pith. sign in

arxiv: 2605.02559 · v1 · submitted 2026-05-04 · 📡 eess.SP

Frequency Diverse Arrays: Fundamentals, Key Insights, and Future Directions

Bang Huang , Sajid Ahmed , Wenkai Jia , Mohamed-Slim Alouini , Wen-QinWang This is my paper

Pith reviewed 2026-05-08 17:59 UTC · model grok-4.3

classification 📡 eess.SP
keywords frequency diverse arraysirreducibility criterionrange-angle couplingarray manifoldsradar signal processingMIMO arraysphysical degrees of freedom
0
0 comments X

The pith

An irreducibility criterion distinguishes genuine range-domain physical degrees of freedom in frequency diverse arrays from effects replicable by signal processing.

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

The paper reexamines frequency diverse arrays from a manifold-based perspective to clarify what makes their range-dependent behavior distinct from conventional phased arrays and MIMO systems. It introduces an irreducibility criterion that identifies which range-angle effects require actual frequency offsets rather than equivalent transformations applied in signal processing. This distinction matters for designers deciding when FDA hardware complexity is justified in applications such as radar parameter estimation, target detection, imaging, and secure communications. The work compares PA, MIMO, FDA, and FDA-MIMO by tracing their effective degrees of freedom to physical origins like spatial phase, waveform orthogonality, and frequency gradients. It also explains how FDA features including manifold expansion, time variation, and multi-frequency diversity connect to system-level capabilities.

Core claim

FDA produces joint time-range-angle responses through inter-element frequency offsets, and an irreducibility criterion separates genuine physical range-domain degrees of freedom from effects that can be reproduced by equivalent signal-processing transformations. This allows PA, MIMO, FDA, and FDA-MIMO to be interpreted according to the physical sources of their degrees of freedom, including spatial phase, waveform orthogonality, frequency gradients, and their interactions, while clarifying the distinct role of frequency versus time-coding architectures.

What carries the argument

The irreducibility criterion, a test that determines whether a given range-domain effect originates from physical frequency diversity or can be achieved through signal-processing equivalents.

If this is right

  • Range-angle coupling in FDA directly enables improved parameter estimation and target detection without relying solely on post-processing.
  • Time variation of FDA responses limits the feasibility of time-invariant focusing and must be accounted for in system design.
  • Multi-frequency diversity supports new capabilities in physical-layer security and integrated sensing and communication.
  • FDA properties such as manifold expansion translate into concrete advantages for imaging and detection tasks.
  • Contrasts with time-coding architectures highlight frequency as a distinct source of diversity.

Where Pith is reading between the lines

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

  • The criterion could be tested on other array types to evaluate their unique physical contributions.
  • Hardware experiments could measure whether claimed FDA benefits persist after optimal signal processing on simpler arrays.
  • If the separation holds, it would inform cost-benefit trade-offs when choosing between frequency control hardware and additional processing power.
  • Connections to manifold geometry suggest potential for deriving optimal array configurations without exhaustive simulation.

Load-bearing premise

The manifold-based perspective and irreducibility criterion provide a complete and physically accurate separation of degrees of freedom without needing further empirical validation.

What would settle it

A specific calculation or measurement showing an FDA range-angle coupling pattern that cannot be exactly reproduced by any waveform or processing transformation applied to a conventional phased array.

Figures

Figures reproduced from arXiv: 2605.02559 by Bang Huang, Mohamed-Slim Alouini, Sajid Ahmed, Wenkai Jia, Wen-QinWang.

