Pith

open record

sign in

arxiv: 2606.06723 · v1 · pith:YUKBCQRW · submitted 2026-06-04 · eess.SP

Deep Learning Based Sparse Array Design with Pre-Steering for Adaptive Beamforming

Ian Straub , Syed A Hamza This is my paper

Reviewed by Pith T0 review T1 audit T2 compute T3 formal T4 reserved 2026-06-27 23:49 UTCgrok-4.3pith:YUKBCQRWrecord.jsonopen to challenge →

Figure 1
Figure 1. Figure 1: Sector array vs optimal array SINR percent error over [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] reproduced from arXiv: 2606.06723
classification eess.SP
keywords deep learningsparse array designadaptive beamformingpre-steeringconvolutional neural networksarray configurationsignal to interference ratio
0
0 comments X

The pith

A convolutional neural network trained only at broadside can select sparse array configurations for near-optimal beamforming at arbitrary angles using pre-steering.

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

The paper shows that CNNs can learn to pick sparse array layouts that give good beamforming performance when a desired signal and an interferer come from changing directions. Pre-steering shifts the inputs so the network trains once for broadside and then handles any source angle without retraining. Robust training with small steering errors keeps accuracy high even when the steering is not perfect. If this holds, it offers a fast alternative to slow optimization methods for reconfiguring arrays in changing environments.

Core claim

The authors demonstrate that a CNN classifier, trained on pre-steered data with added angular perturbations, can identify sparse array configurations that achieve near-optimal SINR with over 90 percent test accuracy across wide ranges of source and interference angles, for both fixed and varying source directions.

What carries the argument

Convolutional neural network that classifies optimal sparse array configurations from pre-steered array response inputs.

If this is right

  • The method allows rapid array reconfiguration without per-angle retraining.
  • Accuracy remains high even with pre-steering errors due to error-augmented training.
  • It supports both fixed and varying desired source directions.
  • The approach achieves over 90% test accuracy for single source and single interferer scenarios.

Where Pith is reading between the lines

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

  • If the simulation results hold, this could enable real-time adaptive beamforming in practical systems with changing conditions.
  • Extending the training to include multiple interferers might broaden applicability without major changes to the pre-steering idea.
  • The pre-steering strategy could be tested on other array processing tasks like direction finding.

Load-bearing premise

That the simulated single-source single-interferer scenarios with pre-steering represent real propagation environments closely enough for the accuracy to carry over to actual systems.

What would settle it

A hardware experiment measuring actual SINR in a real propagation environment with varying angles, where performance falls well below the simulated levels predicted by the 90% accuracy.

Figures

Figures reproduced from arXiv: 2606.06723 by Ian Straub, Syed A Hamza.

Figure 2
Figure 2. Figure 2: Sector array vs optimal array SINR percent error over [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Sector array vs optimal array SINR percent error over [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Beampattern, source, and interference angles before [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

This paper investigates the use of convolutional neural networks (CNNs) for learning sparse array configurations that achieve near-optimal beamforming under varying source and interference angles. Unlike conventional or convex optimization based algorithms, the proposed deep learning approach enables rapid reconfiguration of sparse arrays in highly dynamic propagation environments. The paper considers a single desired source and a single interference signal at arbitrary angles, analyzing scenarios with both fixed and varying desired source directions. To avoid retraining for each possible source angle, an array pre-steering strategy is introduced, whereby the network is trained only at broadside, while test inputs are pre-steered to align with the broadside direction. To account for practical imperfections, the effect of pre-steering errors is examined, and a robust error-augmented training is adopted. The approach systematically incorporates small, structured pre-steering perturbations during training, enabling the network to maintain high classification accuracy and maximize the signal-to-interference-plus-noise ratio (SINR) even under angular uncertainty. The results demonstrate that the proposed method achieves over 90% test accuracy across wide ranges of source and interference angles, highlighting its potential for real-time, robust sparse array configuration in dynamic environments.

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

3 major / 2 minor

Summary. The manuscript proposes using convolutional neural networks to select sparse array configurations for adaptive beamforming. A pre-steering strategy aligns test inputs to broadside so that a single network trained at broadside can handle varying source angles; error-augmented training is added for robustness to pre-steering imperfections. Evaluation is performed exclusively on simulated single-source, single-interferer scenarios, with the central empirical claim being that the method achieves over 90% test accuracy and near-optimal SINR across wide angular ranges.

