Pith. sign in

REVIEW 2 major objections 5 minor 30 references

A Group-Wise Narrow Beam Design for Uplink Channel Estimation in Hybrid Beamforming Systems

T0 review · 2 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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

Pith's one-line read A group-wise narrow beam design makes single-pilot uplink channel estimation in partially connected hybrid massive MIMO accurate and fast.

desk verdict A plausible incremental contribution to PC-HBF channel estimation, but the load-bearing narrow-beam filter design is never specified, so the simulations cannot be reproduced. read the letter →

arxiv 2506.01043 v1 pith:2CJPCQWC submitted 2025-06-01 eess.SP

Yufan Zhou , Yongbo Xiao , An Liu This is my paper
classification eess.SP
keywords uplinkchannelestimationhybridbeamformingpartiallyconnectedstructuremassiveMIMOgroup-wisenarrowbeamvariationalBayesianinferencecompressivesensingantennagroupingoptimization
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

The paper tries to establish that uplink channel estimation in partially connected hybrid beamforming massive MIMO systems can be made both accurate and real-time using a single uplink pilot symbol. Its central proposal is a group-wise narrow beam design that divides the columns of the uniform planar array into groups and assigns each group a narrow beam covering one sub-interval of the vertical angle range, removing the vertical-angle ambiguity that plagues wide beams while preserving array gain. A second ingredient optimizes which columns go to which group, balancing interference suppression and angular resolution in the horizontal dimension. A low-complexity inference algorithm, GW-SC-VBI, then splits the large compressive-sensing problem into parallel smaller ones with a final joint refinement step. If right, the scheme gives a practical trade-off: estimation accuracy close to the best Bayesian baselines at roughly one third of their computation time.

What carries the argument

The load-bearing object is the set of narrow beam matrices $W_g = \operatorname{blkdiag}(a_z(\omega_g), \ldots, a_z(\omega_g))$, one per group, where $a_z(\omega_g)$ is a constant-modulus narrow beam pointing to the center $\omega_g$ of the vertical sub-interval $\Phi_g$; these are intended to act as bandpass filters from filter-design theory. The analog beam matrix takes the form $\mathbf{F}_a = \sum_{g=1}^{G} W_g \otimes \operatorname{diag}(s_g)$, with binary grouping vectors $s_g$ that assign UPA columns to groups. The argument runs on the approximation that the out-of-band attenuation of these filters makes cross-group terms in the observation model negligible, reducing the full compressive-sensing problem to per-group problems of dimension roughly $N_{RF}L/G^2$, which are solved in parallel by the SC-VBI module and then stitched together by a joint-processing step. The same grouping vectors also determine the horizontal ambiguity function, so the EDA optimization targets integrated side-lobe level and statistical resolution limit to balance interference suppression against resolution.

What would settle it

Design concrete constant-modulus narrow-beam filters for a given subarray size $M$ and compute the ratio $\|F_g A_i(\Omega_i)\|/\|F_g A_g(\Omega_g)\|$ for $i\neq g$; if this cross-group ratio is not small, the approximation in equation (26) fails and the group-wise decomposition loses its foundation. A direct experiment would compare GW-SC-VBI with the cross terms removed versus included: any visible gap in NMSE at fixed SNR would show that the neglected interference is load-bearing rather than negligible.

Watch

Extended reading notes

Core claim

The paper's central claim is that the vertical compression inherent to PC-HBF, where each RF chain sees only a vertical subarray, does not have to limit channel estimation provided the analog beams are designed as a bank of narrow bandpass beams matched to the prior vertical angle interval. Each group of UPA columns receives a constant-modulus narrow beam pointing to one vertical sub-interval, so different vertical angles produce distinguishable responses and the array gain is not wasted outside the interval. The paper further claims that a matched antenna grouping pattern, found offline by an estimation-of-distribution algorithm using integrated side-lobe level and statistical resolution limit metrics, improves horizontal angle estimation, and that the resulting group structure lets the channel estimation decompose into low-dimensional parallel SC-VBI subproblems followed by a joint refinement. Together these pieces are claimed to yield single-pilot, real-time estimation with lower complexity than the baseline SC-VBI algorithm and better normalized mean-square error than random or wide beam designs.

