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arxiv: 1907.04423 · v1 · pith:SUGNGDRXnew · submitted 2019-07-09 · 📡 eess.SP

Off-Grid Aware Channel and Covariance Estimation in mmWave Networks

Chethan Kumar Anjinappa , Ali Cafer Gurbuz , Yavuz Yapici , Ismail Guvenc This is my paper

Pith reviewed 2026-05-24 23:53 UTC · model grok-4.3

classification 📡 eess.SP
keywords mmWavechannel estimationcovariance estimationoff-gridcompressed sensingSOMPparameter perturbation
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The pith

A perturbation mechanism with SOMP jointly solves off-grid angles and weights for mmWave channel and covariance estimation.

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

The paper addresses the off-grid problem that arises when compressed sensing discretizes the continuous angular domain for mmWave networks, which degrades parameter estimation accuracy. It proposes a parameter-perturbation framework that works together with simultaneous orthogonal matching pursuit to estimate both the angle deviations and the signal weights at the same time. This yields more precise channel and covariance estimates than methods that treat the grid as exact. A sympathetic reader would care because these estimates directly affect beam steering and tracking performance in high-frequency wireless systems.

Core claim

The proposed algorithms employ a smart perturbation mechanism in conjunction with a low-complexity greedy framework of simultaneous orthogonal matching pursuit (SOMP), and jointly solve for the off-grid parameters and weights, yielding significant performance improvement in channel and covariance estimation for mmWave networks.

What carries the argument

The parameter-perturbation framework integrated with simultaneous orthogonal matching pursuit (SOMP) that jointly optimizes off-grid angles and coefficients.

If this is right

  • Channel estimates achieve higher accuracy by recovering parameters in the continuous angular space.
  • Covariance estimates improve, supporting downstream network operations.
  • Beam steering and tracking functionalities gain reliability from reduced discretization error.
  • Numerical results demonstrate gains over conventional sparse estimation algorithms that ignore off-grid effects.

Where Pith is reading between the lines

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

  • The same joint perturbation approach could reduce discretization errors in other compressed-sensing applications that involve continuous parameters.
  • It might allow coarser initial grids without accuracy loss, lowering memory and computation in large arrays.
  • Integration with online tracking loops could be tested by feeding the refined angle estimates into subsequent time slots.

Load-bearing premise

A low-dimensional perturbation around a fixed angular grid is sufficient to capture continuous-angle mismatch without introducing bias.

What would settle it

Run a simulation with true angles offset from the discretization grid by amounts exceeding the assumed perturbation range and measure whether the proposed method still shows lower estimation error than standard SOMP.

Figures

Figures reproduced from arXiv: 1907.04423 by Ali Cafer Gurbuz, Chethan Kumar Anjinappa, Ismail Guvenc, Yavuz Yapici.

Figure 1
Figure 1. Figure 1: Block diagram of a mmWave HADB MIMO system. [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of channel estimation error reconstruction performance versus the number of snapshots ( [PITH_FULL_IMAGE:figures/full_fig_p022_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of relative efficiency between different methods versus the number of snapshots ( [PITH_FULL_IMAGE:figures/full_fig_p023_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of NMSE-C between different methods versus the number of snapshots ( [PITH_FULL_IMAGE:figures/full_fig_p023_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Relative efficiency (Left) and NMSE-C (Right) performance based on the sampling scheme employed ( [PITH_FULL_IMAGE:figures/full_fig_p024_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Impact of the grid size employed on the relative efficiency ( [PITH_FULL_IMAGE:figures/full_fig_p025_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Comparison of relative efficiency of PPCOMP and DCOMP at different SNR level ( [PITH_FULL_IMAGE:figures/full_fig_p026_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Relative efficiency performance with different measurements (SNR [PITH_FULL_IMAGE:figures/full_fig_p027_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Relative efficiency dependence on the number of antennas for the PPCOMP and COMP algorithms with the number of [PITH_FULL_IMAGE:figures/full_fig_p027_9.png] view at source ↗
read the original abstract

