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REVIEW 3 major objections 6 minor 2 cited by

Antenna Position Optimization for Movable Antenna-Empowered Near-Field Sensing

T0 review · 3 major / 6 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read This paper claims that for near-field sensing, half the movable antennas should sit at each end of a line segment to minimize worst-case angle or distance estimation error, while joint angle-distance estimation calls for a three-group…

desk verdict Solid near-field MA sensing extension with a deferred but recoverable proof; the stress-test concern about the reduction is overstated. read the letter →

arxiv 2502.03169 v4 pith:E3QEZYCW submitted 2025-02-05 eess.SP

Yushen Wang , Weidong Mei , Xin Wei , Boyu Ning , Zhi Chen This is my paper · ORCID
classification eess.SP
keywords movableantennanear-fieldsensingCramér-RaoboundMUSICpositionoptimizationangle-of-arrivalestimationdistance6G
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 asks where to place movable antennas inside a fixed linear region to make near-field estimates of a target's angle and distance as accurate as possible. It claims that for estimating either the angle alone or the distance alone, the worst-case Cramer-Rao bound is minimized by splitting the antennas into two clusters at the two ends of the region. For joint angle-distance estimation, the paper finds a different geometry: three half-wavelength-spaced groups, obtained by a sequential discrete-sampling search, which cuts the worst-case sum of CRBs by 73.0%, 34.0%, and 18.1% over three fixed-array benchmarks at 20 dB. This matters because it gives concrete placement rules for movable-antenna sensing in near-field 6G scenarios, where fixed-position arrays are the current baseline.

What carries the argument

The argument is carried by three scalar statistics of the antenna positions: the variance of the positions $\operatorname{var}(x)$, the variance of their squares $\operatorname{var}(\tilde{x})$ with $\tilde{x}_n=x_n^2$, and their covariance $\operatorname{cov}(x,\tilde{x})$. These enter the CRB expressions through the Fisher information matrix built from the Fresnel-approximated near-field steering vector, where the phase of the $n$-th antenna is $e^{j 2\pi/\lambda}(x_n u - x_n^2(1-u^2)/(2r))$. For angle-only and distance-only estimation, maximizing the relevant FIM statistic over the worst-case parameter values forces the two-cluster endpoint geometry. For joint estimation, the determinant $\operatorname{var}(x)\operatorname{var}(\tilde{x})-\operatorname{cov}^2(x,\tilde{x})$ and the coupling terms make the objective non-convex, so the paper optimizes by uniformly discretizing the region into M sampling points and updating one antenna at a time while keeping the others fixed, iterating until convergence.

What would settle it

For a moderate case such as N=6, A=10λ, and d=λ/2, enumerate all feasible discretized antenna position vectors on a fine grid, compute the worst-case CRB from the paper's own FI expressions over u in [0,1) and r in [R_FS, R_RL/2], and compare the minimum with the two-cluster placement of Theorem 1; any placement with a strictly lower worst-case CRB would falsify the theorem.

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Extended reading notes

Core claim

The central claim is that, for a linear movement region of length A with N movable antennas and minimum spacing d, the antenna position vector minimizing the worst-case CRB for angle-only or distance-only estimation is given by $x_n^*=(n-1)d$ for $n\le \lfloor N/2\rfloor$ and $x_n^*=A-(N-n)d$ for the remaining antennas: two dense clusters at the two ends. The paper states that this follows by the same argument as the far-field AoA result in [13] and is identical to the far-field optimal geometry. For joint angle-distance estimation, the Fisher information matrix couples the angle and distance parameters, and the CRB minimization becomes non-convex; the proposed Algorithm 1, a discrete sampling-based sequential update, yields a three-group geometry with the outermost antennas at the endpoints. The paper reports that this optimized geometry lowers the worst-case sum CRB by 73.0% over a uniform linear array, 34.0% over the far-field-optimal two-cluster array, and 18.1% over a sparse full-aperture array at 20 dB SNR.

Load-bearing premise

The closed-form two-cluster optimum is not proven inside the paper; it is asserted by analogy with a far-field proof in [13], so the entire closed-form design rule rests on that unverified analogy.