Significance. If the accuracy claim were shown to correspond to measurable SINR gains over standard sparse-array design methods and if the simulation distribution were demonstrated to be representative, the pre-steering technique could reduce the need for repeated optimization or retraining in time-varying environments. The current manuscript supplies no such comparisons or generalization evidence.

major comments (3)
  1. [Abstract] Abstract: the claim that the method 'achieves near-optimal beamforming' and 'maximizes the SINR' is unsupported because no baseline (random selection, convex optimization, or conventional sparse-array algorithms) is reported and no quantitative definition of 'near-optimal' or SINR computation procedure is supplied.
  2. [Abstract] Abstract and results description: the reported >90% test accuracy is given without error bars, confidence intervals, or statistical tests, and without stating the number of Monte-Carlo trials or the precise train/test split, rendering the accuracy figure impossible to interpret as evidence of reliable performance.
  3. [Abstract] Abstract: the evaluation is restricted to single-source/single-interferer synthetic data with only angular uncertainty; this setup does not address multi-interferer, multipath, or measured-channel conditions that are central to the stated goal of 'highly dynamic propagation environments,' so the generalization claim rests on an untested assumption.
minor comments (2)
  1. Notation for array geometry, steering vectors, and the precise CNN architecture (layer counts, filter sizes, output classes) should be defined explicitly in the methods section rather than left implicit.
  2. The manuscript should include a clear statement of the loss function used for training and the exact mapping from network output to array configuration.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment point by point below and will revise the manuscript to improve clarity and support for the claims where feasible.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that the method 'achieves near-optimal beamforming' and 'maximizes the SINR' is unsupported because no baseline (random selection, convex optimization, or conventional sparse-array algorithms) is reported and no quantitative definition of 'near-optimal' or SINR computation procedure is supplied.

    Authors: We agree that the abstract makes claims of near-optimal performance and SINR maximization without direct baseline comparisons or explicit definitions. The manuscript positions the CNN approach as an alternative to conventional and convex optimization methods but does not report quantitative comparisons. In the revision we will add a dedicated results subsection with comparisons to random selection, convex optimization, and conventional sparse-array algorithms, along with a precise definition of near-optimality (e.g., SINR within X dB of the optimal configuration) and a clear description of the SINR computation procedure. revision: yes

  2. Referee: [Abstract] Abstract and results description: the reported >90% test accuracy is given without error bars, confidence intervals, or statistical tests, and without stating the number of Monte-Carlo trials or the precise train/test split, rendering the accuracy figure impossible to interpret as evidence of reliable performance.

    Authors: We acknowledge that the reported accuracy figure lacks supporting statistical details. The manuscript states 'over 90% test accuracy' without error bars, trial counts, or split information. We will revise the abstract and results sections to specify the number of Monte-Carlo trials, the exact train/test split, and to include error bars or confidence intervals for the accuracy metrics. revision: yes

  3. Referee: [Abstract] Abstract: the evaluation is restricted to single-source/single-interferer synthetic data with only angular uncertainty; this setup does not address multi-interferer, multipath, or measured-channel conditions that are central to the stated goal of 'highly dynamic propagation environments,' so the generalization claim rests on an untested assumption.

    Authors: The work deliberately focuses on single-source/single-interferer scenarios with angular uncertainty to isolate and validate the pre-steering and error-augmented training technique. We agree this does not cover multi-interferer, multipath, or measured channels. We will revise the abstract and discussion to explicitly limit the scope of the claims, remove over-generalization language, and identify multi-interferer and real-channel extensions as future work. No additional simulations will be performed for this revision. revision: partial

Circularity Check

0 steps flagged

No circularity: empirical CNN training on simulated data with held-out test accuracy

full rationale

The paper trains a CNN to classify sparse array configurations from pre-steered inputs generated under single-source/single-interferer simulation; reported >90% test accuracy is measured on held-out samples drawn from the identical simulation distribution. No equations, fitted parameters, or self-citations are presented as load-bearing derivations that reduce the claimed performance to the training inputs by construction. Pre-steering and error-augmented training are explicit data-preprocessing choices whose effect is evaluated on separate test data, not tautological re-labeling of the same quantities.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No free parameters, axioms, or invented entities are introduced or required by the abstract; the method is a standard supervised classification pipeline on simulated angle data.

pith-pipeline@v0.9.1-grok · 5735 in / 1097 out tokens · 16793 ms · 2026-06-27T23:49:45.153598+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

47 extracted references · 4 canonical work pages · 2 internal anchors

  1. [1]

    Haykin,Array Processing: Application to Radar

    S. Haykin,Array Processing: Application to Radar. Dowden, Hutchin- son, &: Ross, Stroudsburg, Pennsylvania, 1980

    1980

  2. [2]