The spectrum scarcity at sub-6 GHz spectrum has made millimeter-wave (mmWave) frequency band a key component of the next-generation wireless networks. While mmWave spectrum offers extremely large transmission bandwidths to accommodate ever-increasing data rates, unique characteristics of this new spectrum need special consideration to achieve the promised network throughput. In this work, we consider the off-grid problem for mmWave communications, which has a significant impact on basic network functionalities involving beam steering and tracking. The off-grid effect naturally appears in compressed sensing (CS) techniques adopting a discretization approach for representing the angular domain. This approach yields a finite set of discrete angle points, which are an approximation to the continuous angular space, and hence degrade the accuracy of related parameter estimation. In order to cope with the off-grid effect, we present a novel parameter-perturbation framework to efficiently estimate the channel and the covariance for mmWave networks. The proposed algorithms employ a smart perturbation mechanism in conjunction with a low-complexity greedy framework of simultaneous orthogonal matching pursuit (SOMP), and jointly solve for the off-grid parameters and weights. Numerical results show a significant performance improvement through our novel framework as a result of handling the off-grid effects, which is totally ignored in the conventional sparse mmWave channel or covariance estimation algorithms.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes a parameter-perturbation framework for handling off-grid effects in compressed-sensing-based channel and covariance estimation for mmWave networks. It integrates a smart perturbation mechanism with the low-complexity simultaneous orthogonal matching pursuit (SOMP) algorithm to jointly recover off-grid parameters and weights, claiming that this yields significant performance gains over conventional grid-based methods that ignore continuous-angle mismatch.

Significance. If the joint perturbation-SOMP procedure can be shown to recover continuous angles without systematic bias, the work would provide a practical, low-complexity enhancement to mmWave beam steering and tracking. The emphasis on greedy algorithms aligns with real-time network constraints, and any reproducible code or parameter-free derivations would strengthen its contribution.

major comments (2)
  1. [Proposed Framework (perturbation mechanism)] The central claim rests on the assertion that a low-dimensional perturbation around a fixed angular grid suffices to capture arbitrary continuous-angle mismatch. No derivation or guarantee is supplied showing that the joint optimization remains unbiased when the true angle lies outside the local linearization regime of the perturbation, nor is any regularization on perturbation magnitude specified.
  2. [Numerical Results] Numerical results are invoked to demonstrate 'significant performance improvement,' yet the abstract (and visible description) supplies no equations, error-bar details, dataset descriptions, or ablation studies. This leaves the empirical support for the off-grid handling claim unverified and load-bearing for the paper's contribution.
minor comments (1)
  1. [Abstract] The phrasing 'which is totally ignored in the conventional sparse mmWave channel or covariance estimation algorithms' is imprecise; conventional methods do not ignore the effect but approximate it via discretization.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment below and outline the revisions planned to strengthen the paper.

read point-by-point responses

  1. Referee: The central claim rests on the assertion that a low-dimensional perturbation around a fixed angular grid suffices to capture arbitrary continuous-angle mismatch. No derivation or guarantee is supplied showing that the joint optimization remains unbiased when the true angle lies outside the local linearization regime of the perturbation, nor is any regularization on perturbation magnitude specified.

    Authors: The perturbation mechanism relies on a first-order Taylor approximation of the array response vector around the nearest grid point, which is standard in off-grid CS methods and assumes the mismatch remains within the linear regime for a sufficiently fine grid. We acknowledge that the manuscript does not include an explicit derivation of unbiasedness for large deviations or a regularization constraint on the perturbation variable. In the revised version, we will add a dedicated subsection discussing the validity conditions of the linearization (including a bound on maximum perturbation size relative to grid spacing) and introduce a simple quadratic penalty term on the perturbation magnitude to enforce locality. These additions will clarify the operating regime without claiming global guarantees. revision: partial

  2. Referee: Numerical results are invoked to demonstrate 'significant performance improvement,' yet the abstract (and visible description) supplies no equations, error-bar details, dataset descriptions, or ablation studies. This leaves the empirical support for the off-grid handling claim unverified and load-bearing for the paper's contribution.

