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ISAC Super-Resolution Receiver via Lifted Atomic Norm Minimization

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A single lifted convex program recovers radar target parameters and communication symbols together from received echoes, with no pilot link.

desk verdict Plausible LANM extension to 4D ISAC, but the main theorem's proof has a load-bearing independence flaw that the authors need to fix. read the letter →

arxiv 2411.09495 v1 pith:BMNOHSRG submitted 2024-11-14 cs.IT eess.SPmath.IT

Iman Valiulahi , Christos Masouros , Athina P. Petropulu This is my paper · ORCID
classification cs.ITeess.SPmath.IT MSC 94A1290C2294A20
keywords ISACliftedatomicnormminimizationoff-the-gridsuper-resolutionsemidefiniterelaxationMIMOradarjointandcommunicationestimationdualcertificateblinddeconvolution
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 an integrated sensing and communication (ISAC) receiver can simultaneously locate radar targets and decode the data-carrying transmit signal, even though neither the channel nor the transmit waveform is known. The proposed estimator, lifted atomic norm minimization (LANM), is a convex program whose exact-recovery guarantee is Theorem 1: with probability at least $1-\delta$, the lifted matrix $U = \sum_k |\alpha_k| h_k a(\tau_k)^H$ is recovered exactly from the linear measurements $y = \mathcal{X}(U)$ as soon as $L^4 \geq C\mu K T \log(10KT/\delta)$, under a minimum-separation condition on the target parameters. If this is right, a single off-the-grid estimator can replace pilot-aided channel estimation and radar-only super-resolution at the same order of computational cost. Simulations support the theorem and show performance comparable to pilot-aided atomic norm minimization, which knows the transmit signal.

What carries the argument

The load-bearing object is the lifted atomic norm and its dual. The atom set is $\mathcal{A} = \{v a(\tau)^H : \tau \in [0,1)^4, \|v\|_2 = 1\}$, and the lifted atomic norm of $U$ is the gauge of $\mathrm{conv}(\mathcal{A})$; minimizing it under the measurement constraint $y = \mathcal{X}(U)$ turns the unknown-waveform problem into a low-rank matrix recovery problem. The proof machinery is a randomized vector-valued dual polynomial $Q(\tau) = \mathcal{X}^*(q) a(\tau)$, built from the squared Fejér kernel and its derivatives, that interpolates the sign patterns at the true target parameters and is bounded away from 1 elsewhere; concentration of the random Gram matrix $\Gamma$ around its expectation $\Phi \otimes I_L$ supplies the sample-complexity bound. Computationally, the infinite-dimensional dual constraint $\|Q(\tau)\|_2 \leq 1$ is implemented by a semidefinite relaxation using Toeplitz matrix constraints from trigonometric polynomial theory.

What would settle it

Run the proposed SDR (20) with two targets satisfying the separation condition but with $D$ chosen as a deterministic low-coherence matrix (for example, a partial Fourier or DCT matrix) at a sample size around the theorem's bound; if recovery fails consistently while a random Gaussian $D$ of the same size succeeds, the randomness assumption is load-bearing and the guarantee does not extend to deterministic coding matrices. Directly, compute $\|\Gamma - \mathbb{E}\Gamma\|$ for such a $D$: Lemma 3 predicts concentration below $\epsilon$ for $L^4 \geq C\mu K T \log(10KT/\delta)$, so a persistent large deviation would falsify the key concentration step.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the bilinear ISAC reception problem—unknown target parameters multiplied by unknown communication vectors—can be lifted into a linear inverse problem over a low-rank matrix $U = \sum_{k=1}^K |\alpha_k| h_k a(\tau_k)^H$, where $a(\tau_k)$ encodes the four continuous parameters (delay, Doppler, angle of departure, angle of arrival) and $h_k$ carries the communication data. The lifted atomic norm $\|U\|_{\mathcal{A}}$ over the atom set $\{v a(\tau)^H : \tau \in [0,1)^4, \|v\|_2=1\}$ promotes exactly this structured low-rankness, and its dual certificate $Q(\tau) = \mathcal{X}^*(q) a(\tau)$ is constructed from a randomized Fejér kernel so that it peaks at the true target locations and stays below 1 elsewhere. Theorem 1 states that this dual certificate exists with high probability once the sample count satisfies $L^4 \geq C\mu K T \log(10KT/\delta)$, yielding exact recovery of the target parameters and the data-carrying vectors $h_k$.