Editorial extensions

If this is right

  • If the closed-form result holds, near-field single-parameter sensing inherits the far-field endpoint-clustering rule, so existing far-field antenna-position designs transfer directly to near-field angle or distance estimation.
  • The optimal geometry spreads the array to the full movement-region aperture, making the region length A the dominant design lever for angle-only or distance-only accuracy.
  • For joint angle-distance estimation, the optimal layout is not endpoint-only: the three-group structure balances angular resolution (large aperture) against distance resolution (sampling of quadratic phase).
  • The reported CRB reductions give quantitative targets for comparing future MA-based near-field sensing schemes with fixed-position arrays.
  • Because the joint-optimum depends on both $u$ and $r$, the worst-case design is inherently conservative; designers may choose a smaller operating region if peak worst-case error matters more than average error.

Reading between the lines

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

  • An implicit next question is whether the three-group joint-optimal geometry has a closed-form description; the simulation pattern of equal gaps and half-wavelength spacing suggests one may exist, but the paper does not derive it.
  • If the CRB is not attained by MUSIC at the single-snapshot setting used in the simulations, the true MSE improvements could differ from the reported percentages; a Monte Carlo comparison of MUSIC MSE against these CRBs would settle that directly.
  • The near-field advantage over far-field is likely concentrated in the distance dimension, where the quadratic phase term $x_n^2(1-u^2)/(2r)$ matters; this suggests hybrid designs that keep some antennas fixed and move only a few may capture most of the gain.
  • Because the worst-case CRB is minimized over all possible target locations, a target outside the assumed range could invalidate the placement rule; extending the optimization to a larger or multi-region target set is a natural test of robustness.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The manuscript studies a near-field sensing system with movable antennas arranged in a linear array of length A. For AoA-only and distance-only estimation, it derives worst-case CRBs and claims closed-form optimal antenna position vectors with two clusters at the array endpoints (Theorem 1, Eq. (14)). For joint AoA-distance estimation, it derives the CRB matrix and proposes a sequential discrete sampling algorithm (Algorithm 1) that produces a three-group geometry. Numerical results compare the proposed geometries against fixed uniform arrays and a far-field-optimal array.

Significance. If the closed-form optimality in Theorem 1 is valid, the paper provides a useful extension of movable-antenna position optimization to near-field sensing, showing an equivalence with far-field array geometry for individual parameter estimation and a different three-group geometry for joint estimation. The CRB expressions in (21)-(22) are algebraically consistent, and the numerical comparisons are clearly presented. However, the paper's central optimality claim is not verifiable from the text because the proof of Theorem 1 is omitted and the deferred citation to [13] does not obviously cover the near-field objective. The paper also leaves several stated equivalences and optimality claims without proof.