Figure 1
Figure 1. Figure 1: Representative development trajectory of FDA view at source ↗
Figure 3
Figure 3. Figure 3: Geometry of a uniform linear transmit array with view at source ↗
Figure 2
Figure 2. Figure 2: Organization of this paper. The organization of this paper is illustrated in view at source ↗
Figure 4
Figure 4. Figure 4: In phased-array, the progressive phase shifts across view at source ↗
Figure 5
Figure 5. Figure 5: In an FDA, each antenna element slightly offset view at source ↗
Figure 6
Figure 6. Figure 6: Range–angle response comparison based on the corresponding array-factor formulations of four array paradigms. view at source ↗
Figure 7
Figure 7. Figure 7: Angular AF comparison at a fixed range–time slice. view at source ↗
Figure 8
Figure 8. Figure 8: Taxonomy of FDA–MIMO architectures based on the orthogonality mechanism used to separate transmit view at source ↗
Figure 9
Figure 9. Figure 9: Mechanism of frequency-orthogonal FDA–MIMO. view at source ↗
Figure 10
Figure 10. Figure 10: Pulse-compression outputs for different channels in a coherent FDA system. Because each transmit element view at source ↗
Figure 11
Figure 11. Figure 11: Comparison of beam behavior in FDA and PA view at source ↗
Figure 12
Figure 12. Figure 12: Time evolution of the FDA transmit beampattern view at source ↗
Figure 13
Figure 13. Figure 13: Illustration of two FDA operating regimes determined by the product view at source ↗
Figure 14
Figure 14. Figure 14: Integrated transmit beampattern of FDA for view at source ↗
Figure 15
Figure 15. Figure 15: Range-cut of the FDA ambiguity function for view at source ↗
Figure 16
Figure 16. Figure 16: Time-varying RCS of an FDA radar target as a function of time and observation angle. The periodic fluc￾tuations demonstrate that, due to the element-dependent frequency offsets, the coherent superposition of scattering contributions evolves over time, resulting in a time-varying equivalent RCS even for a static target [159] However, the aforementioned time-varying RCS behav￾ior relies on the coherence of … view at source ↗
Figure 18
Figure 18. Figure 18: Illustration of the EPC structure. Each array view at source ↗
Figure 19
Figure 19. Figure 19: Illustration of the STCA structure. Each transmit view at source ↗
Figure 20
Figure 20. Figure 20: Detection performance under mainlobe decep view at source ↗
Figure 21
Figure 21. Figure 21: High-speed target detection performance under view at source ↗
Figure 22
Figure 22. Figure 22: Probability of detection versus SCR for different view at source ↗
Figure 23
Figure 23. Figure 23: Comparison of the joint transmit–receive spatial view at source ↗
Figure 24
Figure 24. Figure 24: Intercepted power trajectories at a passive receiver view at source ↗
Figure 25
Figure 25. Figure 25: Example of scene-template-based deceptive jam view at source ↗
Figure 26
Figure 26. Figure 26: Ergodic secrecy rate versus SNR for PA ( view at source ↗
Figure 27
Figure 27. Figure 27: BER performance of index modulation schemes view at source ↗
Figure 28
Figure 28. Figure 28: Comparison of area surveillance performance be view at source ↗
Figure 29
Figure 29. Figure 29: Communication sum rate versus SNR, showing view at source ↗
read the original abstract

Frequency diverse arrays (FDA) have attracted sustained interest as a promising architecture for introducing range-dependent responses into array systems. Unlike conventional phased arrays (PA), whose transmit behavior is primarily angle-dependent, FDA employs inter-element frequency offsets to generate time-and range-dependent phase structures, thereby producing a joint time-range-angle array response. Despite extensive research, the physical meaning of FDA-induced degrees of freedom remains debated, particularly in relation to range-angle coupling, the feasibility of time-invariant focusing, and the distinction between frequency-driven and waveform-driven range selectivity. This paper reexamines FDA from a structural and manifold-based perspective. A central contribution is the introduction of an irreducibility criterion, which distinguishes genuine range-domain physical degrees of freedom from effects that can be reproduced by equivalent signal-processing transformations. Based on this perspective, PA, multiple-input multiple-output (MIMO), FDA, and FDA-MIMO are comparatively interpreted according to the physical origin of their effective degrees of freedom, including spatial phase, waveform orthogonality, frequency gradients, and their interaction. The paper further clarifies the role of frequency across different array paradigms, contrasts FDA with time-coding-based architectures, and explains how key FDA properties such as manifold expansion, range--angle coupling, time variation, and multi-frequency diversity translate into system capabilities. Building on these structural insights, the paper connects FDA to a broad range of radar and communication functionalities, including parameter estimation, target detection, imaging, physical-layer security, and integrated sensing and communication.

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 / 2 minor

Summary. The paper reexamines frequency diverse arrays (FDA) from a structural and manifold-based perspective. It introduces an irreducibility criterion to distinguish genuine range-domain physical degrees of freedom from effects reproducible by signal-processing transformations. Using this lens, the work comparatively interprets phased arrays (PA), MIMO, FDA, and FDA-MIMO according to the physical origins of their effective degrees of freedom (spatial phase, waveform orthogonality, frequency gradients, and interactions). It clarifies the role of frequency across paradigms, contrasts FDA with time-coding architectures, explains properties such as manifold expansion, range-angle coupling, time variation, and multi-frequency diversity, and connects these insights to applications including parameter estimation, target detection, imaging, physical-layer security, and integrated sensing and communication.

Significance. If the irreducibility criterion can be formalized as a precise, testable distinction, the manuscript could offer a unifying conceptual framework for array architectures that resolves ongoing debates about FDA range selectivity and time-invariance. The comparative interpretation of PA/MIMO/FDA/FDA-MIMO and the linkage to practical functionalities would then provide value for guiding system design in radar and ISAC contexts.

