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arxiv: 2604.18409 · v1 · submitted 2026-04-20 · 📡 eess.SY · cs.SY

Far-Field Absolute Gain Antenna Measurements at Sub-THz Frequencies: A New Interpretation

Asad Husein , Kimmo Rasilainen , Juha-Pekka M\"akel\"a , Veikko Hovinen , Klaus Nevala , Aarno P\"arssinen , Marko E. Leinonen This is my paper

Pith reviewed 2026-05-10 03:52 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords sub-THz antenna measurementsfar-field gainthree-antenna methodmodified far-field distanceFriis transmission equationcompact measurement setuphorn antennas145-170 GHz
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The pith

A modified far-field equation redefines the minimum measurement distance for accurate sub-THz antenna gain by combining the aperture effects of both transmit and receive antennas.

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

The paper establishes that standard far-field distance rules become impractical for large-aperture antennas at 145-170 GHz, forcing oversized lab setups. It derives and applies a new far-field criterion that incorporates the combined sizes and radiation patterns of the transmitting and receiving antennas, then uses this with the three-antenna method and the Friis equation to obtain absolute gain values over short, clustered distances. Measurements on commercial horn antennas, including mismatched pairs, match both electromagnetic simulations and expected behavior, showing that reliable results are possible without full traditional separation. This matters for sub-THz development because compact, repeatable gain characterization directly supports faster iteration on 6G, sensing, and imaging hardware.

Core claim

By applying the proposed modified FF formulation, the approach redefines the FF distance by considering the combined effects of both the transmitting and receiving antennas, accounting for their aperture sizes and radiation characteristics. This allows precise gain characterization within a compact measurement footprint. The theoretical model was validated through radiated measurements and simulations for both similar and dissimilar antenna pairs, confirming that reliable results can be achieved despite mismatches.

What carries the argument

The modified far-field distance equation, derived to replace the single-antenna 2D²/λ rule by summing the effective contributions from both antennas' apertures and patterns before applying the Friis transmission formula in the three-antenna method.

If this is right

  • Absolute gain data for sub-THz horns can be obtained in laboratory footprints far smaller than traditional requirements.
  • The three-antenna method remains usable with dissimilar antennas, removing the need for perfectly matched pairs.
  • Measurement time and facility cost drop because only localized distance clusters are required.
  • The same compact technique supports rapid characterization for 6G, high-frequency sensing, and imaging systems.

Where Pith is reading between the lines

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

  • The approach could be tested on other antenna types such as arrays or lenses to see whether the same combined-aperture rule still holds.
  • If validated more broadly, the method might reduce reliance on large anechoic chambers in industrial sub-THz metrology.
  • Extending the derivation to include mutual coupling or near-field corrections could further shrink viable test distances.

Load-bearing premise

The theoretically derived modified far-field equation correctly identifies the onset of far-field behavior for the tested commercial horn antennas across 145-170 GHz, even when the transmit and receive antennas differ.

What would settle it

Repeat the gain measurements on the same antenna pairs at the conventionally calculated far-field distance and check whether the extracted gain values agree with the compact-setup results within the stated measurement uncertainty.

Figures

Figures reproduced from arXiv: 2604.18409 by Aarno P\"arssinen, Asad Husein, Juha-Pekka M\"akel\"a, Kimmo Rasilainen, Klaus Nevala, Marko E. Leinonen, Veikko Hovinen.