major comments (3)
  1. [Section III-B, Theorem 1 and Eq. (14)] The proof of Theorem 1 is omitted and the reader is referred to Appendix A of [13]. This is not sufficient: the objective in (11), F_u(x,u)=var(x)+(2u/r*)cov(x,~x)+(u^2/r*^2)var(~x), contains covariance and second-moment terms that do not appear in the far-field problem solved in [13]. To conclude that the two-cluster APV in (14) is optimal for (P1), the authors must show that the inner minimizer u_opt is 0 for every feasible x, or otherwise prove the min-max solution directly. Without this step, the claimed optimality of (14) is unverified, and the subsequent use of (14) as Benchmark 3 and as the initial point of Algorithm 1 inherits the gap.
  2. [Section IV, after Eq. (18)] The statement that "the optimal APV to (P2) is the same as that provided in Theorem 1 via a similar process to Appendix A in [13]" is likewise unsupported. The objective in (18a) is proportional to var(~x), the variance of the squared antenna positions, not the variance of x treated in [13]. The two-cluster geometry may indeed maximize var(~x), but the paper does not provide the required proof, so the distance-only optimality claim is not established.
  3. [Section V, Eq. (23) and Algorithm 1] The transformation from min_x (CRB_u(x)+max_{u,r}CRB_r(x,η)) to max_x Tr^{-1}(CRB_η(x,η))|_{η=η_opt} is stated without proof. Since η_opt is defined as the worst-case parameter for each x, the equivalence requires a min-max/max-min reciprocal argument analogous to (12), and the notation Tr^{-1}(·) is ambiguous between the reciprocal of the trace and the trace of the inverse. The authors should define the notation and provide the short derivation; this is needed to justify the objective optimized by Algorithm 1.
minor comments (6)
  1. [Section VI] The word "Futhermore" should be "Furthermore".
  2. [Section III-A, Eq. (11)] The definitions of var(~x) and cov(x,~x) appear after their first use in (11); placing them before the equation would improve readability.
  3. [Section V, Eq. (23)] The symbol Tr^{-1} should be explicitly defined, for example as 1/Tr(·), to avoid confusion with the trace of the inverse matrix.
  4. [Section VI] The simulations use T=1 snapshot, but the CRB is an asymptotic lower bound; the paper should note that MUSIC's finite-sample MSE at T=1 may not attain the CRB.
  5. [Section II, Eq. (2)] The Fresnel approximation is a second-order Taylor expansion; the authors should state its validity condition or cite a reference that quantifies the approximation error over the assumed distance range [R_FS, R_RL/2].
  6. [Algorithm 1] The input list includes "X", but the text defines the initial APV as x_init; the notation in the input line should be made consistent.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: CRB derivations and optimization formulations are self-contained; the deferred proof of Theorem 1 to an external paper is a rigor gap, not a circular reduction.

full rationale

The paper's derivation chain is non-circular. The CRB expressions (10)-(11), (15)-(16), and (21)-(22) follow from the stated near-field signal model and standard FIM/MUSIC formulas; they contain no parameters fitted to simulated data. The optimization problems (P1)-(P3) are genuine minimax problems over the antenna position vector x, and the closed-form solutions are asserted from a proof in [13], which is an external paper by different authors (Ma, Zhu, and Zhang), not a self-citation. The near-field objective in (13a) includes covariance and second-moment terms absent from the far-field var(x) problem in [13], and the paper only says a similar proof applies; this is an unsupported or omitted proof, not a definitional equivalence or fitted prediction. Algorithm 1 is an optimization heuristic adopted from prior work, and it is used only to search for a high-quality APV, not to define the CRB objective. Numerical results evaluate the analytic CRBs at given APVs with no fitted parameters, so no 'prediction' reduces by construction to its inputs. The lack of an internal proof of Theorem 1 is a correctness/completeness concern, not circularity.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new physical entities. The free parameters are the constraint constants (A, d) and the uncharacterized worst-case values u_opt, r_opt. The main assumptions are the Fresnel approximation, the MUSIC-attains-CRB assumption, and the deferred proof of Theorem 1 to [13].

free parameters (3)
  • d = λ/2 in simulations
    Minimum inter-MA distance constraint (13c); treated as a given system parameter, not fitted to the target result, but the optimal APV in (14) depends on it.
  • A = 10λ in simulations
    MA movement region length; a system parameter, not fitted to the result, but the aperture and the optimal APV scale with it.
  • u_opt and r_opt = not characterized
    The worst-case parameter values that define the objectives F*_u(x), F*_r(x), F*_η(x) in (13a), (18a), (23a). The paper never derives or characterizes them; they are implicitly chosen by the max over the parameter range. This is a free choice that affects the optimization objective.
assumptions (4)
  • domain assumption Fresnel approximation (2): exact distance r_n is replaced by the second-order Taylor expansion r - x_n u + x_n^2(1-u^2)/(2r).
    Invoked in Section II to derive the channel model (3). All CRB formulas inherit this approximation. The paper assumes the target is between the Fresnel and Rayleigh distances, but does not quantify the approximation error.
  • domain assumption MUSIC estimation error reaches the CRB.
    The CRBs in (10), (15), (21), (22) are used as the estimation MSE lower bounds without a Monte Carlo verification that MUSIC attains them, especially at T = 1 snapshot.
  • ad hoc to paper The proof of Theorem 1 follows Appendix A of [13].
    The optimality of (14) for P1 and P2 is not proved in this paper; it is deferred to a cited paper by overlapping authors. This is a load-bearing external dependency.
  • domain assumption The min-max to max-min reformulations (12), (17), (23) are equivalence transformations.
    The paper states they are 'easily shown' or 'equivalently transformed' but does not prove them. These reformulations are the foundation of the optimization problems P1-P3.