major comments (2)
  1. [Introduction and the section introducing the irreducibility criterion] The central contribution—the irreducibility criterion—is presented only at a high conceptual level without an explicit mathematical definition or test (e.g., a condition on manifold dimension or coupling terms that checks exact reproducibility via linear waveform transformations or equivalent time-varying phased-array operations). This renders the claimed separation between genuine physical range-domain DOF and signal-processing equivalents interpretive rather than verifiable, directly undermining the comparative reinterpretation of PA/MIMO/FDA/FDA-MIMO.
  2. [Sections on FDA properties and comparative interpretations] No counter-examples, specific manifold calculations, or validation cases are supplied to demonstrate application of the criterion to concrete FDA configurations (e.g., linear frequency offset vs. waveform orthogonality). Without such grounding, the claims about manifold expansion, range-angle coupling, and time variation remain untested against the paper's own structural perspective.
minor comments (2)
  1. [Abstract and Introduction] The abstract and early sections use terms such as 'irreducibility criterion' and 'manifold-based perspective' before they are defined; a brief forward reference or inline clarification would improve readability.
  2. [Applications section] Several application connections (parameter estimation, ISAC, etc.) are listed at a high level; adding one or two concrete references to prior FDA work that would be reinterpreted under the new criterion would strengthen the narrative.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive review and for acknowledging the potential of the irreducibility criterion as a unifying framework for array architectures in radar and ISAC contexts. We agree that the criterion requires a more explicit mathematical formulation and concrete validation examples to strengthen verifiability. We will revise the manuscript to address these points directly.

read point-by-point responses

  1. Referee: [Introduction and the section introducing the irreducibility criterion] The central contribution—the irreducibility criterion—is presented only at a high conceptual level without an explicit mathematical definition or test (e.g., a condition on manifold dimension or coupling terms that checks exact reproducibility via linear waveform transformations or equivalent time-varying phased-array operations). This renders the claimed separation between genuine physical range-domain DOF and signal-processing equivalents interpretive rather than verifiable, directly undermining the comparative reinterpretation of PA/MIMO/FDA/FDA-MIMO.

    Authors: We acknowledge that the presentation of the irreducibility criterion remains at a conceptual level in the current manuscript. To address this, the revised version will include an explicit mathematical definition: a criterion based on the dimension and linear independence of the array response manifold, specifically checking whether frequency-induced phase gradients introduce coupling terms that cannot be exactly reproduced by any linear transformation of the transmit waveforms or by equivalent time-varying operations on a conventional phased array. This definition will be accompanied by a testable procedure (e.g., rank analysis of the manifold matrix under frequency offsets versus waveform orthogonality) and will be used to ground the comparative reinterpretation of PA, MIMO, FDA, and FDA-MIMO. revision: yes

  2. Referee: [Sections on FDA properties and comparative interpretations] No counter-examples, specific manifold calculations, or validation cases are supplied to demonstrate application of the criterion to concrete FDA configurations (e.g., linear frequency offset vs. waveform orthogonality). Without such grounding, the claims about manifold expansion, range-angle coupling, and time variation remain untested against the paper's own structural perspective.

    Authors: We agree that concrete examples are required to demonstrate the criterion's application. In the revision, we will add specific manifold calculations for a uniform linear FDA with linear frequency offsets, contrasting them with MIMO waveform orthogonality. Counter-examples will be provided showing configurations where range selectivity and range-angle coupling are irreducible (cannot be replicated by signal-processing transformations alone), along with numerical validations of manifold expansion, time variation, and multi-frequency diversity. These will directly test and illustrate the claims on FDA properties. revision: yes

Circularity Check

0 steps flagged

No significant circularity; irreducibility criterion is a conceptual reinterpretation without reduction to inputs by construction

full rationale

The paper reexamines FDA architectures from a manifold-based perspective and introduces an irreducibility criterion to distinguish physical range-domain degrees of freedom from signal-processing equivalents. This criterion is presented as a structural insight for comparative interpretation of PA, MIMO, FDA, and FDA-MIMO, without any equations or claims that define the criterion in terms of its own outputs, fit parameters to data and rename them as predictions, or rely on self-citations as the sole load-bearing justification. The derivation chain consists of reinterpretations and clarifications of existing properties (manifold expansion, range-angle coupling, time variation) rather than closed loops that reduce claims to their own inputs. No self-definitional, fitted-input, or uniqueness-imported patterns are exhibited in the provided abstract or framing.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The work rests on domain assumptions about array manifolds and the physical meaning of frequency offsets; it introduces the irreducibility criterion as a new conceptual tool without independent empirical support in the abstract.

axioms (1)
  • domain assumption The manifold-based perspective accurately captures the physical origins of degrees of freedom in phased arrays, MIMO, and FDA systems.
    Invoked throughout the reexamination and comparative interpretation of array architectures.
invented entities (1)
  • irreducibility criterion no independent evidence
    purpose: To distinguish genuine range-domain physical degrees of freedom from effects reproducible by signal-processing transformations.
    Newly introduced as the central contribution; no independent falsifiable evidence is provided in the abstract.

pith-pipeline@v0.9.0 · 5577 in / 1208 out tokens · 58518 ms · 2026-05-08T17:59:07.254136+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