Load-bearing premise

The load-bearing premise is that each transmit probing signal lies on a known random low-dimensional subspace, $x_k = D h_k$, with the coding matrix $D$ having statistically isotropic, incoherent columns; if $D$ is deterministic or the signal is not confined to such a subspace, the concentration arguments and the exact-recovery guarantee of Theorem 1 no longer follow.

Editorial extensions

If this is right

  • An ISAC receiver can drop pilot signaling and the direct transmitter-receiver link; the same received echoes yield target angles, delay, Doppler, and the QAM symbols in the probing signal.
  • Recovery is off the grid: target parameters are continuous, so there is no basis-mismatch error of the kind that degrades grid-based $\ell_1$ methods.
  • The sample complexity scales as $L^4 \gtrsim \mu K T \log(KT/\delta)$, proportionate to the degrees of freedom of the ISAC scene rather than the ambient dimension.
  • With AWGN and jamming, the same framework separates the radar signal, the communication data, and the jammer's angle, using one extra atomic norm for jammers.
  • The overall complexity is the same order as pilot-aided ANM, so data decoding comes at negligible extra computational cost; the paper also points to ADMM as a faster implementation route.

Reading between the lines

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

  • The theorem's randomness assumptions are used only for concentration, and the paper suggests $D$ can be a known coding matrix with $h_k$ drawn from QAM constellations; a natural follow-up is to test whether deterministic low-coherence coding matrices satisfy the same guarantee, since the proof as written needs the isotropy and incoherence of random columns.
  • The bound's logarithmic dependence on the subspace dimension $T$ suggests communication rate can be increased almost for free once the radar parameters are resolvable; if the scaling is tight, the main cost of data rate is in the constant and coherence, not the number of symbols per target.
  • The separation condition takes a max over the four parameters, so targets close in one dimension but separated in another are not covered by the current analysis; a refined condition using a joint metric could enlarge the recoverable regime.
  • For the jamming scenario the paper only conjectures the logarithmic phase-transition scaling; verifying that conjecture with a rigorous sample-complexity bound for the two-atomic-norm problem would complete the robust-recovery story.
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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

4 major / 5 minor

Summary. The paper considers a bistatic MIMO ISAC receiver in which the transmit probing signals are unknown but lie in a known low-dimensional subspace, x_k = D h_k, and the goal is to recover both the communication vectors h_k and the radar target parameters (delay, Doppler, AoA, AoD) from the echoes. The received signal is recast as y = X(U) with U = sum_k |alpha_k| h_k a(tau_k)^H, and a lifted atomic norm minimization (LANM) problem (12) is proposed. The main theoretical claim, Theorem 1, is that under random-coding isotropy/incoherence, random h_k, and a minimum separation condition, exact recovery holds with high probability once L^4 >= C mu K T log(10KT/delta). The paper also gives a semidefinite relaxation of the dual, a robust formulation for AWGN plus jamming, a complexity analysis, and simulations against pilot-aided ANM and ell_1 methods.

Significance. If Theorem 1 were valid, the paper would make a substantial contribution: it would provide the first off-the-grid recovery guarantee for a four-parameter ISAC scenario without a pilot link, with sample complexity proportional to the degrees of freedom, and with a claimed computational cost comparable to pilot-aided ANM. The problem formulation and the proposed SDR are original and potentially useful, and the numerical experiments show encouraging behavior. However, the paper does not provide machine-checked proofs or reproducible code, and the central proof has serious gaps that prevent the main result from being accepted as established.