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Cite this review

Pith. "Pith review of Antenna Position Optimization for Movable Antenna-Empowered Near-Field Sensing." pith.science (2026). https://pith.science/paper/E3QEZYCW

@misc{pith2026250203169,
  author       = {Pith},
  title        = {Pith review of: Antenna Position Optimization for Movable Antenna-Empowered Near-Field Sensing},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/E3QEZYCW}},
  note         = {Machine review of arXiv:2502.03169}
}
read the original abstract

Movable antennas (MAs) show great promise for enhancing the sensing capabilities of future sixth-generation (6G) networks. With the growing prevalence of near-field propagation at ultra-high frequencies, this paper focuses on the application of MAs for near-field sensing to jointly estimate the angle and distance information of a target. First, to gain essential insights into MA-enhanced near-field sensing, we investigate two simplified cases with only the spatial angle-of-arrival (AoA) or distance estimation, respectively, assuming that the other information is already known. We derive the worst-case Cramer-Rao bounds (CRBs) on the mean square errors (MSEs) of the AoA estimation and the distance estimation via the multiple signal classification (MUSIC) algorithm in these two cases. Then, we jointly optimize the positions of the MAs within a linear array to minimize these CRBs and derive their closed-form solutions, which yield an identical array geometry to MA-aided far-field sensing. Furthermore, we proceed to the more challenging case with the joint AoA and distance estimation and derive the worst-case CRB under the two-dimensional (2D) MUSIC algorithm. The corresponding CRB minimization problem is efficiently solved by adopting a discrete sampling-based approach. Numerical results demonstrate that the proposed MA-enhanced near-field sensing significantly outperforms conventional sensing with fixed-position antennas (FPAs). Moreover, the joint angle and distance estimation results in a different array geometry from that in the individual estimation of angle or distance.

Figures

Figures reproduced from arXiv: 2502.03169 by the authors.

Figure 1
Figure 1. MA-enhanced near-field target sensing. been widely investigated under various system setups, in￾cluding multiple-input single-/multiple-output (MISO/MIMO) system [8], [9], physical-layer security [10], over-the-air com￾putation [11], cognitive radio [12], etc. On the other hand, MA technology also shows great potential to empower wireless sensing, which is the focus of this work. By leveraging a broader region at th… view at source ↗
Figure 2
Figure 2. The optimal APV in the AoA or distance estimation. problem can be easily shown equivalent to the following max￾min problem based on (10), i.e., min x max u∈[0,1) CRBu(x, u) ⇐⇒ max x min u∈[0,1) Fu(x, u). (12) The associated optimization problem for the right-hand side of (12) can be formulated as (P1) max x F ⋆ u (x) , var(x) + 2uopt r ⋆ cov(x, x˜) + u 2 opt r ⋆2 var(x˜) (13a) s.t. 0 ≤ xn ≤ A, n ∈ N , (13b) |xn − xn… view at source ↗
Figure 5
Figure 5. The optimal APV in the joint estimation of AoA and distance [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figures from the paper (3 more)
Figure 3
Figure 3. Figure 3: CRB of the AoA estimation MSE versus the received SNR [PITH_FULL_IMAGE:figures/full_fig_p005_3.png]
Figure 6
Figure 6. Figure 6: Sum of the joint estimation CRBs versus the received SNR. 3) Optimal MA array in the far-field AoA estimation (Benchmark 3) [13]: {xn} N n=1 are set the same as those provided in Theorem 1. In [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]
Figure 4
Figure 4. Figure 4: CRB of the distance estimation MSE versus the received SNR. a non-decreasing objective function value of (P3); hence, its convergence is guaranteed. The main procedures of the proposed algorithm for solving problem (P3) are summarized in Algorithm 1. Furthermore, it ca…

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Forward citations

Cited by 2 Pith papers

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  1. Movable Antenna Empowered Secure Near-Field MIMO Communications

    cs.IT 2025-08 conditional novelty 6.0 of 10

    Movable antenna positions and hybrid beamformers are jointly optimized to maximize secrecy rate in near-field MIMO, achieving secure transmission when the eavesdropper is in the same direction and closer to the base station.

