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arxiv: 2604.02498 · v1 · submitted 2026-04-02 · 📡 eess.SP

A Self-Calibrating SDR for High Fidelity Beam- and Null-forming Arrays

Yongjun Kim , Aditya Dhananjay , Sundeep Rangan , Sachin Shetty , C. Nicolas Barati , Michael Zappe , Kimberly Gold , Junil Choi This is my paper

Pith reviewed 2026-05-13 20:24 UTC · model grok-4.3

classification 📡 eess.SP
keywords self-calibrating SDRnull formingbeamformingphase mismatch calibrationspectrum sharingdirectional couplingRF array calibrationanti-jamming
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The pith

A self-calibrating SDR architecture with a coupled reference transmitter corrects phase, timing, and gain mismatches to enable deep null forming.

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

Null forming demands far tighter precision than beam steering because even minor mismatches across RF chains erode suppression depth. The paper presents a self-calibrating SDR that injects a compact reference transmitter through directional couplers at the antenna feeds to measure and correct those mismatches in real time. Validation occurs via simulation and hardware measurements on a platform operating between 3.0 and 3.5 GHz. The approach targets spectrum-sharing and anti-jamming needs where conventional calibration falls short.

Core claim

The architecture uses a directionally coupled reference transmitter to provide ongoing calibration of phase, timing, and gain errors across transmit chains, allowing the array to form and maintain deep nulls that would otherwise be limited by hardware imperfections.

What carries the argument

Compact reference transmitter directionally coupled to antenna feeds, which supplies a known signal for real-time mismatch estimation and correction.

If this is right

  • Deeper nulls become achievable without custom high-precision hardware.
  • The system supports dynamic spectrum sharing and anti-jamming in the 3-3.5 GHz band.
  • Calibration overhead stays low because the reference signal shares the existing antenna paths.
  • The method extends naturally to both transmit beamforming and receive nulling.

Where Pith is reading between the lines

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

  • Similar coupling techniques could reduce calibration time in large-scale MIMO arrays where full channel sounding is costly.
  • If the reference transmitter power is kept low, the approach may integrate into existing deployed SDR nodes without regulatory changes.
  • The same structure might improve performance in frequency bands with higher phase noise or temperature drift.
  • Testable extension: measure how null depth scales with array size under the proposed calibration.

Load-bearing premise

The directional coupling introduces no significant new phase or amplitude errors and remains stable enough to support the targeted null depth.

What would settle it

A direct comparison of measured null depth with the calibration loop enabled versus disabled on the same hardware, or against the theoretical limit set by residual mismatches.

Figures

Figures reproduced from arXiv: 2604.02498 by Aditya Dhananjay, C. Nicolas Barati, Junil Choi, Kimberly Gold, Michael Zappe, Sachin Shetty, Sundeep Rangan, Yongjun Kim.

Figure 1
Figure 1. Figure 1: Receive array self-calibration To estimate these responses without external laboratory equipment, we consider a self-calibration mode in which a known reference signal is injected into all receive channels through a common on-board calibration structure, as shown in [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Overall SDR for self-calibration where an RFSoC [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 1
Figure 1. Figure 1: Rather than using commercial off-the-shelf power [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: (a) Self-observation antenna board used for self￾calibration in the 3.0 to 3.5 GHz bands. The transmission lines for the reference transmitter and receiver are on the bottom side of the PCB through a length-matched Wilkinson divider that is directionally coupled to the antenna feeds on the top side. (b) The SDR mates to the antenna board through a front-end MIMO transceiver board with standard SMA connecto… view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of simulated beampattern pre/post [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of beampatterns before and after [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
read the original abstract

Null forming is increasingly essential in modern wireless systems for spectrum-sharing, anti-jamming, and covert communications in contested and congested environments. Achieving deep nulls, however, is far more demanding than conventional beam steering: nulls are intrinsically narrow, and even small phase, timing, or gain mismatches across RF chains can significantly degrade suppression. This work develops and validates a self-calibrating SDR architecture tailored for high-fidelity null forming using a compact reference transmitter directionally coupled to the antenna feeds. We demonstrate the effectiveness of the approach through simulation and experimental measurements on an SDR platform operating from 3.0 to 3.5GHz, a band of growing importance for Department of Defense spectrum-sharing initiatives.