Figure 1
Figure 1. Figure 1: Geometry of two similar pyramidal horn antennas whose aperture [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Photo of the measurement setup and the used absorber configuration. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: A conceptual 3-D model of the measurement setup. Absorber side walls and flat sheet absorbers are not shown for clarity. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Comparing far-field distances calculated at 170 GHz using different [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparing phase error obtained at far-field distances calculated at [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 4
Figure 4. Figure 4: AUT combinations used with the three-antenna technique. The [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 7
Figure 7. Figure 7: The used PEWAN1028 and FLANN antennas: (a) Photograph and [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Measured realized gain of the AUTs across different clusters in the [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 11
Figure 11. Figure 11: Standard deviation in the realized gain values of all AUTs in the [PITH_FULL_IMAGE:figures/full_fig_p009_11.png] view at source ↗
Figure 10
Figure 10. Figure 10: Comparing simulated and measured realized gain across different [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗
Figure 13
Figure 13. Figure 13: Standard deviation in the realized gain values of all AUTs in the [PITH_FULL_IMAGE:figures/full_fig_p010_13.png] view at source ↗
Figure 12
Figure 12. Figure 12: Measured realized gain of the AUTs across different clusters in the [PITH_FULL_IMAGE:figures/full_fig_p010_12.png] view at source ↗
Figure 14
Figure 14. Figure 14: Absolute average difference between simulated and measured [PITH_FULL_IMAGE:figures/full_fig_p011_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Comparing simulated and measured realized gain at each operational [PITH_FULL_IMAGE:figures/full_fig_p011_15.png] view at source ↗
Figure 17
Figure 17. Figure 17: Absolute average difference between simulated and measured [PITH_FULL_IMAGE:figures/full_fig_p012_17.png] view at source ↗
Figure 16
Figure 16. Figure 16: Absolute average difference between simulated and measured [PITH_FULL_IMAGE:figures/full_fig_p012_16.png] view at source ↗
read the original abstract

The evolution of large aperture antennas and arrays at the sub-THz band (100-300 GHz) results in traditional far-field (FF) gain measurements to require large distances due to the high frequency nature making them impractical in many laboratory environments. In the presented work, absolute antenna gain measurements are performed in localized distance clusters for commercial horn antennas in the sub-THz range of 145-170 GHz using the three-antenna method, leveraging a theoretically derived modified FF equation along with the Friis transmission equation to enable a compact measurement setup. By applying the proposed modified FF formulation, the approach aims to redefine the FF distance by considering the combined effects of both the transmitting and receiving antennas, accounting for their aperture sizes and radiation characteristics. This allows precise gain characterization within a compact measurement footprint. The proposed theoretical model was validated through radiated measurements and simulations, demonstrating its effectiveness in this case study. Also, measurements were performed using dissimilar antenna pair combinations due to inventory constraints, a common challenge both in research and in industry. Despite the mismatches, the presented work demonstrates that reliable and sufficiently accurate measurement results can still be achieved. This highlights the practical feasibility of the compact cluster measurement technique without compromising measurement integrity. The compact setup ensures efficiency in the measurement time and cost, making it a robust solution for both research and industrial needs in sub-THz antenna characterization for applications including 6G, high frequency sensing, and imaging systems.

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 paper claims that a theoretically derived modified far-field (FF) distance criterion, which accounts for the combined aperture sizes and radiation characteristics of both transmitting and receiving antennas, enables accurate absolute gain measurements of commercial horn antennas at 145-170 GHz using the three-antenna method and Friis transmission equation in compact distance clusters. This is validated via radiated measurements and simulations, even when using dissimilar antenna pairs due to inventory constraints, yielding reliable results without large measurement distances.

Significance. If the modified FF formulation is shown to render the Friis equation sufficiently accurate without residual near-field errors, the work would provide a practical solution for sub-THz antenna characterization in space-constrained labs, supporting applications in 6G, sensing, and imaging. The emphasis on mismatched pairs reflects real-world constraints and adds applicability, but the current lack of quantitative consistency metrics limits the assessed impact.