    Authors: The full manuscript contains a dedicated numerical results section with Monte Carlo simulations comparing the proposed perturbation-SOMP against standard grid-based SOMP for both channel and covariance estimation under varying SNR and grid resolutions. However, we agree that the abstract is too terse and that additional details would improve verifiability. In revision we will (i) expand the abstract to mention key metrics (e.g., normalized MSE reduction) and simulation parameters, (ii) add error bars from 500 independent trials to all figures, (iii) include a brief description of the synthetic mmWave channel model (uniform linear array, clustered angles, Rician fading), and (iv) insert an ablation study on the effect of perturbation step size and grid density. These changes will make the empirical claims self-contained. revision: yes

Circularity Check

0 steps flagged

No circularity detected; derivation self-contained

full rationale

The provided abstract and description contain no equations, fitted parameters presented as predictions, or self-citations used to justify uniqueness or ansatzes. The method is described as jointly solving for off-grid parameters and weights via perturbation and SOMP, with performance gains shown via numerical results rather than by construction. No load-bearing step reduces to a self-definition or renamed input. This is the common honest outcome for papers whose central claims rest on empirical validation against conventional baselines rather than internal redefinition.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Review performed on abstract only; no explicit free parameters, axioms, or invented entities are stated in the provided text.

pith-pipeline@v0.9.0 · 5767 in / 1063 out tokens · 19246 ms · 2026-05-24T23:53:49.949747+00:00 · methodology

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Reference graph

Works this paper leans on

40 extracted references · 40 canonical work pages · 1 internal anchor

  1. [1]

    Millimeter-wave beamforming as an enabling technology for 5G cellular communications: Theoretical feasibility and prototype results,

    W. Roh, J.-Y . Seol, J. Park, B. Lee, J. Lee, Y . Kim, J. Cho, K. Cheun, and F. Aryanfar, “Millimeter-wave beamforming as an enabling technology for 5G cellular communications: Theoretical feasibility and prototype results,” IEEE Commun. Mag., vol. 52, no. 2, pp. 106–113, Feb. 2014

    work page 2014

  2. [2]

    Millimeter-wave cellular wireless networks: Potentials and challenges,

    S. Rangan, T. S. Rappaport, and E. Erkip, “Millimeter-wave cellular wireless networks: Potentials and challenges,” Proc. of the IEEE , vol. 102, no. 3, pp. 366–385, Mar. 2014

    work page 2014

  3. [3]

    Hybrid MIMO architectures for millimeter wave communications: Phase shifters or switches?

    R. Mendez-Rial, C. Rusu, N. Gonzalez-Prelcic, A. Alkhateeb, and R. W. Heath, “Hybrid MIMO architectures for millimeter wave communications: Phase shifters or switches?” IEEE Access, vol. 4, pp. 247–267, Jan. 2016

    work page 2016

  4. [4]

    An overview of signal processing techniques for millimeter wave MIMO systems,

    R. W. Heath, N. Gonzlez-Prelcic, S. Rangan, W. Roh, and A. M. Sayeed, “An overview of signal processing techniques for millimeter wave MIMO systems,” IEEE J. Sel. Topics Sig. Proc. , vol. 10, no. 3, pp. 436–453, Apr. 2016

    work page 2016

  5. [5]

    Spatial channel covariance estimation for mmwave hybrid MIMO architecture,

    S. Park and R. W. Heath, “Spatial channel covariance estimation for mmwave hybrid MIMO architecture,” in Proc. IEEE Asilomar Conf. on Signals, Syst., and Comput. , Pacific Grove, CA, Nov. 2016, pp. 1424–1428

    work page 2016

  6. [6]

    Adaptive hybrid precoding and combining in mmwave multiuser MIMO systems based on compressed covariance estimation,

    R. Mendez-Rial, N. Gonzalez-Prelcic, and R. W. Heath, “Adaptive hybrid precoding and combining in mmwave multiuser MIMO systems based on compressed covariance estimation,” in Proc. IEEE Int. Workshop on Comput. Adv. in Multi-Sensor Adaptive Proc. (CAMSAP) . Cancun, Mexico: IEEE, 2015, pp. 213–216. 29

    work page 2015

  7. [7]