Load-bearing premise

The load-bearing premise is that the narrow beams $a_z(\omega_g)$ suppress out-of-band vertical angles strongly enough that interference between groups can be neglected, even though the paper never specifies how these constant-modulus filters are actually designed.

Editorial extensions

If this is right

  • A base station with a UPA and vertical compression can acquire accurate CSI from one pilot symbol, so the scheme fits the practical constraint that many users share one time slot.
  • The proposed beams outperform random and wide beams across SNR and across path counts in the paper's simulations, with the optimized grouping giving an additional improvement over uniform grouping.
  • GW-SC-VBI reduces per-iteration complexity by roughly a factor $1/G^2$ in the group-wise stage and cuts measured CPU time to about one third of the baseline SC-VBI algorithm.
  • Because the analog beam design and grouping pattern are computed offline, the online channel estimation stage carries no extra beam-design cost.
  • The approach is stated to extend naturally to multi-user and multi-antenna scenarios because uplink pilots are orthogonal.

Reading between the lines

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

  • The scheme's practicality hinges on whether real constant-modulus narrow beams with sufficient stopband attenuation exist at the subarray size $M$; the paper invokes filter-design theory but does not provide the actual filter coefficients, so an explicit filter design and a leakage measurement would settle this.
  • A testable extension is to keep the cross-group terms in the observation model instead of dropping them; if the resulting NMSE is noticeably better than the current approximation, the complexity saving comes at a measurable accuracy cost.
  • The offline EDA grouping could be adapted to changing angular statistics or to non-uniform vertical sub-intervals, since the ISL and SRL metrics are computed from the array geometry rather than from a fixed scenario.
  • The group-wise decomposition idea is not tied to SC-VBI: any sparse-recovery estimator that can run on the per-group sensing matrices could inherit the complexity reduction, with the joint-processing stage correcting boundary angles.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The paper addresses single-pilot uplink channel estimation for partially connected hybrid beamforming (PC-HBF) massive MIMO with a uniform planar array (UPA). The vertical angular prior is divided into G sub-intervals, and the Ny UPA columns are partitioned into G groups; each group applies a constant-modulus narrow beam az(omega_g) intended to act as a bandpass filter covering its sub-interval. The antenna grouping pattern is optimized offline by an Estimation of Distribution Algorithm (EDA) using horizontal integrated sidelobe level (ISL) and statistical resolution limit (SRL) metrics. Based on the group-wise beam, the received signal is decomposed into G low-dimensional compressive sensing problems, each solved by the authors' prior SC-VBI algorithm, followed by a joint refinement step. Simulations using QuaDRiGa compare NMSE and runtime against wide/random beams, OMP, Turbo-VBI, and SC-VBI, reporting performance gains and about a factor-of-three CPU-time reduction relative to SC-VBI.

Significance. The practical scenario is well motivated: single-symbol sounding, vertical compression, and phase noise make multi-timeslot training infeasible, so a single-pilot scheme is of genuine interest. The idea of using independent UPA column groups as parallel observations to realize a filter-bank analog beam without additional time slots is attractive and, if the beam filters are realizable, would give a useful complexity-performance trade-off. The paper provides a concrete offline grouping optimization, numerical comparisons, and a runtime table. Its main weakness is that the enabling beam filter az(omega_g) is left unspecified, so the simulations and the central approximation in Eq. (26) cannot be independently checked; this is a reproducibility gap in a load-bearing component rather than a flaw in the overall concept.