major comments (4)
  1. [Section X-A, Eqs. (34), (44), and Appendix B] Assumption 1 supplies only \bar L = 2N+1 independent coding vectors d_l (l = -N, ..., N). In Eq. (34) and Eq. (44), however, the proof averages over four-dimensional multi-indices n in J and treats d_n d_n^H as independent summands, e.g. in Gamma = (1/L^4) sum_{n in J} s_{n1}s_{n2}s_{n3}s_{n4} (v_n v_n^H) tensor (d_n d_n^H). The same d_l is reused whenever a coordinate of n equals l, so the summands S_n in Eq. (44) are dependent. The matrix Bernstein step in Eqs. (69)-(72) therefore does not apply, and the sample-complexity condition L^4 >= C mu K T log(10KT/delta) in Lemma 3 and Theorem 1 is not established for the stated model.
  2. [Eqs. (3), (7), (34)-(35)] There are dimension mismatches that accompany the independence problem. K(tau) in Eq. (34) is declared to lie in C^{L x L}, while d_n d_n^H is T x T; U is typed as C^{K x L^2} in Eq. (7), although U = sum |alpha_k| h_k a(tau_k)^H has row dimension T when h_k is in C^T. The definition of a(tau) in Eq. (3) also produces a vector whose length is not reconciled with L = \bar L N_r. These mismatches make it unclear what object the operator X in Eq. (7) acts on and prevent the proof from being checked.
  3. [Appendix F and Lemma 9] A load-bearing bound is left unsupported: Appendix F states 'we know ||\bar E^{(i)}(tau)||_F <= C1 from []' with an empty citation, and this bound is needed to control I_2^{(i)}(tau) in Lemma 8. In addition, the proof of Lemma 2 is omitted (see the paragraph before Eq. (43)), and Lemma 9 is dismissed as 'based on [31, Lemma 8]' without translating that argument to the present four-dimensional ISAC operator. These gaps mean that the construction of the dual polynomial, which is the core of the proof of Theorem 1, is not fully proven.
  4. [Section VI, Eq. (29)] The complexity calculation is algebraically incorrect. With E approximately ((2N+1)2N_t N_r)^2 ~ 16 N^2 N_t^2 N_r^2, and F+1 of the same order, the interior-point bound O((E+F)^{1.5} E^2) scales as O(N^7 N_t^7 N_r^7) up to constants, not as O((4N^2 N_t N_r)^5). The claimed equivalence of the proposed estimator to pilot-aided ANM is therefore not demonstrated by Eq. (29).
minor comments (5)
  1. [Section II, after Eq. (3)] The definition of the index set J and its relation to L is ambiguous: J is said to consider all elements of s, r, l, k with j = 1, ..., L, but the ranges of l and k and the mapping to j are not specified clearly.
  2. [Assumption 1, Eq. (14)] 'identical matrix' should read 'identity matrix', and the coherence condition max |d^{(i)}|^2 <= mu should specify which entry index i is being ranged over.
  3. [Section VII, Fig. 4 caption] The caption says 'Figs. 4(a), 4(a), and 4(b)' but should refer to 4(a), 4(b), and 4(c).
  4. [Fig. 2 caption and Section IV] The caption mentions the (phi, rho) domain while the text and the panel labels use (tau, v); these should be reconciled.
  5. [Eq. (27)] There is an extra closing parenthesis after '[\hat z]_j)', which makes the expression hard to parse.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: Theorem 1 is a sufficient-condition recovery guarantee proved via external concentration lemmas, not a restatement of fitted inputs or self-cited uniqueness claims.

full rationale

The paper's central claim is Theorem 1: under Assumptions 1-3, if L^4 >= C mu K T log(10KT/delta), then the lifted atomic norm minimization (12) exactly recovers U and hence the radar parameters and communication vectors. This is a conditional recovery guarantee, not a definitional equivalence or a fitted parameter renamed as a prediction. The quantity U is defined from the physical observation model in (6), and the sample-complexity condition (16) is an input sufficient condition obtained from concentration arguments, not from the target recovery itself. The proof constructs a dual certificate using randomized matrix-valued Fejer kernels and invokes external technical results: Lemma 2 from Candes-Fernandez-Granda [38], Lemma 4 from [23, Corollary IV.5], Lemma 9 and the final certificate bound from [31, Lemma 8]. None of these are self-citations by the present authors, and the cited lemmas concern generic trigonometric-polynomial and blind-deconvolution concentration bounds; they are used with stated assumptions rather than being the same as Theorem 1. The paper does contain explicit deferred proofs and external references: "To avoid excessive clutter, we eliminate the proof of Lemma 2. However, eager readers can [38] follow the process to prove this lemma and obtain these bounds" (Appendix X-A, Lemma 2), and "The proof can be found in [31, Lemma 8]" (Appendix X-B). These are completeness/correctness concerns, not circularity: external lemmas are independent support under the reviewing rules. A separate technical concern, outside the scope of circularity, is that the printed concentration argument in (34) and (44) indexes d_n by four-dimensional tuples n in J although Assumption 1 supplies only the columns d_l for l = -N,...,N; if correct, this would be a proof gap, not a circular derivation. No fitted parameter is later called a prediction, no load-bearing self-citation chain appears, and no known result is merely renamed. Therefore the circularity score is 0.