    Minimum-redundancy linear arrays,

    A. Moffet, “Minimum-redundancy linear arrays,”IEEE Transactions on Antennas and Propagation, vol. 16, p. 172–175, March 1968

    1968

  3. [3]

    Nested arrays: A novel approach to array processing with enhanced degrees of freedom,

    P. Pal and P. Vaidyanathan, “Nested arrays: A novel approach to array processing with enhanced degrees of freedom,”IEEE Transactions on Signal Processing, vol. 58, no. 8, pp. 4167–4181,

  4. [4]

    Generalized coprime array configura- tions for direction-of-arrival estimation,

    S. Qin, Y . Zhang, and M. Amin, “Generalized coprime array configura- tions for direction-of-arrival estimation,”IEEE Transactions on Signal Processing, vol. 63, no. 6, pp. 1377–1390,

  5. [5]

    Sparse arrays and sampling for interference mitigation and DOA estimation in gnss,

    M. Amin, X. Wang, Y . Zhang, F. Ahmad, and E. Aboutanios, “Sparse arrays and sampling for interference mitigation and DOA estimation in gnss,”Proceedings of the IEEE, vol. 104, no. 6, pp. 1302–1317,

  6. [6]

    Sparse symmetric linear arrays with low redundancy and a contiguous sum co-array,

    R. R. R ¨aki and V . Koivunen, “Sparse symmetric linear arrays with low redundancy and a contiguous sum co-array,”IEEE Transactions on Signal Processing, vol. 69, pp. 1697–1712

  7. [7]

    M. G. Amin (Editor),Sparse Arrays for Radar , Sonar , and Communi- cations. Wiley-IEEE, December 2023

    2023

  8. [8]

    Sparse array design for adaptive beamforming via semidefinite relaxation,

    Z. Zheng, Y . Fu, W.-Q. Wang, and H. C. So, “Sparse array design for adaptive beamforming via semidefinite relaxation,”IEEE Signal Processing Letters, vol. 27, pp. 925–929, 2020

    2020

  9. [9]

    Reconfigurable sparse array synthesis with phase-only control via consensus-admm-based sparse optimization,

    C. Wen, Y . Huang, J. Peng, G. Zheng, W. Liu, and J.-K. Zhang, “Reconfigurable sparse array synthesis with phase-only control via consensus-admm-based sparse optimization,”IEEE Transactions on V ehicular Technology, vol. 70, no. 7, pp. 6647–6661, 2021

    2021

  10. [10]

    Sensor selection in distributed multiple-radar architectures for localization: A knapsack problem for- mulation,

    H. Godrich, A. Petropulu, and H. Poor, “Sensor selection in distributed multiple-radar architectures for localization: A knapsack problem for- mulation,”IEEE Transactions on Signal Processing, vol. 60, no. 1, pp. 247–260,

  11. [11]

    Reconfigurable adaptive array beamforming by antenna selection,

    X. Wang, E. Aboutanios, M. Trinkle, and M. Amin, “Reconfigurable adaptive array beamforming by antenna selection,”IEEE Transactions on Signal Processing, vol. 62, no. 9, pp. 2385–2396,

  12. [12]

    Massive mimo antenna selection: Switching architectures, capacity bounds, and optimal antenna selection algorithms,

    Y . Gao, H. Vinck, and T. Kaiser, “Massive mimo antenna selection: Switching architectures, capacity bounds, and optimal antenna selection algorithms,”IEEE Transactions on Signal Processing, vol. 66, no. 5, pp. 1346–1360,

  13. [13]

    Comparison of nature-inspired techniques in design optimization of non-uniformly spaced arrays in the presence of mutual coupling,

    E. BouDaher and A. Hoorfar, “Comparison of nature-inspired techniques in design optimization of non-uniformly spaced arrays in the presence of mutual coupling,”Digital Signal Processing, vol. 105, p. 102780, 2020, special Issue on Optimum Sparse Arrays and Sensor Placement for Environmental Sensing. [Online]. Available: https://www.sciencedirect.com/scien...