291 extracted references · 3 canonical work pages

  1. [1]

    Rahman, Fundamental principles of radar

    H. Rahman, Fundamental principles of radar. CRC Press, 2019

    2019

  2. [2]

    Wireless communications–principles and practice, (the book end)

    T. S. Rappaport, “Wireless communications–principles and practice, (the book end). ” Microwave Journal, vol. 45, no. 12, pp. 128–129, 2002

    2002

  3. [3]

    Lütkepohl, Handbook of matrices

    H. Lütkepohl, Handbook of matrices. John Wiley & Sons, 1997

    1997

  4. [4]

    Eaves and E

    J. Eaves and E. Reedy, Principles of modern radar. Springer Science & Business Media, 2012

    2012

  5. [5]

    Skolnik, Introduction to Radar Systems

    M. Skolnik, Introduction to Radar Systems. New York, NY: McGrowHill, 2001

    2001

  6. [6]

    R. J. Mailloux, Phased array antenna handbook. Artech house, 2017

    2017

  7. [7]

    Stoica, R

    P. Stoica, R. L. Moses et al., Spectral analysis of signals. Pearson Prentice Hall Upper Saddle River, NJ, 2005, vol. 452

    2005

  8. [8]

    Modern radar system analysis,

    D. K. Barton, “Modern radar system analysis,” Norwood, 1988

    1988

  9. [9]

    R. M. Buehrer, Code division multiple access (CDMA). Springer Nature, 2022

    2022

  10. [10]

    K. S. Zigangirov, Theory of code division multiple access communication. John Wiley & Sons, 2004

    2004

  11. [11]

    Frequency division multiple access (FDMA),

    S. Faruque, “Frequency division multiple access (FDMA),” in radio frequency multiple access techniques made easy. Springer, 2018, pp. 21–33

    2018

  12. [12]

    Single carrier-frequency division multiple access radar: Waveform design and analysis,

    R. Saadia and N. M. Khan, “Single carrier-frequency division multiple access radar: Waveform design and analysis,” IEEE Access, vol. 8, pp. 35 742–35 751, 2020

    2020

  13. [13]

    Y. G. Li and G. L. Stuber, Orthogonal frequency division multiplexing for wireless communications. Springer Science & Business Media, 2006

    2006

  14. [14]

    The history of orthogonal frequency-division multiplexing [history of communications],

    S. B. Weinstein, “The history of orthogonal frequency-division multiplexing [history of communications],” IEEE Communica- tions Magazine, vol. 47, no. 11, pp. 26–35, 2009

    2009

  15. [15]

    J. R. Hampton, Introduction to MIMO communications. Cambridge university press, 2013

    2013

  16. [16]

    A. B. Gershman and N. D. Sidiropoulos, Space-time processing for MIMO communications. Wiley Online Library, 2005

    2005

  17. [17]

    T. M. Duman and A. Ghrayeb, Coding for MIMO communi- cation systems. John Wiley & Sons, 2008

    2008

  18. [18]

    De Flaviis, Multiantenna systems for MIMO communica- tions

    F. De Flaviis, Multiantenna systems for MIMO communica- tions. Morgan & Claypool Publishers, 2008, vol. 7

    2008

  19. [19]

    Development of frequency diverse array radar technology: a review,

    A. Basit, W. Khan, S. Khan, and I. M. Qureshi, “Development of frequency diverse array radar technology: a review,” IET Radar, Sonar & Navigation, vol. 12, no. 2, pp. 165–175, 2018

    2018

  20. [20]

    Frequency diverse array antenna: New oppor- tunities,

    W.-Q. Wang, “Frequency diverse array antenna: New oppor- tunities,” IEEE Antennas and Propagation Magazine, vol. 57, no. 2, pp. 145–152, 2015

    2015

  21. [21]

    Frequency diverse array radars,

    P. Antonik, M. Wicks, H. Griffiths, and C. Baker, “Frequency diverse array radars,” in 2006 IEEE Conference on Radar, Verona, NY, USA, 2006, pp. 3 pp.–

    2006

  22. [22]

    An investigation of a frequency diverse array,

    P. Antonik, “An investigation of a frequency diverse array,” Ph.D. dissertation, UCL (University College London), London, 2009

    2009

  23. [23]

    An overview of frequency diverse array radar technology,

    J. Xu, S. Zhu, G. Liao, and Y. Zhang, “An overview of frequency diverse array radar technology,” Journal of Radars, vol. 7, no. 2, pp. 167–182, 2018. (Chinese)

    2018

  24. [24]

    An overview on time/frequency modulated array processing,

    W.-Q. Wang, H. C. So, and A. Farina, “An overview on time/frequency modulated array processing,” IEEE Journal of Selected Topics in Signal Processing, vol. 11, no. 2, pp. 228– 246, 2016

    2016

  25. [25]

