⚡ electrical engineering

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

This paper presents a validated, compact measurement technique for determining absolute antenna gain in the sub-THz band (145–170 GHz) by utilizing a modified far-field equation and the three-antenna method to overcome traditional distance constraints, thereby enabling efficient and accurate characterization for 6G and imaging applications even with dissimilar antenna pairs.

Original authors: Asad Husein, Kimmo Rasilainen, Juha-Pekka Mäkelä, Veikko Hovinen, Klaus Nevala, Aarno Pärssinen, Marko E. Leinonen

Published 2026-04-21

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CC BY 4.0

Original authors: Asad Husein, Kimmo Rasilainen, Juha-Pekka Mäkelä, Veikko Hovinen, Klaus Nevala, Aarno Pärssinen, Marko E. Leinonen

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Problem: The "Too Far" Problem

Imagine you are trying to take a perfect photo of a tiny, intricate watch using a giant camera. To get the photo in focus, the rules say you must stand a specific distance away. If you stand too close, the picture is blurry; if you stand just right, it's sharp.

In the world of radio waves (specifically the "Sub-THz" band used for future 6G networks), the "camera" is an antenna, and the "photo" is a measurement of how well it sends signals.

The problem is that because these waves are so tiny (like the size of a grain of sand), the "perfect distance" to stand away from the antenna to get a clear reading is huge. For a large antenna, you might need to stand hundreds of meters away. Most university labs and company R&D centers are just a few rooms big. They literally don't have the space to stand that far back.

The Old Solution: "Guessing" from the Edge

Scientists have tried to solve this by standing closer and using math to "guess" what the signal would look like if they were far away. This is like standing right next to a painting and trying to guess what the whole picture looks like by squinting at the corner. It works okay, but it's tricky and prone to errors.

The New Idea: A "Team Effort" Perspective

This paper introduces a clever new way to measure these antennas in a small room without needing a giant outdoor field.

1. The "Three-Strangers" Game (The Three-Antenna Method)
Imagine you have three people (Antenna A, B, and C) who don't know their own strength, but they need to figure it out.

A talks to B.
A talks to C.
B talks to C.
By listening to how loud the voices are between all three pairs, you can mathematically calculate exactly how loud each person is on their own, without needing a "standard" loudspeaker to compare them against. This is the Three-Antenna Method.

2. The "Two-Headed" Rule (The New Formula)
The authors realized that the old rule for "how far is far enough?" was flawed. The old rule only looked at the biggest antenna and said, "Okay, stand this far away from the big guy."

The authors argued: "Wait, the small guy matters too!"

They compared it to a conversation in a noisy room. If you are talking to a giant (a big antenna) and a tiny person (a small antenna), the "noise" or distortion in the conversation depends on both of them, not just the giant.

Old Way: Only worry about the giant's size.
New Way: Add the sizes of both people together to figure out the perfect distance.

By using this new "Two-Headed" formula, they proved that you can stand much closer than previously thought and still get a perfect, "far-field" reading.

The Experiment: Mixing and Matching

To prove this works, they set up a compact lab in Finland. They had a problem: they didn't have three identical antennas. They had two big ones and one smaller one (a common problem in real life when you are on a budget).

They tried three different combinations:

Big + Big: The standard test.
Small + Big: Mixing sizes.
Big + The "Naked" Wire: They even used the open end of the cable (the frequency extender) as the third "antenna" just to see if it would work.

The Result:
Even though they were mixing different sizes and even using a bare wire, their new math formula worked perfectly. The measurements were accurate enough to satisfy strict industry standards.

The Takeaway: Why This Matters

Think of this like finding a shortcut through a dense forest.

Before: You had to walk all the way around the forest (build a massive outdoor test range) to get a clear view. It was expensive, slow, and many people couldn't do it.
Now: The authors found a hidden trail (the new formula) that lets you walk right through the middle of the forest (a small lab) and still get the same clear view.

Why is this a big deal?

Cost: You don't need to build giant outdoor test ranges.
Speed: You can measure antennas faster.
Flexibility: You can use whatever antennas you have in your inventory, even if they are different sizes or slightly mismatched.

This makes it much easier and cheaper for companies to design the super-fast 6G networks and advanced imaging systems of the future, because they can test their tech in a normal-sized room instead of needing a football field.

1. Problem Statement

The rapid evolution of sub-THz (100–300 GHz) communication systems (e.g., 6G) and imaging technologies has necessitated the use of large aperture antennas and arrays. However, characterizing these antennas presents significant challenges:

Impractical Far-Field (FF) Distances: The traditional Fraunhofer distance ( $d_{FF} = 2D^2/\lambda$ ) scales with the square of the antenna dimension ( $D$ ) and inversely with wavelength ( $\lambda$ ). At sub-THz frequencies, this results in measurement distances that are often too large for standard laboratory environments.
Instrumentation Constraints: Sub-THz components are expensive and scarce. Research and industrial labs often lack a matched set of three antennas with identical frequency bands, forcing the use of dissimilar antenna pairs (different sizes and frequency ranges) for the standard three-antenna gain measurement method.
Reference Point Ambiguity: Determining the precise reference point for distance measurement (e.g., aperture center vs. phase center) is difficult, leading to errors in path loss calculations and gain estimation.
Near-Field Effects: Using compact setups often places antennas in the radiating near-field, where traditional Friis transmission equations fail due to wavefront curvature and phase errors.

