New antenna modeling was introduced in 3GPP Release-19 as part of the channel-modeling study. For background on the channel model update itself, see my earlier post: 7–24 GHz channel model.
In this post, I take a closer look at the standardized procedure for calculating User Terminal (UT) antenna radiation patterns and polarization components, as specified in Clause 7.3 “Antenna Modelling” of the updated Rel-19 TR 38.901.
All figures presented here are generated using Python code that follows the TR specification. The full code is available on GitHub:
6g_ue_antennas.
At the moment, the repository includes:
antenna.ipynb: a Jupyter notebook for plotting antenna radiation patterns.utils.py: a Python module that implements the transformation logic and plotting functions.
In the sections below, I walk through each step of UT antenna modeling and illustrate it using the shared Python code.
For a general overview, you can also peek into our upcoming tutorial paper on Realistic UE Antennas for 6G in the 3GPP Channel Model.
Directional radiation pattern
Before Rel-19, UT antennas were modeled in a simplified way: as two (or more) cross-polarized components with omnidirectional radiation patterns. Antenna elements were typically spaced half a wavelength \( \lambda/2 \) apart—for example, four transmit antennas on the UT side might be arranged in a simple X X configuration.
The new model introduces directional radiation patterns, as defined in Table 7.3-2 of TR 38.901. In this model, the antenna is assumed to be oriented toward \( \theta^{\prime\prime}=90^\circ \) and \( \phi^{\prime\prime}=0^\circ \).
Table 1: Radiation power pattern of a single antenna element for handheld UT (Table 7.3-2 from TR 38.901)
| Parameter | Values |
|---|---|
| Vertical cut of the radiation power pattern (dB) |
$$
A''_{dB}(\theta'', \phi'' = 0^\circ) = -\min \left\{ 12 \left( \frac{\theta'' - 90^\circ}{\theta_{3dB}} \right)^2, \, SLA_V \right\}
$$
with \( \theta_{3dB} = 125^\circ \), \( SLA_V = 22.5 \,\text{dB} \), \( \theta'' \in [0^\circ, 180^\circ] \).
|
| Horizontal cut of the radiation power pattern (dB) |
$$
A''_{dB}(\theta'' = 90^\circ, \phi'') = -\min \left\{ 12 \left( \frac{\phi''}{\phi_{3dB}} \right)^2, \, A_{\max} \right\}
$$
with \( \phi_{3dB} = 125^\circ \), \( A_{\max} = 22.5 \,\text{dB} \), \( \phi'' \in [-180^\circ, 180^\circ] \).
|
| 3D radiation power pattern (dB) |
$$
A''_{dB}(\theta'', \phi'') = -\min \left\{ -\big( A''_{dB}(\theta'', \phi''=0^\circ) + A''_{dB}(\theta''=90^\circ, \phi'') \big), \, A_{\max} \right\}
$$
|
| Maximum directional gain of an antenna element \( G_{E,\max} \) | 5.3 dBi |
The angles \( \theta'' \) and \( \phi'' \) denote zenith/elevation and azimuth, respectively. Their definitions follow Figure 7.1.1 in TR 38.901 and are reproduced below.
\( \hat{\theta} \) and \( \hat{\phi} \) are unit vectors forming an orthogonal basis for each signal arrival/departure direction \( \hat{n} \) associated with angles \( (\theta,\phi) \). The double primes used for the angles and the reference radiation pattern \( A''_{dB}(\theta'',\phi'') \) refer to the reference Antenna Coordinate System (ACS), \( (x'',y'',z'',\theta'',\phi'') \). The radiation pattern at each candidate UT antenna location can be defined in a Local Coordinate System (LCS), denoted with single primes, \( (x',y',z',\theta',\phi') \). A Global Coordinate System (GCS) is used for scenarios involving multiple BSs and UTs and is written without primes, \( (x,y,z,\theta,\phi) \).
The parameters of the reference radiation pattern (shown below) are defined in utils.py in the dictionary RADIATION_PATTERN_DEFAULTS.
Antenna candidate locations
3GPP adopted reference device dimensions of 55 × 7 × 0 mm for handheld UTs. Based on this, eight candidate antenna locations were identified: four at the corners and four at the midpoints of the device edges. For each location, the maximum-gain direction is aligned with the axis pointing from the device center to that location. Accordingly, the reference radiation pattern is rotated and translated to each candidate position. The resulting patterns are shown below.