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 / 0 minor

Summary. The paper presents a self-calibrating SDR architecture for high-fidelity beam- and null-forming arrays. It employs a compact reference transmitter directionally coupled to the antenna feeds to correct phase, timing, and gain mismatches across RF chains. The approach is validated through simulations and experimental measurements on an SDR platform operating in the 3.0-3.5 GHz band, targeting applications in spectrum-sharing, anti-jamming, and covert communications.

Significance. If the experimental results demonstrate deep nulls with the proposed self-calibration, this work could significantly advance practical null-forming in contested wireless environments by eliminating the need for external calibration equipment. The focus on the 3.0-3.5 GHz band aligns with growing DoD spectrum-sharing needs. However, the absence of quantitative performance metrics in the abstract limits the assessed impact.

major comments (2)
  1. The abstract asserts validation through simulation and experimental measurements, but provides no quantitative results, error bars, mismatch magnitudes, or null-depth data, leaving the central claim unsupported by visible evidence.
  2. The central claim relies on the directional coupler providing accurate reference signals without introducing its own errors; however, no analysis or bounds on coupler non-idealities (e.g., directivity, frequency response) are mentioned, which could limit achievable null depth.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive review and for highlighting areas where the manuscript can be strengthened. We address each major comment below and will incorporate revisions to improve clarity and support for the central claims.

read point-by-point responses

  1. Referee: The abstract asserts validation through simulation and experimental measurements, but provides no quantitative results, error bars, mismatch magnitudes, or null-depth data, leaving the central claim unsupported by visible evidence.

    Authors: We agree that the abstract would benefit from explicit quantitative metrics to better support the claims. The body of the manuscript already contains these results from both simulation and the 3.0-3.5 GHz measurements, including achieved null depths, post-calibration mismatch reductions, and associated statistics. In the revised manuscript we will update the abstract to include representative quantitative values (null depth, mismatch correction accuracy, and error characterization) drawn directly from the experimental data. revision: yes

  2. Referee: The central claim relies on the directional coupler providing accurate reference signals without introducing its own errors; however, no analysis or bounds on coupler non-idealities (e.g., directivity, frequency response) are mentioned, which could limit achievable null depth.

    Authors: This observation is correct and points to a useful addition. The current manuscript treats the coupler as a high-directivity reference path based on its datasheet specifications but does not explicitly bound the residual errors. In the revision we will add a short analysis (new subsection or appendix) that quantifies the coupler directivity and frequency-response variation over 3.0-3.5 GHz, derives an upper bound on the resulting calibration error, and shows that this bound remains well below the level that would prevent the reported null depths. This will make the assumptions explicit and demonstrate that coupler non-idealities do not limit the claimed performance. revision: yes

Circularity Check

0 steps flagged

No circularity: architecture is hardware-defined and validated experimentally

full rationale

The paper describes a self-calibrating SDR architecture that uses physical directional coupling of a reference transmitter to antenna feeds, followed by simulation and experimental validation on a 3.0-3.5 GHz platform. No derivation chain, fitted parameters, or equations are presented that reduce by construction to their own inputs. The central claim rests on the physical properties of the coupler and measured null depths rather than any self-referential mathematical step or self-citation load-bearing premise. This is the expected non-finding for an experimental hardware paper with no claimed first-principles derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; the method appears to rely on standard RF coupling and SDR calibration techniques without new postulated components.

pith-pipeline@v0.9.0 · 5441 in / 1064 out tokens · 36507 ms · 2026-05-13T20:24:09.701043+00:00 · methodology