  2. A Derivative-Free Position Optimization Approach for Movable Antenna Multi-User Communication Systems

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    A derivative-free, zeroth-order optimization method positions multiple movable antennas in a multi-user MISO system using only received pilot measurements, outperforming CSI-estimation-based positioning in simulation ...

Reference graph

Works this paper leans on

23 extracted references · 21 canonical work pages · cited by 2 Pith papers

  1. [13]

    Movable Antenna Enhanced Wi reless Sensing via Antenna Position Optimization,

    W. Ma, L. Zhu, and R. Zhang, “Movable Antenna Enhanced Wi reless Sensing via Antenna Position Optimization,” IEEE Trans. Wireless Commun., vol. 23, no. 11, pp. 16575-16589, Nov. 2024

    work page 2024

  2. [1]

    Integrated Sensing and Communications: Toward Dual- Functional Wireless Networks for 6G and Beyond,

    F. Liu et al. , “Integrated Sensing and Communications: Toward Dual- Functional Wireless Networks for 6G and Beyond,” IEEE J. Sel. Areas Commun., vol. 40, no. 6, pp. 1728-1767, Jun. 2022

    work page 2022

  3. [2]

    A Survey on Fundamental Limits of Integrated Sensing and Communication,

    A. Liu et al. , “A Survey on Fundamental Limits of Integrated Sensing and Communication,” IEEE Commun. Surv. Tutorials , vol. 24, no. 2, pp. 994-1034, 2022

    work page 2022

  4. [3]

    6G Wireless Communication Systems: Appli- cations, Requirements, Technologies, Challenges, and Res earch Direc- tions,

    M. Z. Chowdhury et al. , “6G Wireless Communication Systems: Appli- cations, Requirements, Technologies, Challenges, and Res earch Direc- tions,” IEEE Open J. Commun. Soc. , vol. 1, pp. 957-975, 2020

    work page 2020

  5. [4]

    The Road Towards 6G: A Comprehensive Survey,

    W. Jiang et al., “The Road Towards 6G: A Comprehensive Survey,” IEEE Open J. Commun. Soc. , vol. 2, pp. 334-366, 2021

    work page 2021

  6. [5]

    Movable antenna-enhanced wireless communica- tions: General architectures and implementation methods,

    B. Ning et al. , “Movable antenna-enhanced wireless communica- tions: General architectures and implementation methods, ” 2024, arXiv:2407.15448

    arXiv 2024

  7. [6]

    Movable Antennas for Wireles s Com- munication: Opportunities and Challenges,

    L. Zhu, W. Ma, and R. Zhang, “Movable Antennas for Wireles s Com- munication: Opportunities and Challenges,” IEEE Commun. Mag. , vol. 62, no. 6, pp. 114-120, Jun. 2024

    work page 2024

  8. [7]

    Modeling and Performance Ana lysis for Movable Antenna Enabled Wireless Communications,

    L. Zhu, W. Ma, and R. Zhang, “Modeling and Performance Ana lysis for Movable Antenna Enabled Wireless Communications,” IEEE Trans. Wireless Commun., vol. 23, no. 6, pp. 6234-6250, Jun. 2024

    work page 2024

Show all 23 references
  1. [8]

    MIMO Capacity Characterizat ion for Movable Antenna Systems,

    W. Ma, L. Zhu, and R. Zhang, “MIMO Capacity Characterizat ion for Movable Antenna Systems,” IEEE Trans. Wireless Commun. , vol. 23, no. 4, pp. 3392-3407, Apr. 2024