Assumptions & free parameters 1 free parameters · 7 assumptions · 0 invented entities

The central claim rests on the subspace model for transmit signals, the separation condition, and the randomness assumptions on D and h_k. These are stated as assumptions, not derived. The proof also imports several external lemmas without proof, which are listed as axioms.

free parameters (1)
  • lambda = 1
    Regularization parameter balancing the lifted atomic norm and the jamming atomic norm in problem (26); set to 1 in all simulations (Section VII), effectively fixing a constant rather than adapting it to the noise or jammer power.
assumptions (7)
  • domain assumption Columns of D^H are iid with isotropy E[d_l d_l^H] = I_T and incoherence max|d(i)|^2 <= mu (Assumption 1).
    Stated in Section II, Assumption 1; used in the concentration bounds (Lemma 3) and in the construction of the dual certificate.
  • domain assumption The element vectors h_k are randomly selected over the complex unit sphere (Assumption 2).
    Stated in Section II, Assumption 2; used to bound the norm of the lifting matrix and to apply the Bernstein inequality in the proof.
  • domain assumption Radar parameters satisfy minimum separation condition max over delays, Dopplers, AoAs, AoDs >= 10/(Nt Nr - 1) (Assumption 3).
    Stated in Section II, Assumption 3; necessary to avoid the ill-posedness of overlapping targets and to ensure the dual polynomial interpolation is stable.
  • domain assumption The transmit probing signals lie in a known low-dimensional subspace: x_k = D h_k with T << L_bar (Section II).
    Introduced in Section II after Eq. (2); this subspace model is the key structural handle that makes the blind problem tractable. If the signals are arbitrary, the problem is hopelessly ill-posed.
  • domain assumption The jamming signal has the structure z = sum p_r p_r tensor a_Nr(psi_r) (Section V, Eq. (22)).
    Stated in Section V; this Kronecker structure (temporal samples times spatial steering vector) is assumed to define the jamming atomic norm. The paper does not analyze the separation between target and jammer atoms.
  • standard math The received signal is band-limited and approximately time-limited, allowing sampling at rate 1/B over [0,T_t] (Section II).
    Standard sampling theory invoked in Section II to justify the discrete observation model in Eq. (2).
  • standard math External lemmas from prior work are assumed valid, including Lemma 2 (invertibility and norm bounds of the matrix Phi) from [38], Lemma 4 from [23, Corollary IV.5], and Lemma 9 from [31, Lemma 8].
    The paper explicitly omits or merely references proofs for these lemmas (Appendix X: 'we eliminate the proof of Lemma 2', 'The proof is based on [31, Lemma 8]'). The validity of the central theorem depends on these external mathematical facts.

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Cite this review

Pith. "Pith review of ISAC Super-Resolution Receiver via Lifted Atomic Norm Minimization." pith.science (2026). https://pith.science/paper/BMNOHSRG

@misc{pith2026241109495,
  author       = {Pith},
  title        = {Pith review of: ISAC Super-Resolution Receiver via Lifted Atomic Norm Minimization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BMNOHSRG}},
  note         = {Machine review of arXiv:2411.09495}
}
read the original abstract

This paper introduces an off-the-grid estimator for integrated sensing and communication (ISAC) systems, utilizing lifted atomic norm minimization (LANM). The key challenge in this scenario is that neither the transmit signals nor the radar-and-communication channels are known. We prove that LANM can simultaneously achieve localization of radar targets and decoding of communication symbols, when the number of observations is proportional to the degrees of freedom in the ISAC systems. Despite the inherent ill-posed nature of the problem, we employ the lifting technique to initially encode the transmit signals. Then, we leverage the atomic norm to promote the structured low-rankness for the ISAC channel. We utilize a dual technique to transform the LANM into an infinite-dimensional search over the signal domain. Subsequently, we use semidefinite relaxation (SDR) to implement the dual problem. We extend our approach to practical scenarios where received signals are contaminated by additive white Gaussian noise (AWGN) and jamming signals. Furthermore, we derive the computational complexity of the proposed estimator and demonstrate that it is equivalent to the conventional pilot-aided ANM for estimating the channel parameters. Our simulation experiments demonstrate the ability of the proposed LANM approach to estimate both communication data and target parameters with a performance comparable to traditional radar-only super-resolution techniques.