major comments (2)
  1. [Section III-B, Eq. (8); Section V-B, Eq. (26)] The cross-group neglect F_g A_i approx 0 for i != g in Eq. (26) is the basis for the parallel decomposition and all complexity savings, but the filter design that would justify it is never given. The manuscript only says the vectors az(omega_g) are designed based on the filter design theory (Section III-B) and that they satisfy a constant-modulus constraint. For the simulated parameters (M=12, G=4, sub-interval width 0.125 in sin(phi)), it is not obvious that a length-12 constant-modulus filter can provide sufficient stopband attenuation to make the dropped terms negligible. Please specify the exact design criterion, the stopband/transition-band targets, and the algorithm used to obtain the constant-modulus weights, and provide a quantitative validation of Eq. (26), e.g., a table of ||F_g A_i(Omega_i)|| / ||F_g A_g(Omega_g)|| for adjacent sub-intervals. Because the FIM/SRL derivation in Eq. (37) uses the same no-leakage model, this gap also affects the grouping optimization.
  2. [Section V-D] The complexity comparison does not account for the number of groups when converting per-group complexity to total complexity. The text gives per-group costs O(1/G^2 N_RF L + 1/G^3 S^3) and O(1/G^2 L^2 S), but there are G groups. If the groups are processed sequentially, as in the MATLAB CPU-time measurement of Table I, the total per-iteration cost is O(N_RF L / G + S^3 / G^2) for the SC-VBI part and at least O(L^2 S / G) for the GE part, not 1/G^2 of the original. Table I's ratio of about 1/3 at G=4 is consistent with a factor-1/G reduction, not 1/G^2. Please clarify whether the claim refers to wall-clock time under parallel processing or total computational work, and correct the analytic expressions accordingly.
minor comments (5)
  1. [Section I (paper organization)] The outline says 'In Section IV, we introduce the proposed low-complexity GW-SC-VBI algorithm,' but the algorithm is presented in Section V; Section IV contains the antenna grouping optimization.
  2. [Eq. (9)] In the last line of Eq. (9), the second steering vector should be a_R(theta_2, phi_0) rather than a_R(theta_2, phi_2), since the horizontal AF is evaluated at a fixed vertical angle phi_0.
  3. [Fig. 11] The caption of Fig. 11 and the corresponding text say 'NMSE of channel estimation versus the SNR,' but the horizontal axis is the number of paths, not SNR; please correct the caption and the in-text reference.
  4. [Algorithm 1] The input list of Algorithm 1 includes rho_g,1 and rho_g,2, but Problem P defines a single bound rho_g; please align the notation and clarify whether the SRL constraint uses one or two bounds per group.
  5. [Appendix A] Appendix A derives only one entry of the Fisher information matrix and states that the others are omitted for space; please include the complete FIM entries (or a supplementary derivation) so that the SRL in Eq. (15) and the EDA optimization in Algorithm 1 can be reproduced.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the beam-design and grouping arguments are construction-based, and the SC-VBI self-citation is used as an independently evaluated module rather than as a load-bearing circular premise.

full rationale

The paper's derivation chain does not reduce any claimed result to its own input. The group-wise narrow beam in Section III-B is an input construction: az(omega_g) is asserted to act as a bandpass filter, and Eq. (26) then neglects cross-group terms by assuming strong out-of-band suppression. This is an unverified and potentially infeasible assumption about constant-modulus filters, but it is not circular, because the beam response is not defined in terms of the channel-estimation output and no fitted parameter is renamed as a prediction. The EDA grouping optimization in Section IV minimizes an independent ISL proxy subject to an SRL constraint computed offline from assumed fixed parameters; the later NMSE simulations (Figs. 8-10) test the resulting design against random and wide-beam baselines, so the validation is external to the optimization objective. The GW-SC-VBI algorithm uses the authors' prior SC-VBI method [14] as a module, and the joint-processing stage also reapplies it; this is a self-citation, but [14] is also evaluated as a baseline in Section VI-B and its role is that of a building block whose behavior is measured in the same experiments, not a premise that assumes the paper's conclusion. No equation is equal to another by construction, and no claimed improvement is forced by definition. The principal weakness is therefore the unspecified constant-modulus filter design behind Eq. (8) and the unquantified cross-group leakage in Eq. (26); that is a correctness and reproducibility risk, not circularity.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new physical entities. The free parameters are mostly design choices that are not fully specified, and the axioms are a mix of standard sparsity assumptions and a critical, unverified approximation on filter stopband performance.