    2024

  2. [9]

    Movable-Antenna Position Optimization: A Graph-Based Approach,

    W. Mei et al., “Movable-Antenna Position Optimization: A Graph-Based Approach,” IEEE Wireless Commun. Lett. , vol. 13, no. 7, pp. 1853-1857, Jul. 2024

    2024

  3. [10]

    Movable-antenna position optimization for physical-la yer security via discrete sampling,

    W. Mei et al., “Movable-antenna position optimization for physical-la yer security via discrete sampling,” in Proc. IEEE Global Commun. Conf. , Cape Town, South Africa, Dec. 2024, pp. 4739–4744

    2024

  4. [11]

    Over-the-Air Computation via 2-D Movable Antenna Array,

    N. Li et al. , “Over-the-Air Computation via 2-D Movable Antenna Array,” IEEE Wireless Commun. Lett. , vol. 14, no. 1, pp. 33-37, Jan. 2025

    2025

  5. [12]

    Joint Beamforming and Antenna Position Optimization for Movable Antenna-Assisted Spectrum Sharing,

    X. Wei et al., “Joint Beamforming and Antenna Position Optimization for Movable Antenna-Assisted Spectrum Sharing,” IEEE Wireless Commun. Lett., vol. 13, no. 8, pp. 1835-1840, Aug. 2024

    2024

  6. [14]

    Movable Antenna Enhanced In tegrated Sensing and Communication Via Antenna Position Optimizati on,

    W. Ma, L. Zhu, and R. Zhang, “Movable Antenna Enhanced In tegrated Sensing and Communication Via Antenna Position Optimizati on,” 2025, arXiv:2501.07318

    2025 arXiv

  7. [15]

    Movable Antenna Enabled Integrated Sensing and Communication,

    W. Lyu et al. , “Movable Antenna Enabled Integrated Sensing and Communication,” IEEE Trans. Wireless Commun. , early access, 2025, doi: 10.1109/TWC.2025.3525631

    2025

  8. [16]

    Exploiting six-dime nsional movable antenna for wireless sensing,

    X. Shao, R. Zhang, and R. Schober, “Exploiting six-dime nsional movable antenna for wireless sensing,” IEEE Wireless Commun. Lett. , early access, 2024, doi: 10.1109/LWC.2024.3487966

    2024

  9. [17]

    Beamforming technologies for ultra-massive MIMO in terahertz communications,

    B. Ning et al. , “Beamforming technologies for ultra-massive MIMO in terahertz communications,” IEEE Open J. Commun. Soc. , vol. 4, pp. 614-658, 2023

    2023

  10. [18]

    Near-Field Integrated Sensi ng and Communications,

    Z. Wang, X. Mu, and Y . Liu, “Near-Field Integrated Sensi ng and Communications,” IEEE Commun. Lett. , vol. 27, no. 8, pp. 2048-2052, Aug. 2023

    2023

  11. [19]

    Near-Field Communications: A Tutorial Review,

    Y . Liu et al. , “Near-Field Communications: A Tutorial Review,” IEEE Open J. Commun. Soc. , vol. 4, pp. 1999-2049, 2023

    1999

  12. [20]

    Fraunhofer and Fresnel D istances: Unified derivation for aperture antennas,

    K. T. Selvan and R. Janaswamy, “Fraunhofer and Fresnel D istances: Unified derivation for aperture antennas,” IEEE Antennas Propag. Mag. , vol. 59, no. 4, pp. 12-15, Aug. 2017

    2017

  13. [21]

    Cram´ er-Rao Bound Optimization for Joint Radar- Communication Beamforming,

    F. Liu et al. , “Cram´ er-Rao Bound Optimization for Joint Radar- Communication Beamforming,” IEEE Trans. Signal Process. , vol. 70, pp. 240-253, 2022

    2022

  14. [22]

    S. M. Kay, Fundamentals of Statistical Signal Processing: Estimatio n Theory, Prentice-Hall, Inc., 1993

    1993

  15. [23]

    MUSIC, maximum likelihood, a nd Cramer- Rao bound,

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

    1989

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