    2020

  14. [14]

    Hybrid sparse array beamforming design for general rank signal models,

    S. Hamza and M. Amin, “Hybrid sparse array beamforming design for general rank signal models,”IEEE Transactions on Signal Processing, vol. 67, no. 24, pp. 6215–6226,

  15. [15]

    Optimum sparse array beamforming for general rank signal models,

    S. A. Hamza, M. G. Amin, and G. Fabrizio, “Optimum sparse array beamforming for general rank signal models,” in2018 IEEE Radar Conference (RadarConf18), April 2018, pp. 1343–1347

    2018

  16. [16]

    Hybrid sparse array design for under-determined models,

    S. A. Hamza and M. G. Amin, “Hybrid sparse array design for under-determined models,” inICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), May 2019, pp. 4180–4184

    2019

  17. [17]

    Optimum sparse array design for maximizing signal-to-noise ratio in presence of local scatterings,

    S. A. Hamza, M. Amin, and G. Fabrizio, “Optimum sparse array design for maximizing signal-to-noise ratio in presence of local scatterings,” in 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), April 2018

    2018

  18. [18]

    Sparse array beamforming design for wideband signal models,

    S. A. Hamza and M. G. Amin, “Sparse array beamforming design for wideband signal models,”IEEE Transactions on Aerospace and Electronic Systems, pp. 1–1, 2020

    2020

  19. [19]

    Sparse array design for transmit beamforming,

    ——, “Sparse array design for transmit beamforming,” in2020 IEEE International Radar Conference (RADAR), 2020, pp. 560–565

    2020

  20. [20]

    Sparse array design for maximizing the signal-to-interference-plus-noise-ratio by matrix completion,

    S. A. Hamza and M. G. Amin, “Sparse array design for maximizing the signal-to-interference-plus-noise-ratio by matrix completion,”Digital Signal Processing, p. 102678, 2020

    2020

  21. [21]

    Deep learning,

    Y . LeCun, Y . Bengio, and G. Hinton, “Deep learning,”Nature, vol. 521, pp. 436–44, 05 2015

    2015

  22. [22]

    Goodfellow, Y

    I. Goodfellow, Y . Bengio, and A. Courville,Deep Learning. MIT Press, 2016, http://www.deeplearningbook.org

    2016

  23. [23]

    Recent advances in convolutional neural networks,

    J. Gu, Z. Wang, J. Kuen, L. Ma, A. Shahroudy, B. Shuai, T. Liu, X. Wang, G. Wang, J. Cai, and T. Chen, “Recent advances in convolutional neural networks,”Pattern Recognition, vol. 77, pp. 354–377, 2018. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0031320317304120

    2018

  24. [24]

    A survey on deep learning techniques in wireless signal recognition,

    X. Li, F. Dong, S. Zhang, and W. Guo, “A survey on deep learning techniques in wireless signal recognition,”Wireless Communications and Mobile Computing, vol. 2019, p. 5629572, 2019. [Online]. Available: https://doi.org/10.1155/2019/5629572

    work page doi:10.1155/2019/5629572 2019

  25. [25]

    LORM: learning to optimize for resource management in wireless networks with few training samples,

    Y . Shen, Y . Shi, J. Zhang, and K. B. Letaief, “LORM: learning to optimize for resource management in wireless networks with few training samples,”IEEE Trans. Wireless Communications, vol. 19, no. 1, pp. 665–679, 2020

    2020

  26. [26]

    Learning to optimize: Training deep neural networks for interference management,

    H. Sun, X. Chen, Q. Shi, M. Hong, X. Fu, and N. D. Sidiropoulos, “Learning to optimize: Training deep neural networks for interference management,”IEEE Transactions on Signal Processing, vol. 66, no. 20, pp. 5438–5453, 2018

    2018

  27. [27]

    Deep Learning Based MIMO Communications

    T. J. O’Shea, T. Erpek, and T. C. Clancy, “Deep learning based MIMO communications,”CoRR, vol. abs/1707.07980, 2017

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  28. [28]

    Design of sparse arrays via deep learning for enhanced DOA estimation,

    S. Wandale and K. Ichige, “Design of sparse arrays via deep learning for enhanced DOA estimation,”EURASIP Journal on Applied Signal Processing, vol. 2021, no. 1, p. 17, Dec. 2021

    2021

  29. [29]

    Deep learning sparse array design using binary switching configurations,

    S. Hamza, K. Juretus, M. Amin, and F. Ahmad, “Deep learning sparse array design using binary switching configurations,” inaccepted in Proc. IEEE International Conference on Acoustics, Speech and Signal Processing

  30. [30]

    Learning sparse array capon beamformer design using deep learning approach,

    S. A. Hamza and M. G. Amin, “Learning sparse array capon beamformer design using deep learning approach,” in2020 IEEE Radar Conference (RadarConf20), 2020, pp. 1–5

    2020

  31. [31]

    Deep learning based sparse array adaptive beamformer design under class imbalance,