    Exploiting spatial channel covariance for hybrid precoding in massive MIMO systems,

    S. Park, J. Park, A. Yazdan, and R. W. Heath, “Exploiting spatial channel covariance for hybrid precoding in massive MIMO systems,” IEEE Trans. Sig. Proc. , vol. 65, no. 14, pp. 3818–3832, July 2017

    work page 2017

  8. [8]

    A scalable and statistically robust beam alignment technique for millimeter- wave systems,

    X. Song, S. Haghighatshoar, and G. Caire, “A scalable and statistically robust beam alignment technique for millimeter- wave systems,” IEEE Trans. Wireless Commun. , vol. 17, no. 7, pp. 4792–4805, July 2018

    work page 2018

  9. [9]

    Millimeter wave mimo channel tracking systems,

    J. He, T. Kim, H. Ghauch, K. Liu, and G. Wang, “Millimeter wave mimo channel tracking systems,” in Proc. IEEE Global Commun. Conf. Workshops, Austin, TX, Dec. 2014, pp. 416–421

    work page 2014

  10. [10]

    Channel estimation via orthogonal matching pursuit for hybrid MIMO systems in millimeter wave communications,

    J. Lee, G. Gil, and Y . H. Lee, “Channel estimation via orthogonal matching pursuit for hybrid MIMO systems in millimeter wave communications,” IEEE Trans. Commun. , vol. 64, no. 6, pp. 2370–2386, June 2016

    work page 2016

  11. [12]

    Compressed sensing off the grid,

    G. Tang, B. N. Bhaskar, P. Shah, and B. Recht, “Compressed sensing off the grid,” IEEE Trans. Inf. Theory , vol. 59, no. 11, pp. 7465–7490, Nov. 2013

    work page 2013

  12. [13]

    Sensitivity to basis mismatch in compressed sensing,

    Y . Chi, L. L. Scharf, A. Pezeshki, and A. R. Calderbank, “Sensitivity to basis mismatch in compressed sensing,” IEEE Trans. Sig. Proc., vol. 59, no. 5, pp. 2182–2195, May 2011

    work page 2011

  13. [14]

    Sparse channel estimation in millimeter-wave communications via parameter perturbed OMP,

    A. C. Gurbuz, Y . Yapici, and I. Guvenc, “Sparse channel estimation in millimeter-wave communications via parameter perturbed OMP,” in Proc. IEEE Int. Conf. Commun. (ICC) Workshops , Kansas City, MO, May 2018, pp. 1–6

    work page 2018

  14. [16]

    Joint spatial division and multiplexingthe large-scale array regime,

    A. Adhikary, J. Nam, J. Ahn, and G. Caire, “Joint spatial division and multiplexingthe large-scale array regime,” IEEE Trans. Inf. Theory, vol. 59, no. 10, pp. 6441–6463, Oct. 2013

    work page 2013

  15. [18]

    Angular and temporal correlation of V2X channels across sub-6 GHz and mmwave bands,

    C. K. Anjinappa and I. Guvenc, “Angular and temporal correlation of V2X channels across sub-6 GHz and mmwave bands,” in Proc. IEEE Int. Conf. Commun. (ICC) Workshops , Kansas City, MO, May 2018, pp. 1–6

    work page 2018

  16. [19]

    Spatial Covariance Estimation for Millimeter Wave Hybrid Systems using Out-of-Band Information

    A. Ali, N. Gonz ´alez Prelcic, and R. W. H. Jr., “Spatial covariance estimation for millimeter wave hybrid systems using out-of-band information,” CoRR, vol. abs/1804.11204, 2018. [Online]. Available: http://arxiv.org/abs/1804.11204

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  17. [20]

    Millimeter wave MIMO channel estimation based on adaptive compressed sensing,

    S. Sun and T. S. Rappaport, “Millimeter wave MIMO channel estimation based on adaptive compressed sensing,” in Proc. IEEE Int. Conf. Commun. (ICC) Workshops , Paris, France, May 2017, pp. 47–53

    work page 2017

  18. [21]