2. Methodology

The authors propose a Compact Cluster Measurement (CCM) technique that redefines the far-field criteria and adapts the three-antenna method for localized distance clusters.

A. Theoretical Revisions

Revised Far-Field Distance ( $d_{FF,Rev}$ ):
- Traditional theory considers only the largest antenna dimension. The authors argue that FF conditions depend on the combined aperture sizes of both the transmitting and receiving antennas.
- They derive a new expression for the minimum separation distance to ensure the total phase error ( $\phi_{total}$ ) remains within the acceptable limit of $\pi/8$ (22.5°).
- The revised formula is:
  $d_{FF,Rev} = \frac{2(D_1^2 + D_2^2)}{\lambda}$
  where $D_1$ and $D_2$ are the largest dimensions of the two antennas. This allows for shorter measurement distances compared to the traditional $2D^2/\lambda$ (where $D$ is the max dimension of the larger antenna).
Modified Path Loss Calculation:
- Instead of a single fixed distance, the method employs a distance sweep within localized clusters.
- The path loss term in the Friis equation is averaged over the three antenna pair combinations (A-B, A-C, B-C) to account for varying separation distances and aperture sizes, reducing systematic errors.

B. Experimental Setup

Frequency Range: 145–170 GHz (Sub-THz).
Antennas:
- PEWAN1028: Pyramidal horns (110–170 GHz, ~25 dBi gain).
- FLANN 30240: Standard gain horns (145–220 GHz, ~20 dBi gain).
- Frequency Extenders: Used as a third "antenna" (open-ended waveguide) to overcome inventory constraints.
Configuration: Three distinct measurement configurations were tested:
1. Two PEWAN antennas + One FLANN antenna.
2. Two FLANN antennas + One PEWAN antenna.
3. Two PEWAN antennas + One open-ended waveguide (extender).
Procedure: Measurements were taken in three "clusters" of distances (approx. 100–103 cm, 120–123 cm, and 160–163 cm) using motorized rails with $\pm 10 \mu m$ accuracy. Data was averaged over multiple runs to suppress standing wave ripples.

3. Key Contributions

New FF Interpretation: Introduction of a physically derived, revised Fraunhofer distance formula that accounts for the aperture sizes of both antennas, enabling more accurate gain measurements in compact spaces.
Dissimilar Antenna Validation: Demonstration that the three-antenna method yields reliable results even when using mismatched antenna pairs (different sizes and frequency bands) and open-ended waveguides, provided the revised distance criteria are met.
Compact Cluster Technique: A practical measurement workflow that replaces long-distance sweeps with localized, high-density distance clusters, significantly reducing measurement time and facility requirements.
Waveguide Mismatch Handling: Successful emulation and measurement of gain despite waveguide dimension mismatches (WR6.5 to WR5.1) between the frequency extenders and the FLANN antennas.

4. Results

Accuracy:
- The measured realized gains showed excellent agreement with full-wave simulations.
- PEWAN Antennas: Average offset between measured and simulated gain was 0.05–0.06 dB.
- FLANN Antennas: Average offset was 0.12–0.15 dB (higher due to waveguide mismatch and manufacturing tolerances).
- Standard Deviation: The standard deviation of the gain measurements across 150 samples was consistently < 0.09 dB, indicating high repeatability.
Comparison with Extrapolation:
- The CCM results were compared against the classical extrapolation technique (sweeping from near-field to far-field).
- The CCM method produced results nearly identical to the extrapolation method (e.g., differences of < 0.02 dB for PEWAN samples) but with significantly less complexity and time.
Phase Error Analysis:
- At the shortest cluster distance (Cluster 1), the phase error exceeded the $\pi/8$ threshold for the larger antenna pair, confirming the necessity of the revised distance formula.
- Cluster 2 (approx. 120 cm) satisfied the revised FF criteria for all combinations, acting as a "sweet spot" for compact measurements.

5. Significance

Feasibility for 6G and Sensing: This work proves that accurate sub-THz antenna characterization does not require massive anechoic chambers or prohibitively long distances. It enables labs with limited space to perform high-integrity measurements.
Cost and Inventory Efficiency: By validating the use of dissimilar antennas and open-ended waveguides as the third element, the method lowers the barrier to entry for research and industry, reducing the need for expensive, perfectly matched antenna sets.
Standardization Potential: The proposed revised FF distance formula offers a more rigorous theoretical basis for setting measurement standards in the sub-THz regime, where traditional approximations often fail.
Industrial Applicability: The technique meets industry uncertainty requirements (ETSI TR 138 903) and offers a robust, repeatable solution for the mass characterization of antennas required for future high-frequency wireless systems.