Antenna polarization
UT antenna polarization is more complex than for BS because real UT antennas are usually single-feed elements that do not produce a purely vertically or horizontally polarized wave. Instead, the polarization varies with direction and often results in an elliptically polarized field.
The general relationship between the radiation field and the power pattern is:
$$
A''(\theta'',\phi'') = \bigl|F''_{\theta''}(\theta'',\phi'')\bigr|^2 + \bigl|F''_{\phi''}(\theta'',\phi'')\bigr|^2 .
$$
Here, \( F''_{\theta} \) is the field component along \( \hat{\theta}'' \), and \( F''_{\phi} \) is the component along \( \hat{\phi}'' \).
Earlier versions of TR 38.901 already included two polarization modeling options (as also described in the paper 3D Channel Model in 3GPP):
- Model-1: a slanted dipole polarization model. This model is based on the idea that a polarization slant \( \zeta \) can be modelled as a mechanical tilt. This model achieves equal power split in vertical and horizontal directions at the antenna boresight, but the power split ratio depends on both azimuth and elevation direction \( \theta, \phi \).
- Model-2: a constant/angle-independent polarization model. This model assumes that the polarization power split is independent of azimuth and elevation angles \( \theta, \phi \). Considering a \( \zeta=\pm45^\circ \) cross-polarized transmit antenna pair, the constant polarization model assumption leads to an equal power split in vertical and horizontal for all signal directions around the antenna.
For UT antennas, a Model-1-like approach is adopted: polarization depends on the departure/arrival direction and on the antenna/UT orientation. The UT reference radiation pattern is assumed vertically polarized, with all gain in the \( \theta \) component:
$$
F''_{\theta''}(\theta'',\phi'') = \sqrt{A''(\theta'',\phi'')}, \quad F''_{\phi''}(\theta'',\phi'') = 0 .
$$
First step. Rotate each polarized field component of the reference pattern, \( F''_{\theta''}(\theta'',\phi'') \) and \( F''_{\phi''}(\theta'',\phi'') \), according to the orientation and polarization direction of each UT antenna \( u \). This yields the rotated components \( F'_{u,\theta'}(\theta',\phi') \) and \( F'_{u,\phi'}(\theta',\phi') \), using the coordinate-transformation formulas in Clause 7.1.3 of TR 38.901:
$$
\begin{bmatrix}
F_{u,\theta'}'(\theta',\phi') \\
F_{u,\phi'}'(\theta',\phi')
\end{bmatrix}
=
\begin{bmatrix}
\cos \psi_u & -\sin \psi_u \\
\sin \psi_u & \cos \psi_u
\end{bmatrix}
\begin{bmatrix}
F_{\theta''}''(\theta'',\phi'') \\
F_{\phi''}''(\theta'',\phi'')
\end{bmatrix}
$$
where the \( (\theta'', \phi'') \) and \( (\theta', \phi') \) angles after the 3D rotation are related as
$$
\begin{aligned}
\theta''(\alpha_u,\beta_u,\gamma_u;\theta',\phi')
&= \arccos\!\Big(
\cos\beta_u \cos\gamma_u \cos\theta' \\
&\quad + \big( \sin\beta_u \cos\gamma_u \cos(\phi' - \alpha_u) \\
&\qquad - \sin\gamma_u \sin(\phi' - \alpha_u) \big)\sin\theta'
\Big)
\end{aligned}
$$
$$
\begin{aligned}
\phi''(\alpha_u,\beta_u,\gamma_u;\theta',\phi')
&= \arg\!\Big(
(\cos\beta_u \sin\theta' \cos(\phi'-\alpha_u) - \sin\beta_u \cos\theta') \\
&\quad + j\big( \cos\beta_u \sin\gamma_u \cos\theta' \\
&\qquad + (\sin\beta_u \sin\gamma_u \cos(\phi'-\alpha_u)
+ \cos\gamma_u \sin(\phi'-\alpha_u)) \sin\theta' \big)
\Big)
\end{aligned}
$$
$$
\begin{aligned}
\cos \psi_u &=
\frac{
\cos\beta_u \cos\gamma_u \sin\theta'
-\big( \sin\beta_u \cos\gamma_u \cos(\phi' - \alpha_u)
- \sin\gamma_u \sin(\phi' - \alpha_u) \big)\cos\theta'
}{
\sqrt{1 - \Big(\cos\beta_u \cos\gamma_u \cos\theta'
+ (\sin\beta_u \cos\gamma_u \cos(\phi' - \alpha_u)
- \sin\gamma_u \sin(\phi' - \alpha_u))\sin\theta' \Big)^2}
}
\\[6pt]
\sin \psi_u &=
\frac{
\sin\beta_u \cos\gamma_u \sin(\phi' - \alpha_u)
+ \sin\gamma_u \cos(\phi' - \alpha_u)
}{
\sqrt{1 - \Big(\cos\beta_u \cos\gamma_u \cos\theta'
+ (\sin\beta_u \cos\gamma_u \cos(\phi' - \alpha_u)
- \sin\gamma_u \sin(\phi' - \alpha_u))\sin\theta' \Big)^2}
}
\end{aligned}
$$
The rotation angles (\(\alpha_u,\beta_u,\gamma_u\)) are derived from each antenna’s orientation and polarization direction in the LCS. Figure 4 illustrates these orientations: the bold arrows lie in the plane of the handheld device and are perpendicular to the axis connecting the device center to each candidate antenna location.