    J. Kobak and S. A. Hamza, “Deep learning based sparse array adaptive beamformer design under class imbalance,” in2025 IEEE International Radar Conference (RADAR), 2025, pp. 1–5

    2025

  32. [32]

    S. A. Hamza, K. Juretus, and M. G. Amin,Sparse Array Design for Optimum Beamforming Using Deep Learning. John Wiley & Sons, Ltd, 2024, ch. 7, pp. 215–250. [Online]. Available: https://onlinelibrary.wiley.com/doi/abs/10.1002/9781394191048.ch7

    work page doi:10.1002/9781394191048.ch7 2024

  33. [33]

    Sparse array design for optimum beamforming using deep learning,

    S. A. Hamza and M. G. Amin, “Sparse array design for optimum beamforming using deep learning,”IEEE Transactions on Aerospace and Electronic Systems, vol. 60, no. 1, pp. 133–144, 2024

    2024

  34. [34]

    Deep learning of the sparse array configurations in optimum beamforming,

    K. Juretus, M. Amin, and S. A. Hamza, “Deep learning of the sparse array configurations in optimum beamforming,”IEEE Transactions on Aerospace and Electronic Systems, vol. 61, no. 3, pp. 5718–5730, 2025

    2025

  35. [35]

    Sparse array reconfigurability for source identification and angle estimation in cogni- tive sensing,

    S. A. Hamza, M. G. Amin, B. Kirk, and A. Martone, “Sparse array reconfigurability for source identification and angle estimation in cogni- tive sensing,” inInternational Conference on Radar Systems, Edinburgh, Scotland

  36. [36]

    Cognitive dynamic systems: Radar, control, and radio,

    S. Haykin, “Cognitive dynamic systems: Radar, control, and radio,” Proceedings of the IEEE, vol. 7, pp. 2095–2103, July 2012

    2095

  37. [37]

    Guerci,Cognitive Radar: The Knowledge-Aided Fully Adaptive Ap- proach

    J. Guerci,Cognitive Radar: The Knowledge-Aided Fully Adaptive Ap- proach. Boston, MA: Artech House, 2020, vol. Second Edition

    2020

  38. [38]

    High-resolution frequency-wavenumber spectrum analysis,

    J. Capon, “High-resolution frequency-wavenumber spectrum analysis,” Proc. IEEE, vol. 2

  39. [39]

    An algorithm for linear constrained adaptive array processing,

    O. Frost, III, “An algorithm for linear constrained adaptive array processing,”Proc. IEEE, vol. 60, pp. 926 935,

  40. [40]

    A signal subspace method for adaptive interference cancellation,

    B. Friedlander, “A signal subspace method for adaptive interference cancellation,” inIEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 36, no. 12, Dec. 1988, pp. 1835–1845

    1988

  41. [41]

    Perfor- mance comparison of superresolution array processing algorithms,

    A. Barabell, J. Capon, D. DeLong, J. Johnson, and K. Senne, “Perfor- mance comparison of superresolution array processing algorithms,” May 2014

    2014

  42. [42]

    Robust adaptive beamforming for general-rank signal models,

    S. Shahbazpanahi, A. Gershman, Z.-Q. Luo, and K. Wong, “Robust adaptive beamforming for general-rank signal models,”IEEE Transac- tions on Signal Processing, vol. 51, no. 9, pp. 2257–2269,

  43. [43]

    Analysis and design of optimum sparse array configurations for adaptive beamforming,

    X. Wang, M. Amin, and X. Cao, “Analysis and design of optimum sparse array configurations for adaptive beamforming,”IEEE Transactions on Signal Processing, vol. 66, no. 2, p. 340–351

  44. [44]

    On the roles of sparse array configuration and weights in optimum beamforming,

    S. A. Hamza, K. Juretus, and M. G. Amin, “On the roles of sparse array configuration and weights in optimum beamforming,” inIEEE Wireless Communications and Network Conference, 2024, p. pp

    2024

  45. [45]

    Sparse array configuration analysis and deep learning classifications for beamfornming,

    M. G. Amin, S. A. Hamza, and K. Juretus, “Sparse array configuration analysis and deep learning classifications for beamfornming,” in2024 IEEE Radar Conference (RadarConf24), 2024, pp. 1–6

    2024

  46. [46]

    Adam: A method for stochastic optimization,

    D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,”

  47. [47]

    Adam: A Method for Stochastic Optimization

    [Online]. Available: https://arxiv.org/abs/1412.6980

    work page internal anchor Pith review Pith/arXiv arXiv