    Digital phased arrays: Challenges and opportunities,

    C. Fulton, M. Yeary, D. Thompson, J. Lake, and A. Mitchell, “Digital phased arrays: Challenges and opportunities,” Pro- ceedings of the IEEE, vol. 104, no. 3, pp. 487–503, 2016

    2016

  26. [26]

    H. J. Visser, Array and phased array antenna basics. John Wiley & Sons, 2006

    2006

  27. [27]

    Frequency diverse array radar with logarithmically increasing frequency offset,

    W. Khan, I. M. Qureshi, and S. Saeed, “Frequency diverse array radar with logarithmically increasing frequency offset,” IEEE Antennas and Wireless Propagation Letters, vol. 14, pp. 499–502, 2015

    2015

  28. [28]

    Dot-shaped beamforming analysis based on osb log-FDA,

    B. Wang, J. Xie, J. Zhang, and H. Zhang, “Dot-shaped beamforming analysis based on osb log-FDA,” Journal of Systems Engineering and Electronics, vol. 31, no. 2, pp. 312– 320, 2020. 43

    2020

  29. [30]

    Decoupled frequency diverse array range–angle-dependent beampattern synthesis using non-linearly increasing frequency offsets,

    K. Gao, W.-Q. Wang, J. Cai, and J. Xiong, “Decoupled frequency diverse array range–angle-dependent beampattern synthesis using non-linearly increasing frequency offsets,” IET Microwaves, Antennas & Propagation, vol. 10, no. 8, pp. 880– 884, 2016

    2016

  30. [31]

    Frequency diverse ar- ray beampattern synthesis with modified sinusoidal frequency offset,

    X. Shao, T. Hu, Z. Xiao, and J. Zhang, “Frequency diverse ar- ray beampattern synthesis with modified sinusoidal frequency offset,” IEEE Antennas and Wireless Propagation Letters, vol. 20, no. 9, pp. 1784–1788, 2021

    2021

  31. [32]

    Beam pattern synthesis for an FDA radar with hamming window-based nonuniform frequency offset,

    A. Basit, I. M. Qureshi, W. Khan, S. ur Rehman, and M. M. Khan, “Beam pattern synthesis for an FDA radar with hamming window-based nonuniform frequency offset,” IEEE Antennas and Wireless Propagation Letters, vol. 16, pp. 2283– 2286, 2017

    2017

  32. [33]

    Frequency diverse array beampattern synthesis with taylor windowed frequency offsets,

    Y. Liao, H. Tang, X. Chen, and W.-Q. Wang, “Frequency diverse array beampattern synthesis with taylor windowed frequency offsets,” IEEE Antennas and Wireless Propagation Letters, vol. 19, no. 11, pp. 1901–1905, 2020

    1901

  33. [34]

    Antenna beampattern with range null control using weighted frequency diverse array,

    Y. Liao, H. Tang, X. Chen, W.-Q. Wang, M. Xing, Z. Zheng, J. Wang, and Q. H. Liu, “Antenna beampattern with range null control using weighted frequency diverse array,” IEEE Access, vol. 8, pp. 50 107–50 117, 2020

    2020

  34. [35]

    Tangent hyperbolic circular frequency diverse array radars,

    S. Saeed, I. M. Qureshi, W. Khan, and A. Salman, “Tangent hyperbolic circular frequency diverse array radars,” the Journal of Engineering, vol. 2016, no. 3, pp. 23–28, 2016

    2016

  35. [36]

    Range-azimuth decouple beamforming for frequency diverse array with costas-sequence modulated frequency offsets,

    Z. Wang, W.-Q. Wang, and H. Shao, “Range-azimuth decouple beamforming for frequency diverse array with costas-sequence modulated frequency offsets,” EURASIP Journal on Advances in Signal Processing, vol. 2016, no. 1, p. 124, 2016

    2016

  36. [37]

    Anal- ysis of exponential frequency-diverse array for short-range beam-focusing technology,

    W. Choi, A. Georgiadis, M. M. Tentzeris, and S. Kim, “Anal- ysis of exponential frequency-diverse array for short-range beam-focusing technology,” IEEE Transactions on Antennas and Propagation, vol. 71, no. 2, pp. 1437–1447, 2023

    2023

  37. [38]

    The random fre- quency diverse array: A new antenna structure for uncoupled direction-range indication in active sensing,

    Y. Liu, H. Ruan, L. Wang, and A. Nehorai, “The random fre- quency diverse array: A new antenna structure for uncoupled direction-range indication in active sensing,” IEEE Journal of Selected Topics in Signal Processing, vol. 11, no. 2, pp. 295– 308, 2016

    2016

  38. [39]

    Frequency diverse array with random logarithmically increasing frequency offset,

    G. Huang, Y. Ding, S. Ouyang, and V. Fusco, “Frequency diverse array with random logarithmically increasing frequency offset,” Microwave and Optical Technology Letters, vol. 62, no. 7, pp. 2554–2561, 2020