free parameters (5)
  • Narrow beam weights az(omega_g) = not specified
    The core of the beam design; the paper only states they are designed using filter theory but does not provide the design algorithm or weights.
  • Number of groups G = 4 (simulation)
    Chosen for simulation; no rule given for selecting G.
  • ISL sidelobe region Rs = not specified
    Required in eq. (11) for the ISL metric used in EDA optimization, but never defined.
  • SRL upper bounds rho_g = derived from random pattern reference
    Set based on the SRL of a random grouping pattern in Section IV-B, an ad hoc choice.
  • Fixed noise variance and gains for SRL = sigma_g=0.18, alpha1,g=alpha2,g=1
    Used in the offline SRL calculation; the paper claims little effect but this is not demonstrated.
assumptions (4)
  • domain assumption Vertical angles are confined to a prior interval Phi, typically [-pi/6, 0].
    Justifies the vertical compression and the beam coverage. If a user's elevation angle falls outside Phi, the group-wise narrow beams will not cover it.
  • domain assumption The angular domain channel is sparse, with K << L significant paths.
    Basis for the compressive sensing model in eq. (22) and the Bayesian inference algorithm.
  • ad hoc to paper Cross-group interference is negligible after the group-wise narrow beam, F_g A_i approx 0 for i != g.
    Used to decompose the observation model into per-group problems in eq. (26). Validity depends on the unspecified beam filter design.
  • standard math The SC-VBI algorithm from [14] is correct and applicable per group.
    The paper treats SC-VBI as a black box from the authors' own prior work; no derivation or verification is included here.

how reviews work

0 comments
Cite this review

Pith. "Pith review of A Group-Wise Narrow Beam Design for Uplink Channel Estimation in Hybrid Beamforming Systems." pith.science (2026). https://pith.science/paper/2CJPCQWC

@misc{pith2026250601043,
  author       = {Pith},
  title        = {Pith review of: A Group-Wise Narrow Beam Design for Uplink Channel Estimation in Hybrid Beamforming Systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2CJPCQWC}},
  note         = {Machine review of arXiv:2506.01043}
}
read the original abstract

In this paper, we consider uplink channel estimation for massive multi-input multi-output (MIMO) systems with partially connected hybrid beamforming (PC-HBF) structures. Existing beam design and channel estimation schemes are usually based on ideal assumptions and require transmitting pilots across multiple timeslots, making them unsuitable for practical PC-HBF systems. To overcome these drawbacks, we propose a novel beam design and a corresponding channel estimation algorithm to achieve accurate and real-time uplink channel estimation. Firstly, we introduce a group-wise narrow beam design in the vertical dimension to suppress interference from undesired angular components and improve vertical angle estimation accuracy,which divides the columns of the uniform planar array (UPA)into groups and the vertical angle interval into sub-intervals.In this way, each group is assigned with a narrow beam to cover one vertical angle sub-interval, and the set of narrow beams is designed based on the filter design theory. Secondly, we optimize the antenna grouping pattern using the Estimation of Distribution Algorithm (EDA), balancing interference suppression and resolution capability in the horizontal dimension, leading to a better horizontal angle estimation performance. Finally, we design a low-complexity group-wise subspace constrained variational Bayesian inference (GW-SC-VBI) algorithm to fully take advantage of the proposed beam design to achieve both low-complexity and high-accurate channel estimation. Simulation results demonstrate that the proposed scheme achieves notable performance gains over baseline methods.

Figures

Figures reproduced from arXiv: 2506.01043 by the authors.