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Reference graph

Works this paper leans on

19 extracted references · 19 canonical work pages

  1. [1]

    Simultaneous Bea mforming and Nullforming for Covert Wireless Communications,

    J. Kong, F. T. Dagefu, and B. M. Sadler, “Simultaneous Bea mforming and Nullforming for Covert Wireless Communications,” in VTC2020- Spring, May 2020

    work page 2020

  2. [2]

    RF Anti-Jamming via Multi-Level Howells- Applebaum Null-Forming: 32-Channels, 5.8 GHz/100 MHz/Bea m on Xilinx Sx475T FPGA,

    U. Kumarasiri et al. , “RF Anti-Jamming via Multi-Level Howells- Applebaum Null-Forming: 32-Channels, 5.8 GHz/100 MHz/Bea m on Xilinx Sx475T FPGA,” IEEE Journal of Radio Frequency Identification , Jun. 2025

    work page 2025

  3. [3]

    Nullforming-Bas ed Precoder for Spectrum Sharing Between HAPS and Terrestrial Mobile Ne tworks,

    K. Tashiro, K. Hoshino, and A. Nagate, “Nullforming-Bas ed Precoder for Spectrum Sharing Between HAPS and Terrestrial Mobile Ne tworks,” IEEE Access , vol. 10, pp. 55 675–55 693, May 2022

    work page 2022

  4. [4]

    Cellular Wireless Networks in the Upper Mid-Band,

    S. Kang et al. , “Cellular Wireless Networks in the Upper Mid-Band,” IEEE Open Journal of the Communications Society , vol. 5, pp. 2058– 2075, Mar. 2024

    work page 2058

  5. [5]

    Joint Detection, Channel Estimation and Interference Nulling for Terrestrial-Satellite Downlink Co-Existence in the Upper Mid-Band,

    S. Jia et al. , “Joint Detection, Channel Estimation and Interference Nulling for Terrestrial-Satellite Downlink Co-Existence in the Upper Mid-Band,” arXiv preprint arXiv:2510.08824 , Oct. 2025

    work page arXiv 2025

  6. [6]

    Practical Null Steering in Millimeter Wave Networks,

    S. Madani et al., “Practical Null Steering in Millimeter Wave Networks,” in 18th USENIX Symposium on Networked Systems Design and Imple - mentation (NSDI 21) , Apr. 2021, pp. 903–921

    work page 2021

  7. [7]

    Over-the-Air Array Calibration of mmWave Phased Array in Beam-Steering Mode Based on Measured Complex Signa ls,

    Z. Wang et al. , “Over-the-Air Array Calibration of mmWave Phased Array in Beam-Steering Mode Based on Measured Complex Signa ls,” IEEE Transactions on Antennas and Propagation , vol. 69, no. 11, pp. 7876–7888, May 2021

    work page 2021

  8. [8]

    Fully Digital Beamforming Receiver With a Real- Time Calibration for 5G Mobile Communication,

    D.-C. Kim et al. , “Fully Digital Beamforming Receiver With a Real- Time Calibration for 5G Mobile Communication,” IEEE Transactions on Antennas and Propagation, vol. 67, no. 6, pp. 3809–3819, Mar. 2019

    work page 2019

  9. [9]

    Enabling Super-Resolution Parameter Estimation for mm-Wave Channel Sounding,

    R. Wang et al. , “Enabling Super-Resolution Parameter Estimation for mm-Wave Channel Sounding,” IEEE Transactions on Wireless Commu- nications, vol. 19, no. 5, pp. 3077–3090, Feb. 2020

    work page 2020

  10. [10]

    Pi-Radio v1: Calibration techniques to enable fully-digital beamforming at 60 GHz,

    A. Dhananjay et al. , “Pi-Radio v1: Calibration techniques to enable fully-digital beamforming at 60 GHz,” Computer Networks, vol. 196, p. 108220, Sep. 2021

    work page 2021

  11. [11]

