensing: A new approach to estimating sparse multipath chan- nels,” Proceedings of the IEEE , vol. 98, no. 6, pp. 1058–1076

  6. [14]

    Application of com- pressive sensing to sparse channel estimation,

    C. R. Berger, Z. Wang, J. Huang, and S. Zhou, “Application of com- pressive sensing to sparse channel estimation,” IEEE Communications Magazine, vol. 48, no. 11, pp. 164–174

  7. [15]

    Massive-MIMO sparse uplink channel estimation using implicit training and compressed sensing,

    B. Mansoor, S. Nawaz, and S. Gulfam, “Massive-MIMO sparse uplink channel estimation using implicit training and compressed sensing,” Applied Sciences , vol. 7, no. 1, p. 63

  8. [16]

    Joint burst LASSO for sparse channel estimation in multi-user massive MIMO,

    A. Liu, V . Lau, and W. Dai, “Joint burst LASSO for sparse channel estimation in multi-user massive MIMO,” in 2016 IEEE International Conference on Communications (ICC) , 2016, pp. 1–6

    2016

  9. [17]

    Channel estimation and precoder design for millimeter-wave communications: The sparse way,

    P. Schniter and A. Sayeed, “Channel estimation and precoder design for millimeter-wave communications: The sparse way,” in 2014 48th Asilomar Conference on Signals, Systems and Computers , 2014, pp. 273–277

    2014

  10. [18]

    Leveraging sparsity into massive MIMO channel estimation with the adaptive-LASSO,

    G. Destino, M. Juntti, and S. Nagaraj, “Leveraging sparsity into massive MIMO channel estimation with the adaptive-LASSO,” in 2015 IEEE Global Conference on Signal and Information Processing (GlobalSIP) , 2015, pp. 166–170

    2015

  11. [19]

    Joint visibility region detection and channel estimation for XL-MIMO systems via alternating MAP

    W. Xu, A. Liu, and M.-j. Zhao, “Joint visibility region detection and channel estimation for XL-MIMO systems via alternating MAP.”

  12. [20]

    Channel esti- mation for XL-RIS-aided millimeter-wave systems,

    X. Yu, W. Shen, R. Zhang, C. Xing, and T. Q. S. Quek, “Channel esti- mation for XL-RIS-aided millimeter-wave systems,” IEEE Transactions on Communications , vol. 71, no. 9, pp. 5519–5533, 2023

    2023

  13. [21]

    Hierarchical-block sparse bayesian learning for spatial non-stationary massive MIMO channel estimation,

    J. Chen, P. Zhang, N. Ma, and X. Xu, “Hierarchical-block sparse bayesian learning for spatial non-stationary massive MIMO channel estimation,” IEEE Wireless Communications Letters , vol. 11, no. 5, pp. 888–892, 2022

    2022

  14. [22]

    Adaptive grouping sparse bayesian learning for channel estimation in non-stationary uplink massive MIMO systems,

    X. Cheng, K. Xu, J. Sun, and S. Li, “Adaptive grouping sparse bayesian learning for channel estimation in non-stationary uplink massive MIMO systems,” IEEE Transactions on Wireless Communications , vol. 18, no. 8, pp. 4184–4198, 2019

    2019

  15. [23]

    Greed is good: Algorithmic results for sparse approximation,

    J. Tropp, “Greed is good: Algorithmic results for sparse approximation,” IEEE Transactions on Information Theory , vol. 50, no. 10, pp. 2231– 2242

  16. [24]

    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 Transactions on Communications , vol. 70, no. 4, pp. 2663–2677

  17. [25]

    Spatial non- stationary near-field channel modeling and validation for massive MIMO systems,

    Z. Yuan, J. Zhang, Y . Ji, G. F. Pedersen, and W. Fan, “Spatial non- stationary near-field channel modeling and validation for massive MIMO systems,” IEEE Transactions on Antennas and Propagation , vol. 71, no. 1, pp. 921–933

  18. [26]

    Channel estimation for extremely large-scale massive MIMO systems,

    Y . Han, S. Jin, C.-K. Wen, and X. Ma, “Channel estimation for extremely large-scale massive MIMO systems,” IEEE Wireless Communications Letters, vol. 9, no. 5, pp. 633–637

  19. [27]

    Non-stationary channel estimation for extremely large-scale MIMO,

    Y . Chen and L. Dai, “Non-stationary channel estimation for extremely large-scale MIMO,” IEEE Transactions on Wireless Communications , vol. 23, no. 7, pp. 7683–7697

  20. [28]

    Joint visibility region and channel estimation for extremely large-scale MIMO systems,

    A. Tang, J.-B. Wang, Y . Pan, W. Zhang, X. Zhang, Y . Chen, H. Yu, and R. C. De Lamare, “Joint visibility region and channel estimation for extremely large-scale MIMO systems,” IEEE Transactions on Com- munications, vol. 72, no. 10, pp. 6087–6101

  21. [29]

    Properties of focused apertures in the fresnel region,

    J. Sherman, “Properties of focused apertures in the fresnel region,” IRE Transactions on Antennas and Propagation , vol. 10, no. 4, pp. 399–408

  22. [30]

    Propagation by diffraction,

    “Propagation by diffraction,” Geneva, Zwitserland, 2019, Rec. ITU-R P.526–15

    2019

  23. [31]

    The viterbi algorithm,

    G. Forney, “The viterbi algorithm,” Proceedings of the IEEE , vol. 61, no. 3, pp. 268–278, 1973

    1973

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.