Figures

Figures reproduced from arXiv: 2411.09495 by the authors.

Figure 1
Figure 1. System model. ANM can be considered as a continuous version of the ℓ1 norm minimization, which is able to minimize the number of atoms required for the construction of the signal of interest over a continuous dictionary [25]. This method has found application in various communication and signal processing problems, including MIMO radar [26], line spectral estimation [27], the elimination of impulsive noise in OFDM s… view at source ↗
Figure 2
Figure 2. The magnitude of the dual polynomial in (ϕ, ρ) and (τ, v) domains in Figs. 2(a) and 2(b), respectively. Note that red circles represent the recovered radar parameters, respectively. V. ROBUSTNESS AGAINST AWGN NOISE AND JAMMING SIGNALS In this section, we propose a robust LANM to show that the proposed estimator can work in the case when the received signal is contaminated by AWGN noise and jamming signals as shown i… view at source ↗
Figure 3
Figure 3. The NMSE and SER of the proposed estimator com [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: The average success rate of LANM with respect to the number of targets and the subspace dimension [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: SER versus NMSE for different numbers of observa [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: The dual polynomials for detecting the locations of the target and jammer. The red bar in Fig. 6(a) shows the jammer’s [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: The NMSE and SER of the proposed estimator com [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]

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Reference graph

Works this paper leans on

39 extracted references · 13 canonical work pages · cited by 1 Pith paper

  1. [1]

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

    F. Liu, C. Masouros, A. P. Petropulu, H. Griffiths, and L. Hanzo, “Joint radar and communication design: Applications, state-of-the-art, and the road ahead,” IEEE Transactions on Communications , vol. 68, no. 6, pp. 3834–3862, 2020

    2020

  2. [2]

    Joint transmit designs for coexistence of mimo wireless communications and sparse sensing radars in clutter,

    B. Li and A. P. Petropulu, “Joint transmit designs for coexistence of mimo wireless communications and sparse sensing radars in clutter,” IEEE Transactions on Aerospace and Electronic Systems , vol. 53, no. 6, pp. 2846–2864, 2017

    work page 2017

  3. [3]

    Survey of rf communications and sensing convergence research,

    B. Paul, A. R. Chiriyath, and D. W. Bliss, “Survey of rf communications and sensing convergence research,” IEEE Access , vol. 5, pp. 252–270, 2016

    work page 2016

  4. [4]

    Dual-blind deconvolution for overlaid radar-communications systems,

    E. Vargas, K. V . Mishra, R. Jacome, B. M. Sadler, and H. Arguello, “Dual-blind deconvolution for overlaid radar-communications systems,” IEEE Journal on Selected Areas in Information Theory , 2023

    2023

  5. [5]

    Optimum co-design for spectrum sharing between matrix completion based mimo radars and a mimo com- munication system,

    B. Li, A. P. Petropulu, and W. Trappe, “Optimum co-design for spectrum sharing between matrix completion based mimo radars and a mimo com- munication system,” IEEE Transactions on Signal Processing , vol. 64, no. 17, pp. 4562–4575, 2016

    2016

  6. [6]

    Cooper- ative isac networks: Opportunities and challenges,

    K. Meng, C. Masouros, A. P. Petropulu, and L. Hanzo, “Cooper- ative isac networks: Opportunities and challenges,” arXiv preprint arXiv:2405.06305, 2024

    arXiv 2024

  7. [7]

    Net-zero energy dual- functional radar-communication systems,

    I. Valiulahi, C. Masouros, and A. Salem, “Net-zero energy dual- functional radar-communication systems,” IEEE Transactions on Green Communications and Networking , vol. 7, no. 1, pp. 356–369, 2023

    2023

  8. [8]

    Robust joint active-passive beamforming design for irs-assisted isac systems,

    M. AlaaEldin, E. Alsusa, K. G. Seddik, C. Masouros, and I. Valiulahi, “Robust joint active-passive beamforming design for irs-assisted isac systems,” arXiv preprint arXiv:2309.00978 , 2023

    arXiv 2023

Show all 39 references
  1. [9]

    5g mmwave positioning for vehicular networks,

    H. Wymeersch, G. Seco-Granados, G. Destino, D. Dardari, and F. Tufvesson, “5g mmwave positioning for vehicular networks,” IEEE Wireless Communications, vol. 24, no. 6, pp. 80–86, 2017

    2017

  2. [10]