    Scalable Synchronization and Reciprocity Calibra- tion for Distributed Multiuser MIMO,

    R. Rogalin et al. , “Scalable Synchronization and Reciprocity Calibra- tion for Distributed Multiuser MIMO,” IEEE transactions on wireless communications, vol. 13, no. 4, pp. 1815–1831, Mar. 2014

    work page 2014

  12. [12]

    Self- Calibration of Joint RF Impairments in a Loopback Wideband Transceiver,

    J.-H. Deng, C.-F. Lee, M.-L. Ku, and J.-K. Hwang, “Self- Calibration of Joint RF Impairments in a Loopback Wideband Transceiver, ” IEEE Access, vol. 8, pp. 45 607–45 617, Feb. 2020

    work page 2020

  13. [13]

    Internal Self-Calibration Met hods for Large Scale Array Transceiver Software-Defined Radios,

    A. Benzin and G. Caire, “Internal Self-Calibration Met hods for Large Scale Array Transceiver Software-Defined Radios,” in WSA 2017; 21th International ITG W orkshop on Smart Antennas . VDE, Mar. 2017, pp. 1–8

    work page 2017

  14. [14]

    A Self-Calibra tion Method for 5G Full-Digital TDD Beamforming Systems Using an Embedd ed Transmission Line,

    C. Guo, L. Tian, Z. H. Jiang, and W. Hong, “A Self-Calibra tion Method for 5G Full-Digital TDD Beamforming Systems Using an Embedd ed Transmission Line,” IEEE Transactions on Antennas and Propagation , vol. 69, no. 5, pp. 2648–2659, Oct. 2020

    work page 2020

  15. [15]

    A Self-Calibrating Q uadrature Mix- ing Front-End for SDR,

    J. J. de Witt and G.-J. van Rooyen, “A Self-Calibrating Q uadrature Mix- ing Front-End for SDR,” in 2008 IEEE Radio and Wireless Symposium . IEEE, Jan. 2008, pp. 117–120

    work page 2008

  16. [16]

    NTIA, FCC, Navy Work To Expand Innovative 3.5 GHz Spectrum Sharing Framework,

    National Telecommunications and Information Adminis tration, “NTIA, FCC, Navy Work To Expand Innovative 3.5 GHz Spectrum Sharing Framework,” https://www.ntia.gov/press-release/2024/ ntia-fcc-navy- work-expand-innovative-35-ghz-spectrum-sharing-framework, Mar. 2024, press Release

    work page 2024

  17. [17]

    Impact of the Asymmetric Signal Routing on the Wideband Spatial Behav ior of Large Modular Phased Arrays,

    D. Delfini, N. Tervo, M. E. Leinonen, and A. P¨ arssinen, “ Impact of the Asymmetric Signal Routing on the Wideband Spatial Behav ior of Large Modular Phased Arrays,” in 2023 17th European Conference on Antennas and Propagation (EuCAP) . IEEE, Mar. 2023, pp. 1–5

    work page 2023

  18. [18]

    Achieving Phase Coherency and Gain Stability in Active Antenna Arrays for Sub-6 GHz FDD and TDD FD-MIMO: Challenges and Solutions,

    R. M. V aghefi et al. , “Achieving Phase Coherency and Gain Stability in Active Antenna Arrays for Sub-6 GHz FDD and TDD FD-MIMO: Challenges and Solutions,” IEEE Access , vol. 8, pp. 152 680–152 696, Aug. 2020

    work page 2020

  19. [19]

    Wideband Power Amplifier Modeling Incorp orating Carrier Frequency Dependent AM/AM and AM/PM Characteristi cs,

    A. Tkacenko, “Wideband Power Amplifier Modeling Incorp orating Carrier Frequency Dependent AM/AM and AM/PM Characteristi cs,” Interplanetary Network Progress Report , vol. 42, pp. 1–34, 2010

    work page 2010