Figure 1
Figure 1. b, resulting in the vertical angles constrained within a certain prior interval Φ, typically ranging from − 1 6 π to 0. By leveraging this property, vertical compression can achieve a higher compression ratio, thereby improving the efficiency of the system. Specially, we propose a novel group-wise narrow beam design and a corresponding low-complexity channel estimation algorithm only based on a single uplink pilot s… view at source ↗
Figure 2
Figure 2. An illustration of group-wise narrow beam for Ny = 6 and G = 3 with uniform grouping pattern, and different colors correspond to different groups. for each group are non-overlapping and adjusted inde￾pendently. In the final few iterations, a joint estimation is conducted to enhance angle estimation performance, particularly for angles that lie between the boundaries of two adjacent groups. This group-wise approach r… view at source ↗
Figure 3
Figure 3. Vertical AF when the wide beam is adopted. [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Vertical AFs for different analog beams. [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: Convergence behavior of the EDA. domain. Meanwhile, the random beam cannot be aligned with the vertical angle range, resulting in a loss of array gain. Consequently, the proposed design achieves significantly improved vertical angle estimation performance. 2) Convergen…
Figure 6
Figure 6. Figure 6: An illustration of the optimized antenna grouping [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 7
Figure 7. Figure 7: Horizontal AFs for three different antenna groupi [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 10
Figure 10. Figure 10: NMSE of channel estimation versus the SNR. Table I: CPU times of different algorithms. Algorithms CPU times (s) OMP 2.1 Turbo-VBI 63 SC-VBI 12.8 GW-SC-VBI 4.1 lems, but suffers from high computational complexity due to high-dimensional matrix inversions. • SC-VBI algo…

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

30 extracted references · 29 canonical work pages

  1. [14]

    Subspace constrained variat ional bayesian inference for structured compressive sensing with a dynami c grid,

    A. Liu, Y . Zhou, and W. Xu, “Subspace constrained variat ional bayesian inference for structured compressive sensing with a dynami c grid,” IEEE Transactions on Signal Processing , 2025

    work page 2025

  2. [1]

    An overview of massive MIMO: Benefits and challenges,

    L. Lu, G. Y . Li, A. L. Swindlehurst, A. Ashikhmin, and R. Zh ang, “An overview of massive MIMO: Benefits and challenges,” IEEE journal of selected topics in signal processing , vol. 8, no. 5, pp. 742–758, 2014

    2014

  3. [2]

    Analog beamfor ming in MIMO communications with phase shift networks and online ch annel estimation,

    V . V enkateswaran and A.-J. van der V een, “Analog beamfor ming in MIMO communications with phase shift networks and online ch annel estimation,” IEEE Transactions on Signal Processing , vol. 58, no. 8, pp. 4131–4143, 2010

    work page 2010

  4. [3]

    Fully-/partially-conn ected hybrid beamforming architectures for mmwave MU-MIMO,

    X. Song, T. Kühne, and G. Caire, “Fully-/partially-conn ected hybrid beamforming architectures for mmwave MU-MIMO,” IEEE Transac- tions on Wireless Communications , vol. 19, no. 3, pp. 1754–1769, 2019

    work page 2019

  5. [4]

    Performance evaluation of the SRS based MIMO channel estimation on 5G NR open source channel model,

    A. Kalachikov and A. Stenin, “Performance evaluation of the SRS based MIMO channel estimation on 5G NR open source channel model,” in Proc. IEEE 22nd Int. Conf. Young Prof. Electron Devices Mate r . (EDM).IEEE, 2021, pp. 124–127

    work page 2021

  6. [5]

    Fundamentals of statistical signal pr ocessing: Estima- tion theory,

    S. K. Sengijpta, “Fundamentals of statistical signal pr ocessing: Estima- tion theory,” 1995

    work page 1995

  7. [6]

    Performance analysis of channel extrapolation in FDD mass ive MIMO systems,

    F. Rottenberg, T. Choi, P . Luo, C. J. Zhang, and A. F. Molis ch, “Performance analysis of channel extrapolation in FDD mass ive MIMO systems,” IEEE Transactions on Wireless Communications , vol. 19, no. 4, pp. 2728–2741, 2020

    work page 2020

  8. [7]