    2020

  39. [40]

    Frequency diverse array transmit beampattern optimization with genetic algorithm,

    J. Xiong, W.-Q. Wang, H. Shao, and H. Chen, “Frequency diverse array transmit beampattern optimization with genetic algorithm,” IEEE Antennas and Wireless Propagation Letters, vol. 16, pp. 469–472, 2017

    2017

  40. [41]

    Frequency-modulated diverse array transmit beamforming with bat metaheuristic optimi- sation,

    S. Yaw Nusenu and A. Basit, “Frequency-modulated diverse array transmit beamforming with bat metaheuristic optimi- sation,” IET Radar, Sonar & Navigation, vol. 14, no. 9, pp. 1338–1342, 2020

    2020

  41. [42]

    Fuzzy entropy for frequency diverse array beampattern synthesis,

    J. Ge, J. Xie, B. Wang, and C. Chen, “Fuzzy entropy for frequency diverse array beampattern synthesis,” IEEE Trans- actions on Antennas and Propagation, vol. 70, no. 11, pp. 11 172–11 176, 2022

    2022

  42. [43]

    Frequency diverse array with independent modulation of frequency, amplitude, and phase,

    M. C. Wicks and P. Antonik, “Frequency diverse array with independent modulation of frequency, amplitude, and phase,” Patent

  43. [44]

    Method and apparatus for a frequency diverse array,

    ——, “Method and apparatus for a frequency diverse array,” Patent

  44. [45]

    Frequency diverse array radar,

    A. Aytun, “Frequency diverse array radar,” Ph.D. dissertation, Monterey, California, 2010

    2010

  45. [46]

    Range-angle localization of targets by a double-pulse frequency diverse array radar,

    W.-Q. Wang and H. Shao, “Range-angle localization of targets by a double-pulse frequency diverse array radar,” IEEE Journal of Selected Topics in Signal Processing, vol. 8, no. 1, pp. 106– 114, 2013

    2013

  46. [47]

    Linear frequency diverse array manifold geometry and ambiguity analysis,

    Y. Wang, W.-Q. Wang, and H. Chen, “Linear frequency diverse array manifold geometry and ambiguity analysis,” IEEE Sensors Journal, vol. 15, no. 2, pp. 984–993, 2014

    2014

  47. [48]

    Generalized linear fre- quency diverse array manifold curve analysis,

    T. Liao, Y. Pan, and W.-Q. Wang, “Generalized linear fre- quency diverse array manifold curve analysis,” IEEE Signal Processing Letters, vol. 25, no. 6, pp. 768–772, 2018

    2018

  48. [49]

    Transmit beam- pattern synthesis for the FDA radar,

    B. Chen, X. Chen, Y. Huang, and J. Guan, “Transmit beam- pattern synthesis for the FDA radar,” IEEE Antennas and Wireless Propagation Letters, vol. 17, no. 1, pp. 98–101, 2017

    2017

  49. [50]

    Accurate models of time-invariant beampatterns for frequency diverse arrays,

    K. Chen, S. Yang, Y. Chen, and S.-W. Qu, “Accurate models of time-invariant beampatterns for frequency diverse arrays,” IEEE Transactions on Antennas and Propagation, vol. 67, no. 5, pp. 3022–3029, 2019

    2019

  50. [51]

    Time-variance analysis for frequency-diverse array beampatterns,

    Y. Liao, G. Zeng, Z. Luo, and Q. H. Liu, “Time-variance analysis for frequency-diverse array beampatterns,” IEEE Transactions on Antennas and Propagation, vol. 71, no. 8, pp. 6558–6567, 2023

    2023

  51. [52]

    Optimization of sparse frequency diverse array with time-invariant spatial-focusing beampattern,

    Y.-Q. Yang, H. Wang, H.-Q. Wang, S.-Q. Gu, D.-L. Xu, and S.- L. Quan, “Optimization of sparse frequency diverse array with time-invariant spatial-focusing beampattern,” IEEE Antennas and Wireless Propagation Letters, vol. 17, no. 2, pp. 351–354, 2018

    2018

  52. [54]

    Transmit subaperturing for range and angle estimation in frequency diverse array radar,

    W.-Q. Wang and H.-C. So, “Transmit subaperturing for range and angle estimation in frequency diverse array radar,” IEEE Transactions on Signal Processing, vol. 62, no. 8, pp. 2000– 2011, 2014

    2000

  53. [55]

    Subarray-based frequency diverse array radar for target range-angle estimation,

    W.-Q. Wang, “Subarray-based frequency diverse array radar for target range-angle estimation,” IEEE Transactions on Aerospace and Electronic Systems, vol. 50, no. 4, pp. 3057– 3067, 2014

    2014

  54. [56]

    Flat-top beampattern synthesis in range and angle domains for frequency diverse array via second-order cone programming,