    Wifi-based indoor positioning,

    C. Yang and H.-R. Shao, “Wifi-based indoor positioning,” IEEE Com- munications Magazine , vol. 53, no. 3, pp. 150–157, 2015

    2015

  3. [11]

    Intrapulse radar-embedded com- munications,

    S. D. Blunt, P. Yatham, and J. Stiles, “Intrapulse radar-embedded com- munications,” IEEE Transactions on Aerospace and Electronic Systems , vol. 46, no. 3, pp. 1185–1200, 2010

    2010

  4. [12]

    Isac receiver design: A learning- based two-stage joint data-and-target parameter estimation,

    J. Hu, I. Valiulahi, and C. Masouros, “Isac receiver design: A learning- based two-stage joint data-and-target parameter estimation,” IEEE Wire- less Communications Letters , 2024

    2024

  5. [13]

    Integrated sensing and communications: Toward dual-functional wire- less networks for 6g and beyond,

    F. Liu, Y . Cui, C. Masouros, J. Xu, T. X. Han, Y . C. Eldar, and S. Buzzi, “Integrated sensing and communications: Toward dual-functional wire- less networks for 6g and beyond,” IEEE journal on selected areas in communications, vol. 40, no. 6, pp. 1728–1767, 2022

    2022

  6. [14]

    To- ward dual-functional radar-communication systems: Optimal waveform design,

    F. Liu, L. Zhou, C. Masouros, A. Li, W. Luo, and A. Petropulu, “To- ward dual-functional radar-communication systems: Optimal waveform design,” IEEE Transactions on Signal Processing , vol. 66, no. 16, pp. 4264–4279, 2018

    2018

  7. [15]

    Cooperative isac networks: Performance analysis, scaling laws and optimization,

    K. Meng, C. Masouros, A. P. Petropulu, and L. Hanzo, “Cooperative isac networks: Performance analysis, scaling laws and optimization,” arXiv preprint arXiv:2404.14514, 2024

    2024 arXiv

  8. [16]

    Antenna selection for energy-efficient dual-functional radar-communication systems,

    I. Valiulahi, C. Masouros, A. Salem, and F. Liu, “Antenna selection for energy-efficient dual-functional radar-communication systems,” IEEE Wireless Communications Letters , vol. 11, no. 4, pp. 741–745, 2022

    2022

  9. [17]

    Multiple emitter location and signal parameter estimation,

    R. Schmidt, “Multiple emitter location and signal parameter estimation,” IEEE transactions on antennas and propagation , vol. 34, no. 3, pp. 276– 280, 1986

    1986

  10. [18]

    Two-stage esprit for unambiguous an- gle and range estimation in fda-mimo radar,

    Y . Yan, J. Cai, and W.-Q. Wang, “Two-stage esprit for unambiguous an- gle and range estimation in fda-mimo radar,” Digital Signal Processing , vol. 92, pp. 151–165, 2019

    2019

  11. [19]

    High-resolution radar via compressed sensing,

    M. A. Herman and T. Strohmer, “High-resolution radar via compressed sensing,” IEEE transactions on signal processing , vol. 57, no. 6, pp. 2275–2284, 2009

    2009

  12. [20]

    Mimo radar using compressive sampling,

    Y . Yu, A. P. Petropulu, and H. V . Poor, “Mimo radar using compressive sampling,” IEEE Journal of Selected Topics in Signal Processing , vol. 4, no. 1, pp. 146–163, 2010

    2010

  13. [21]

    Spatial compressive sensing in mimo radar with random arrays,

    M. Rossi, A. M. Haimovich, and Y . C. Eldar, “Spatial compressive sensing in mimo radar with random arrays,” in 2012 46th Annual Conference on Information Sciences and Systems (CISS) . IEEE, 2012, pp. 1–6

    2012

  14. [22]

    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 Transactions on Signal Processing, vol. 59, no. 5, pp. 2182–2195, 2011

    2011

  15. [23]

    Compressed sensing off the grid,

    G. Tang, B. N. Bhaskar, P. Shah, and B. Recht, “Compressed sensing off the grid,” IEEE transactions on information theory , vol. 59, no. 11, pp. 7465–7490, 2013

    2013

  16. [24]

    Robustness of two-dimensional line spectral estimation against spiky noise,

    I. Valiulahi, F. Haddadi, and A. Amini, “Robustness of two-dimensional line spectral estimation against spiky noise,” IEEE Transactions on Signal Processing, vol. 67, no. 23, pp. 5998–6008, 2019