    Angle domain channel estimation in hybrid millimeter wave massive MIMO systems,

    D. Fan, F. Gao, Y . Liu, Y . Deng, G. Wang, Z. Zhong, and A. Nal lanathan, “Angle domain channel estimation in hybrid millimeter wave massive MIMO systems,” IEEE Transactions on Wireless Communications , vol. 17, no. 12, pp. 8165–8179, 2018

    work page 2018

Show all 30 references
  1. [8]

    Convolutional beamspa ce for array signal processing,

    P . V aidyanathan and P .-C. Chen, “Convolutional beamspa ce for array signal processing,” in ICASSP 2020-2020 IEEE International Confer- ence on Acoustics, Speech and Signal Processing (ICASSP) . IEEE, 2020, pp. 4707–4711

    2020

  2. [9]

    Channel estimation for mmwave using the convolutional beamspace approach,

    P .-C. Chen and P . V aidyanathan, “Channel estimation for mmwave using the convolutional beamspace approach,” IEEE Transactions on Signal Processing, 2024

    2024

  3. [10]

    Closed-loop autonomous pilot and compressive CSIT feedback resource adaptation in multi -user FDD massive MIMO systems,

    A. Liu, F. Zhu, and V . K. N. Lau, “Closed-loop autonomous pilot and compressive CSIT feedback resource adaptation in multi -user FDD massive MIMO systems,” IEEE Transactions on Signal Processing , vol. 65, no. 1, pp. 173–183, 2017

    2017

  4. [11]

    Compres- sive sensing techniques for next-generation wireless comm unications,

    Z. Gao, L. Dai, S. Han, I. Chih-Lin, Z. Wang, and L. Hanzo, “Compres- sive sensing techniques for next-generation wireless comm unications,” IEEE Wireless Communications , vol. 25, no. 3, pp. 144–153, 2018

    2018

  5. [12]

    Chan nel estimation and hybrid precoding for millimeter wave cellul ar systems,

    A. Alkhateeb, O. El Ayach, G. Leus, and R. W. Heath, “Chan nel estimation and hybrid precoding for millimeter wave cellul ar systems,” IEEE Journal of Selected Topics in Signal Processing , vol. 8, no. 5, pp. 831–846, 2014

    2014

  6. [13]

    Hybrid beamforming and DFT-based channel estimation for m illimeter wave MIMO systems,

    M. Soleimani, R. C. Elliott, W. A. Krzymien, J. Melzer, a nd P . Mousavi, “Hybrid beamforming and DFT-based channel estimation for m illimeter wave MIMO systems,” in 2017 IEEE 28th Annual International Sympo- sium on Personal, Indoor , and Mobile Radio Communications ( PIMRC),...

    2017

  7. [15]

    Robust multi-use r channel tracking scheme for 5G new radio,

    Y . Wan, G. Liu, A. Liu, and M.-J. Zhao, “Robust multi-use r channel tracking scheme for 5G new radio,” IEEE Transactions on Wireless Communications, 2023

    2023

  8. [16]

    NR : The new 5G radio access technology,

    S. Parkvall, E. Dahlman, A. Furuskar, and M. Frenne, “NR : The new 5G radio access technology,” IEEE Communications Standards Magazine , vol. 1, no. 4, pp. 24–30, 2017

    2017

  9. [17]

    Dimension-deficient cha nnel esti- mation of hybrid beamforming based on compressive sensing,

    Y . Xiao, Y . Wang, and W. Xiang, “Dimension-deficient cha nnel esti- mation of hybrid beamforming based on compressive sensing, ” IEEE Access, vol. 7, pp. 13 791–13 798, 2019

    2019

  10. [18]

    Limited fe edforward waveform design for OFDM dual-functional radar-communica tions,

    M. F. Keskin, V . Koivunen, and H. Wymeersch, “Limited fe edforward waveform design for OFDM dual-functional radar-communica tions,” IEEE Transactions on Signal Processing , vol. 69, pp. 2955–2970, 2021