    Y. Xu, X. Shi, W. Li, and J. Xu, “Flat-top beampattern synthesis in range and angle domains for frequency diverse array via second-order cone programming,” IEEE Antennas and Wireless Propagation Letters, vol. 15, pp. 1479–1482, 2015

    2015

  55. [57]

    Range– angle-decoupled beampattern synthesis with subarray-based frequency diverse array,

    Y. Xu, X. Shi, J. Xu, L. Huang, and W. Li, “Range– angle-decoupled beampattern synthesis with subarray-based frequency diverse array,” Digital Signal Processing, vol. 64, pp. 49–59, 2017

    2017

  56. [58]

    Frequency diverse coprime arrays with coprime frequency offsets for multitarget localization,

    S. Qin, Y. D. Zhang, M. G. Amin, and F. Gini, “Frequency diverse coprime arrays with coprime frequency offsets for multitarget localization,” IEEE Journal of Selected Topics in Signal Processing, vol. 11, no. 2, pp. 321–335, 2016

    2016

  57. [59]

    Range-dependent beam- forming using space-frequency virtual difference coarray,

    T. Ni, S. Liu, Z. Mao, and Y. Huang, “Range-dependent beam- forming using space-frequency virtual difference coarray,” in 2021 IEEE Radar Conference (RadarConf21), Atlanta, GA, USA, 2021, pp. 1–5

    2021

  58. [61]

    Range–angle transceiver beam- forming based on semicircular-FDA scheme,

    Y. Xu, A. Wang, and J. Xu, “Range–angle transceiver beam- forming based on semicircular-FDA scheme,” IEEE Transac- tions on Aerospace and Electronic Systems, vol. 58, no. 2, pp. 834–843, 2022

    2022

  59. [62]

    Wavelength-diverse mimo radar: parameter-coupling, array-carrier optimization and direction- of-arrival estimation,

    M. Ulrich and B. Yang, “Wavelength-diverse mimo radar: parameter-coupling, array-carrier optimization and direction- of-arrival estimation,” IEEE Transactions on Aerospace and Electronic Systems, vol. 55, no. 4, pp. 1920–1932, 2018

    1920

  60. [63]

    Correction analysis of frequency diverse array radar about time,

    M. Tan, C. Wang, and Z. Li, “Correction analysis of frequency diverse array radar about time,” IEEE Transactions on An- tennas and Propagation, vol. 69, no. 2, pp. 834–847, 2021

    2021

  61. [64]

    Frequency diverse MIMO techniques for radar,

    P. F. Sammartino, C. J. Baker, and H. D. Griffiths, “Frequency diverse MIMO techniques for radar,” IEEE Transactions on Aerospace and Electronic Systems, vol. 49, no. 1, pp. 201–222, 2013

    2013

  62. [65]

    Joint range and angle estimation using MIMO radar with frequency diverse array,

    J. Xu, G. Liao, S. Zhu, L. Huang, and H. C. So, “Joint range and angle estimation using MIMO radar with frequency diverse array,” IEEE Transactions on Signal Processing, vol. 63, no. 13, pp. 3396–3410, 2015

    2015

  63. [66]

    A double pulse MIMO frequency diverse array radar for improved range- angle localization of target,

    W. Khan, I. M. Qureshi, A. Basit, and M. Zubair, “A double pulse MIMO frequency diverse array radar for improved range- angle localization of target,” Wireless Personal Communica- tions, vol. 82, pp. 2199–2213, 2015

    2015

  64. [67]

    FDA-MIMO radar range– angle estimation: CRLB, MSE, and resolution analysis,

    J. Xiong, W.-Q. Wang, and K. Gao, “FDA-MIMO radar range– angle estimation: CRLB, MSE, and resolution analysis,” IEEE Transactions on Aerospace and Electronic Systems, vol. 54, no. 1, pp. 284–294, 2018. 44

    2018

  65. [68]

    Range ambiguous clutter suppres- sion for airborne FDA-STAP radar,

    J. Xu, S. Zhu, and G. Liao, “Range ambiguous clutter suppres- sion for airborne FDA-STAP radar,” IEEE Journal of Selected Topics in Signal Processing, vol. 9, no. 8, pp. 1620–1631, 2015

    2015

  66. [69]

    Space-time adaptive processing with vertical frequency diverse array for range-ambiguous clutter suppression,

    J. Xu, G. Liao, and H. C. So, “Space-time adaptive processing with vertical frequency diverse array for range-ambiguous clutter suppression,” IEEE Transactions on Geoscience and Remote Sensing, vol. 54, no. 9, pp. 5352–5364, 2016

    2016

  67. [70]

    An adap- tive range-angle-doppler processing approach for FDA-MIMO radar using three-dimensional localization,

    J. Xu, G. Liao, Y. Zhang, H. Ji, and L. Huang, “An adap- tive range-angle-doppler processing approach for FDA-MIMO radar using three-dimensional localization,” IEEE Journal of Selected Topics in Signal Processing, vol. 11, no. 2, pp. 309– 320, 2017