    2019

  17. [25]

    Noncoherent ofdm transmission via off-the-grid joint channel and data estimation,

    M. Bigdeli, H. Fathi, I. Valiulahi, and C. Masouros, “Noncoherent ofdm transmission via off-the-grid joint channel and data estimation,” IEEE Wireless Communications Letters , vol. 12, no. 1, pp. 99–103, 2022

    2022

  18. [26]

    Range-angle decoupling and estimation for fda-mimo radar via atomic norm minimization and accelerated proximal gradient,

    W.-G. Tang, H. Jiang, and Q. Zhang, “Range-angle decoupling and estimation for fda-mimo radar via atomic norm minimization and accelerated proximal gradient,” IEEE Signal Processing Letters , vol. 27, pp. 366–370, 2020

    2020

  19. [27]

    Two-dimensional super-resolution via convex relaxation,

    I. Valiulahi, S. Daei, F. Haddadi, and F. Parvaresh, “Two-dimensional super-resolution via convex relaxation,” IEEE Transactions on Signal Processing, vol. 67, no. 13, pp. 3372–3382, 2019

    2019

  20. [28]

    Eliminating impulsive noise in pilot-aided ofdm channels via dual of penalized atomic norm,

    I. Valiulahi, F. Parvaresh, and A. A. Beheshti, “Eliminating impulsive noise in pilot-aided ofdm channels via dual of penalized atomic norm,” IEEE Communications Letters , vol. 23, no. 11, pp. 2059–2062, 2019

    2019

  21. [29]

    Super-resolution radar,

    R. Heckel, V . I. Morgenshtern, and M. Soltanolkotabi, “Super-resolution radar,” Information and Inference: A Journal of the IMA , vol. 5, no. 1, pp. 22–75, 2016

    2016

  22. [30]

    Super-resolution mimo radar,

    R. Heckel, “Super-resolution mimo radar,” in 2016 IEEE international symposium on information theory (ISIT) . IEEE, 2016, pp. 1416–1420

    2016

  23. [31]

    Guaranteed blind sparse spikes deconvolution via lifting and convex optimization,

    Y . Chi, “Guaranteed blind sparse spikes deconvolution via lifting and convex optimization,” IEEE Journal of Selected Topics in Signal Pro- cessing, vol. 10, no. 4, pp. 782–794, 2016

    2016

  24. [32]

    Mathematical theory of atomic norm de- noising in blind two-dimensional super-resolution,

    M. A. Suliman and W. Dai, “Mathematical theory of atomic norm de- noising in blind two-dimensional super-resolution,” IEEE Transactions on Signal Processing , vol. 69, pp. 1681–1696, 2021

    2021

  25. [33]

    Super-resolution delay-doppler estimation for ofdm passive radar,

    L. Zheng and X. Wang, “Super-resolution delay-doppler estimation for ofdm passive radar,” IEEE Transactions on Signal Processing , vol. 65, no. 9, pp. 2197–2210, 2017

    2017

  26. [34]

    Dumitrescu, Positive trigonometric polynomials and signal processing applications

    B. Dumitrescu, Positive trigonometric polynomials and signal processing applications. Springer, 2007, vol. 103

    2007

  27. [35]

    Cvx: Matlab software for disciplined convex programming, version 2.1,

    M. Grant and S. Boyd, “Cvx: Matlab software for disciplined convex programming, version 2.1,” 2014

    2014

  28. [36]

    M. A. Richards et al. , Fundamentals of radar signal processing . Mcgraw-hill New York, 2005, vol. 1

    2005

  29. [37]

    Space-time adaptive processing for airborne radar,

    J. Ward, “Space-time adaptive processing for airborne radar,” 1998

    1998

  30. [38]

    Towards a mathematical theory of super-resolution,

    E. J. Cand `es and C. Fernandez-Granda, “Towards a mathematical theory of super-resolution,” Communications on pure and applied Mathematics , vol. 67, no. 6, pp. 906–956, 2014

    2014

  31. [39]

    Super-resolution of complex exponentials from modulations with unknown waveforms,

    D. Yang, G. Tang, and M. B. Wakin, “Super-resolution of complex exponentials from modulations with unknown waveforms,” IEEE Trans- actions on Information Theory , vol. 62, no. 10, pp. 5809–5830, 2016

    2016

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.