    2021

  11. [19]

    Statistical resolution limits and the com plexified crame/spl acute/r-rao bound,

    S. T. Smith, “Statistical resolution limits and the com plexified crame/spl acute/r-rao bound,” IEEE Transactions on Signal Processing , vol. 53, no. 5, pp. 1597–1609, 2005

    2005

  12. [20]

    Pilot patt ern optimization for sparse channel estimation in OFDM systems ,

    H. Wang, Q. Guo, G. Zhang, G. Li, and W. Xiang, “Pilot patt ern optimization for sparse channel estimation in OFDM systems ,” IEEE Communications Letters , vol. 19, no. 7, pp. 1233–1236, 2015

    2015

  13. [21]

    MIMO rad ar ambi- guity functions,

    G. San Antonio, D. R. Fuhrmann, and F. C. Robey, “MIMO rad ar ambi- guity functions,” IEEE Journal of Selected Topics in Signal Processing , vol. 1, no. 1, pp. 167–177, 2007

    2007

  14. [22]

    Ambiguity function for a bistatic radar,

    T. Tsao, M. Slamani, P . V arshney, D. Weiner, H. Schwarzl ander, and S. Borek, “Ambiguity function for a bistatic radar,” IEEE Transactions on Aerospace and Electronic Systems , vol. 33, no. 3, pp. 1041–1051, 1997

    1997

  15. [23]

    Avoiding ambiguity in be amspace processing,

    A. N. Amini and T. T. Georgiou, “Avoiding ambiguity in be amspace processing,” IEEE Signal Processing Letters , vol. 12, no. 5, pp. 372– 375, 2005

    2005

  16. [24]

    Millimeter-wave channel e stimation based on 2-D beamspace MUSIC method,

    Z. Guo, X. Wang, and W. Heng, “Millimeter-wave channel e stimation based on 2-D beamspace MUSIC method,” IEEE transactions on wireless communications, vol. 16, no. 8, pp. 5384–5394, 2017

    2017

  17. [25]

    Fundamentals of statistical signal p rocessing: Estima- tion theory,

    S. K. Sengijpta, “Fundamentals of statistical signal p rocessing: Estima- tion theory,” 1995

    1995

  18. [26]

    On the convergence of a clas s of esti- mation of distribution algorithms,

    Q. Zhang and H. Muhlenbein, “On the convergence of a clas s of esti- mation of distribution algorithms,” IEEE Transactions on evolutionary computation, vol. 8, no. 2, pp. 127–136, 2004

    2004

  19. [27]

    A two-stage 2D channel extrapolation scheme for TDD 5G NR systems,

    Y . Wan and A. Liu, “A two-stage 2D channel extrapolation scheme for TDD 5G NR systems,” IEEE Transactions on Wireless Communications, 2024

    2024

  20. [28]

    Q uadriga: A 3-D multi-cell channel model with time evolution for enabling v irtual field trials,

    S. Jaeckel, L. Raschkowski, K. Börner, and L. Thiele, “Q uadriga: A 3-D multi-cell channel model with time evolution for enabling v irtual field trials,” IEEE Trans. Antennas Propag. , vol. 62, no. 6, pp. 3242–3256, 2014

    2014

  21. [29]

    Signal recovery from rand om mea- surements via orthogonal matching pursuit,

    J. A. Tropp and A. C. Gilbert, “Signal recovery from rand om mea- surements via orthogonal matching pursuit,” IEEE Transactions on information theory , vol. 53, no. 12, pp. 4655–4666, 2007

    2007

  22. [30]

    Robu st recovery of structured sparse signals with uncertain sensing matrix : A Turbo-VBI approach,

    A. Liu, G. Liu, L. Lian, V . K. N. Lau, and M.-J. Zhao, “Robu st recovery of structured sparse signals with uncertain sensing matrix : A Turbo-VBI approach,” IEEE Trans. Wireless Commun. , vol. 19, no. 5, pp. 3185– 3198, 2020

    2020

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.