The reference pattern, polarized along \( Z'' \), must therefore be rotated to align with these indicated directions. The table below lists the corresponding 3D rotation angles for each candidate antenna.
Table 2: 3D rotation angles per candidate antenna
| \(\alpha_u\) | \(\beta_u\) | \(\gamma_u\) | Antenna # |
|---|---|---|---|
| -155° | 0° | 90° | 1 |
| -90° | 0° | 90° | 2 |
| -25° | 0° | 90° | 3 |
| 0° | 0° | 90° | 4 |
| 25° | 0° | 90° | 5 |
| 90° | 0° | 90° | 6 |
| 155° | 0° | 90° | 7 |
| 180° | 0° | 90° | 8 |
The provided Jupyter notebook can generate 3D plots of the total radiation pattern and the polarization components for each antenna. For example, Figures 5–7 show the total power,\( \theta \)-polarized component, and \( \phi\)-polarized component for Antenna 5.
Once the antenna-level rotation is applied, in the second step, the resulting polarized components \( F'_{u,\theta'}(\theta',\phi') \) and \( F'_{u,\phi'}(\theta',\phi') \) must be rotated again according to the orientation of the UT in the global coordinate system (GCS). This step uses the rotation angles defined in Clause 7.1.3 of TR 38.901. The following equations, similar to (7.1-11), (7.1-7), (7.1-8), (7.1-16), and (7.1-17) from Clause 7.1.3 of TR 38.901, are used to perform the transformations.
Table 3: 3D rotation angles per typical UT orientations
| UT orientation | \( \Omega_{\text{UT},\alpha} \) | \( \Omega_{\text{UT},\beta} \) | \( \Omega_{\text{UT},\gamma} \) |
|---|---|---|---|
| One-hand hold/blockage | 0–360° | 45° | 0° |
| Dual-hand hold/blockage | 0–360° | 0° | 45° |
| Hand hold and head blockage | 0–360° | 90° | 0° |
| Free space browsing | 0–360° | 45° | 0° |
| Horizontal on the surface | 0–360° | 0° | 0° |
It is worth noting that the two-step rotation procedure (antenna-level rotation followed by UT-level rotation) can be combined into a single equivalent rotation. However, the resulting angles differ from those applied in the two-step approach. For example, for antenna (6) in the free space browsing case, the two-step sequence is \( (\alpha_6=90^\circ, \beta_6=0^\circ, \gamma_6=90^\circ) \) followed by \( (\Omega_{\alpha}=0^\circ, \Omega_{\beta}=45^\circ, \Omega_{\gamma}=0^\circ) \). The equivalent single rotation would instead be \( (\alpha=90^\circ, \beta=0^\circ, \gamma=-45^\circ) \).
The Jupyter notebook also allows visualization of the polarization components together with the UT orientation. For example, Figures 8–10 show the radiation patterns and polarization components for all candidate antenna locations when the UT is in a dual-hand grip.
Key takeaways
- Rel-19 introduces directional UT antenna patterns to replace the earlier simplistic omnidirectional model.
- Antenna placement matters: eight candidate locations are standardized on a handheld device, with radiation patterns rotated accordingly.
- Polarization is modeled realistically: UT antennas are assumed vertically polarized in the reference pattern, with orientation-dependent transformations applied.
- Two rotation steps are required: first at the antenna level (local orientation), then at the device level (UT orientation in GCS). These can also be combined into a single equivalent rotation.
- Python code is available: all figures in this post were generated using the 6g_ue_antennas repository, which provides both plotting and transformation utilities.
© 2025 6ghow.com. This content is licensed under CC BY-NC 4.0. Attribution required.