    2017

  68. [71]

    Deceptive jamming suppression with frequency diverse MIMO radar,

    J. Xu, G. Liao, S. Zhu, and H. C. So, “Deceptive jamming suppression with frequency diverse MIMO radar,” Signal Pro- cessing, vol. 113, pp. 9–17, 2015

    2015

  69. [72]

    Space-time-range adaptive processing for airborne radar systems,

    J. Xu, S. Zhu, and G. Liao, “Space-time-range adaptive processing for airborne radar systems,” IEEE Sensors Journal, vol. 15, no. 3, pp. 1602–1610, 2015

    2015

  70. [73]

    Sup- pression approach to main-beam deceptive jamming in FDA- MIMO radar using nonhomogeneous sample detection,

    L. Lan, G. Liao, J. Xu, Y. Zhang, and F. Fioranelli, “Sup- pression approach to main-beam deceptive jamming in FDA- MIMO radar using nonhomogeneous sample detection,” IEEE Access, vol. 6, pp. 34 582–34 597, 2018

    2018

  71. [74]

    Enhanced three- dimensional joint domain localized STAP for airborne FDA- MIMO radar under dense false-target jamming scenario,

    C. Wen, J. Peng, Y. Zhou, and J. Wu, “Enhanced three- dimensional joint domain localized STAP for airborne FDA- MIMO radar under dense false-target jamming scenario,” IEEE Sensors Journal, vol. 18, no. 10, pp. 4154–4166, 2018

    2018

  72. [75]

    Low-complexity GLRT for FDA radar without training data,

    R. Gui, W. Wang, and Z. Zheng, “Low-complexity GLRT for FDA radar without training data,” Digital Signal Processing, vol. 107, 2020

    2020

  73. [76]

    Adaptive moving target detection without training data for FDA-MIMO radar,

    B. Huang, A. Basit, R. Gui, and W.-Q. Wang, “Adaptive moving target detection without training data for FDA-MIMO radar,” IEEE Transactions on Vehicular Technology, vol. 71, no. 1, pp. 220–232, 2022

    2022

  74. [77]

    GLRT-based adaptive target detection in FDA- MIMO radar,

    L. Lan, A. Marino, A. Aubry, A. De Maio, G. Liao, J. Xu, and Y. Zhang, “GLRT-based adaptive target detection in FDA- MIMO radar,” IEEE Transactions on Aerospace and Electronic Systems, pp. 1–1, 2020

    2020

  75. [79]

    Range ambiguous clutter suppression for FDA-MIMO forward looking airborne radar based on main lobe correction,

    ——, “Range ambiguous clutter suppression for FDA-MIMO forward looking airborne radar based on main lobe correction,” IEEE Transactions on Vehicular Technology, vol. 70, no. 3, pp. 2032–2046, 2021

    2032

  76. [82]

    Main-beam range deceptive jamming suppression with simulated annealing FDA-MIMO radar,

    Y. Wang and S. Zhu, “Main-beam range deceptive jamming suppression with simulated annealing FDA-MIMO radar,” IEEE Sensors Journal, vol. 20, no. 16, pp. 9056–9070, 2020

    2020

  77. [83]

    Suppression of mainbeam deceptive jammer with FDA- MIMO radar,

    L. Lan, J. Xu, G. Liao, Y. Zhang, F. Fioranelli, and H. C. So, “Suppression of mainbeam deceptive jammer with FDA- MIMO radar,” IEEE Transactions on Vehicular Technology, vol. 69, no. 10, pp. 11 584–11 598, 2020

    2020

  78. [84]

    Coherent pulsed- FDA radar receiver design with time-variance consideration: SINR and CRB analysis,

    R. Gui, W.-Q. Wang, C. Cui, and H. C. So, “Coherent pulsed- FDA radar receiver design with time-variance consideration: SINR and CRB analysis,” IEEE Transactions on Signal Pro- cessing, vol. 66, no. 1, pp. 200–214, 2018

    2018

  79. [85]

    Adaptive distributed target detection for FDA-MIMO radar in Gaussian clutter without training data,

    B. Huang, J. Jian, A. Basit, R. Gui, and W.-Q. Wang, “Adaptive distributed target detection for FDA-MIMO radar in Gaussian clutter without training data,” IEEE Transactions on Aerospace and Electronic Systems, vol. 58, no. 4, pp. 2961– 2972, 2022

    2022

  80. [86]

    Adaptive detection with Bayesian framework for FDA-MIMO radar,

    B. Huang, A. Basit, W.-Q. Wang, and S. Zhang, “Adaptive detection with Bayesian framework for FDA-MIMO radar,” IEEE Geoscience and Remote Sensing Letters, vol. 19, pp. 1– 5, 2022

    2022

Showing first 80 references.