    Joint frame synchronization and channel estimation: Sparse recovery approach and USRP implementation,

    O. Ozdemir, C. K. Anjinappa, R. Hamila, N. Al-Dhahir, and . Guven, “Joint frame synchronization and channel estimation: Sparse recovery approach and USRP implementation,” IEEE Access, vol. 7, pp. 39 041–39 053, Mar. 2019

    work page 2019

  19. [22]

    Spatial channel covariance estimation for the hybrid MIMO architecture: A compressive sensing-based approach,

    S. Park and R. W. Heath, “Spatial channel covariance estimation for the hybrid MIMO architecture: A compressive sensing-based approach,” IEEE Trans. Wireless Commun. , vol. 17, no. 12, pp. 8047–8062, Dec. 2018

    work page 2018

  20. [23]

    DOA estimation by covariance matrix sparse reconstruction of coprime array,

    C. Zhou, Z. Shi, Y . Gu, and N. A. Goodman, “DOA estimation by covariance matrix sparse reconstruction of coprime array,” in Proc. IEEE Int. Conf. Acoustics, Speech, and Sig. Proc. (ICASSP) , Shanghai, China, Apr. 2015, pp. 2369–2373

    work page 2015

  21. [24]

    A generalized ESPRIT approach to direction-of-arrival estimation,

    F. Gao and A. B. Gershman, “A generalized ESPRIT approach to direction-of-arrival estimation,” IEEE Sig. Proc. Lett. , vol. 12, no. 3, pp. 254–257, Mar. 2005

    work page 2005

  22. [25]

    Spatial channel covariance estimation for the hybrid architecture at a base station: A tensor-decomposition-based approach,

    S. Park, A. Ali, N. Gonzlez-Prelcic, and R. W. Heath, “Spatial channel covariance estimation for the hybrid architecture at a base station: A tensor-decomposition-based approach,” in Proc. IEEE Global Conf. Sig. Inform. Proc. (GlobalSIP) , Los Angeles, CA, Nov. 2018, pp. 1008–1012

    work page 2018

  23. [26]

    Massive MIMO channel subspace estimation from low-dimensional projections,

    S. Haghighatshoar and G. Caire, “Massive MIMO channel subspace estimation from low-dimensional projections,” IEEE Trans. Sig. Proc., vol. 65, no. 2, pp. 303–318, Jan. 2017. 30

    work page 2017

  24. [27]

    Deconstructing multiantenna fading channels,

    A. M. Sayeed, “Deconstructing multiantenna fading channels,” IEEE Trans. Sig. Proc. , vol. 50, no. 10, pp. 2563–2579, Oct. 2002

    work page 2002

  25. [28]

    Perturbed orthogonal matching pursuit,

    O. Teke, A. C. Gurbuz, and O. Arikan, “Perturbed orthogonal matching pursuit,” IEEE Trans. Sig. Proc. , vol. 61, no. 24, pp. 6220–6231, Dec. 2013

    work page 2013

  26. [29]

    Channel estimation in mmwave hybrid MIMO system via off-grid dirichlet kernels,

    C. K. Anjinappa, Y . Zhou, Y . Yapici, D. Baron, and I. Guvenc, “Channel estimation in mmwave hybrid MIMO system via off-grid dirichlet kernels,” under review IEEE Globecom, May 2019

    work page 2019

  27. [30]

    The restricted isometry property and its implications for compressed sensing,

    E. J. Candes, “The restricted isometry property and its implications for compressed sensing,” Comptes rendus mathematique, vol. 346, no. 9-10, pp. 589–592, 2008

    work page 2008

  28. [31]

    A robust compressive sensing based technique for reconstruction of sparse radar scenes,

    O. Teke, A. C. Gurbuz, and O. Arikan, “A robust compressive sensing based technique for reconstruction of sparse radar scenes,” Digit. Sig. Proc. , vol. 27, pp. 23–32, 2014

    work page 2014

  29. [32]

    Off-grid sparse bayesian learning-based channel estimation for mmwave massive MIMO uplink,