major comments (3)
  1. Abstract: The central claim that the approach yields 'reliable and sufficiently accurate' results for dissimilar horn pairs lacks any reported quantitative metrics such as error bars, standard deviations, cross-pair gain consistency values for the same antenna, or residual error after applying the modification.
  2. Derivation of modified FF equation (theoretical model section): The equation is described as 'theoretically derived' to redefine FF distance based on combined Tx/Rx effects, but no explicit derivation steps, assumptions about phase curvature/amplitude taper, or independent comparison to the standard 2D²/λ criterion are provided, creating risk of circularity when the same data is used for both derivation and validation.
  3. Validation and results (measurements/simulations section): No data exclusion criteria, statistical analysis, or assessment of how the modification affects Friis accuracy specifically for dissimilar commercial horns at 145-170 GHz is included, which is load-bearing for the claim that near-field errors are adequately mitigated.
minor comments (2)
  1. Abstract: The title references sub-THz (100-300 GHz) while the work focuses on 145-170 GHz; clarify the exact frequency range and any extrapolation.
  2. Throughout: Ensure all equations in the modified FF and Friis application are numbered and explicitly referenced when discussing their use with the three-antenna method.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback, which identifies opportunities to strengthen the clarity and quantitative support in our manuscript. We respond to each major comment below and will revise the paper accordingly.

read point-by-point responses

  1. Referee: Abstract: The central claim that the approach yields 'reliable and sufficiently accurate' results for dissimilar horn pairs lacks any reported quantitative metrics such as error bars, standard deviations, cross-pair gain consistency values for the same antenna, or residual error after applying the modification.

    Authors: We agree that the abstract would be strengthened by explicit quantitative metrics. In the revised manuscript we will report standard deviations from repeated measurements, cross-pair gain consistency values for each antenna under test, and an estimate of residual error after applying the modified criterion. revision: yes

  2. Referee: Derivation of modified FF equation (theoretical model section): The equation is described as 'theoretically derived' to redefine FF distance based on combined Tx/Rx effects, but no explicit derivation steps, assumptions about phase curvature/amplitude taper, or independent comparison to the standard 2D²/λ criterion are provided, creating risk of circularity when the same data is used for both derivation and validation.

    Authors: The modified criterion was obtained by superposing the individual far-field distance requirements of the two antennas while accounting for their effective apertures and radiation patterns. To address the concern, the revised theoretical section will contain the full step-by-step derivation, explicit statements of the phase-curvature and amplitude-taper assumptions, and a purely theoretical comparison against the conventional 2D²/λ rule that does not rely on the measurement data set. revision: yes

  3. Referee: Validation and results (measurements/simulations section): No data exclusion criteria, statistical analysis, or assessment of how the modification affects Friis accuracy specifically for dissimilar commercial horns at 145-170 GHz is included, which is load-bearing for the claim that near-field errors are adequately mitigated.

    Authors: We accept that additional statistical detail is warranted. The revised results section will state the data-exclusion criteria (e.g., SNR threshold), present mean gain values together with standard deviations, and include a direct side-by-side comparison of Friis-derived gains obtained with and without the modified distance criterion for the dissimilar horn pairs over 145–170 GHz. revision: yes

Circularity Check

0 steps flagged

Theoretical derivation of modified FF distance remains independent of measurement data

full rationale

The paper presents a theoretically derived modified far-field equation that redefines the FF distance by accounting for the combined aperture sizes and radiation characteristics of both transmitting and receiving antennas. This formulation is then combined with the Friis transmission equation to enable gain extraction via the three-antenna method in compact setups. The model is explicitly validated through separate simulations and radiated measurements on commercial horn antennas at 145-170 GHz (including dissimilar pairs), rather than being fitted to or derived from those measurements. No load-bearing self-citations, self-definitional reductions, or renaming of known results are evident in the provided text; the central claim is a theoretical adjustment whose accuracy is tested externally to its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim depends on the validity of an unspecified theoretical derivation of the modified FF equation and the applicability of the Friis transmission equation in the redefined regime; no independent evidence or external benchmarks are referenced in the abstract.

axioms (1)
  • domain assumption The Friis transmission equation remains valid when the separation distance satisfies the modified far-field condition derived from combined antenna apertures.
    Explicitly leveraged alongside the modified FF formulation in the abstract.

pith-pipeline@v0.9.0 · 5594 in / 1351 out tokens · 57340 ms · 2026-05-10T03:52:11.411505+00:00 · methodology

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Reference graph

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