    H. Tang, J. Wang, and L. He, “Off-grid sparse bayesian learning-based channel estimation for mmwave massive MIMO uplink,” IEEE Wireless Commun. Lett. , vol. 8, no. 1, pp. 45–48, Feb. 2019

    work page 2019

  30. [33]

    Efficient channel estimation for massive MIMO systems via truncated two-dimensional atomic norm minimization,

    Y . Wang, P. Xu, and Z. Tian, “Efficient channel estimation for massive MIMO systems via truncated two-dimensional atomic norm minimization,” in Proc. IEEE Int. Conf. Commun. (ICC) , Paris, France, May 2017, pp. 1–6

    work page 2017

  31. [34]

    Optimizing channel-statistics-based analog beamforming for millimeter-wave multi-user massive MIMO downlink,

    Z. Li, S. Han, and A. F. Molisch, “Optimizing channel-statistics-based analog beamforming for millimeter-wave multi-user massive MIMO downlink,” IEEE Trans. Wireless Commun. , vol. 16, no. 7, pp. 4288–4303, July 2017

    work page 2017

  32. [35]

    Millimeter-wave V2X channels: Propagation statistics, beamforming, and blockage,

    C. K. Anjinappa and I. Guvenc, “Millimeter-wave V2X channels: Propagation statistics, beamforming, and blockage,” in Proc. IEEE Veh. Technol. Conf. (VTC-Fall) , Chicago, IL, Aug. 2018, pp. 1–6

    work page 2018

  33. [36]

    Millimeter wave channel modeling and cellular capacity evaluation,

    M. R. Akdeniz, Y . Liu, M. K. Samimi, S. Sun, S. Rangan, T. S. Rappaport, and E. Erkip, “Millimeter wave channel modeling and cellular capacity evaluation,” IEEE J. Sel. Areas Commun. , vol. 32, no. 6, pp. 1164–1179, June 2014

    work page 2014

  34. [37]

    The impact of beamwidth on temporal channel variation in vehicular channels and its implications,

    V . Va, J. Choi, and R. W. Heath, “The impact of beamwidth on temporal channel variation in vehicular channels and its implications,” IEEE Trans. Veh. Technol., vol. 66, no. 6, pp. 5014–5029, June 2017

    work page 2017

  35. [38]

    Channel estimation and hybrid precoding for millimeter wave cellular systems,

    A. Alkhateeb, O. El Ayach, G. Leus, and R. W. Heath, “Channel estimation and hybrid precoding for millimeter wave cellular systems,” IEEE J. Sel. Topics Sig. Proc. , vol. 8, no. 5, pp. 831–846, Oct. 2014

    work page 2014

  36. [39]

    Robust location-aided beam alignment in millimeter wave massive MIMO,

    F. Maschietti, D. Gesbert, P. de Kerret, and H. Wymeersch, “Robust location-aided beam alignment in millimeter wave massive MIMO,” in Proc. IEEE Global Commun. Conf. , Dec. 2017, pp. 1–6

    work page 2017

  37. [40]

    Algorithms for simultaneous sparse approximation. Part I: Greedy pursuit,

    J. A. Tropp, A. C. Gilbert, and M. J. Strauss, “Algorithms for simultaneous sparse approximation. Part I: Greedy pursuit,” Digit. Sig. Proc. , vol. 86, no. 3, pp. 572–588, 2006

    work page 2006

  38. [41]

    Conjugate gradient acceleration of the EM algorithm,

    M. Jamshidian and R. I. Jennrich, “Conjugate gradient acceleration of the EM algorithm,” Journal of the American Statistical Association, vol. 88, no. 421, pp. 221–228, 1993

    work page 1993

  39. [42]

    A fast improvement to the em algorithm on its own terms,

    I. Meilijson, “A fast improvement to the em algorithm on its own terms,” Journal of the Royal Statistical Society, Series B: Methodological, vol. 51, pp. 127–138, 1989

    work page 1989

  40. [43]

    A quasi-newton acceleration of the EM algorithm,

    K. Lange, “A quasi-newton acceleration of the EM algorithm,” Statistica Sinica, vol. 5, pp. 1–18, 1995

    work page 1995