# Sub-Terahertz Channel Measurements and Characterization in a Factory
Building

Shihao Ju, Yunchou Xing, Ojas Kanhere, and Theodore S. Rappaport This research
is supported by the NYU WIRELESS Industrial Affiliates Program and National
Science Foundation (NSF) Research Grants: 1909206 and 2037845. NYU WIRELESS,
Tandon School of Engineering, New York University, Brooklyn, NY, 11201
{shao, ychou, ojask<EMAIL_ADDRESS>
###### Abstract

Sub-Terahertz (THz) frequencies between 100 GHz and 300 GHz are being
considered as a key enabler for the sixth-generation (6G) wireless
communications due to the vast amounts of unused spectrum. The 3rd Generation
Partnership Project (3GPP) included the indoor industrial environments as a
scenario of interest since Release 15. This paper presents recent sub-THz
channel measurements using directional horn antennas of 27 dBi gain at 142 GHz
in a factory building, which hosts equipment manufacturing startups.
Directional measurements with co-polarized and cross-polarized antenna
configurations were conducted over distances from 6 to 40 meters.
Omnidirectional and directional path loss with two antenna polarization
configurations produce the gross cross-polarization discrimination (XPD) with
a mean of 27.7 dB, which suggests that dual-polarized antenna arrays can
provide good multiplexing gain for sub-THz wireless systems. The measured
power delay profile and power angular spectrum show the maximum root mean
square (RMS) delay spread of 66.0 nanoseconds and the maximum RMS angular
spread of 103.7 degrees using a 30 dB threshold, indicating the factory
scenario is a rich-scattering environment due to a massive number of metal
structures and objects. This work will facilitate emerging sub-THz
applications such as super-resolution sensing and positioning for future smart
factories.

###### Index Terms:

Channel Measurement; Channel Modeling; Channel Statistics; Indoor Factory;
Sub-Terahertz; 140 GHz; 5G; 6G

##  I Introduction

With the advent of manufacturing and information technologies, the next
industry evolution, Industry 4.0, has been widely proposed and studied
worldwide, aiming to escalate the production capability for future decades
[1]. As a crucial part of Industry 4.0, smart factory presents the
digitization and intellectualization of the vertical and horizontal
integration of all participants in the production process. Integrating the
physical machines with the virtual software into a single cyber-physical
system will drastically increase production efficiency. Furthermore, creating
a digital copy of all components in a physical factory called digital twin can
provide unprecedented fine control and monitoring capability of every
production piece [2]. Core applications such as the industrial Internet of
things (IIoT) and artificial intelligence require multiple sensors connected,
data collected and processed, and finally, responses made in a timely and
intelligent manner [3]. Thus, the wireless network needs to support data rates
of tens of Gigabits per second (Gbps), low-latency connections of less than
one millisecond, and provide high-resolution sensing and imaging capabilities.

To fulfill such demanding requirements, moving to the sub-Terahertz (THz)
spectrum (100 – 300 GHz) is paramount due to the vast available bandwidth of
tens of GHz [4]. The ultrawide bandwidth can be leveraged to offer an
extremely high data rate and signal resolution, which leads to better wireless
connectivity and sensing capability. The Federal Communications Commission
(FCC) has authorized four unlicensed bands (116-122, 174.8-182, 185-190, and
244-246 GHz) in 2019 [5]. Since signal propagation characteristics in such a
wide range of frequencies can be drastically distinct, it is essential to gain
fundamental knowledge of propagation characteristics at sub-THz frequencies.
Factories have been proposed as a distinct environment in the 3rd Generation
Partnership Project (3GPP) Release 15 [6] for wireless propagation from other
indoor environments such as offices and shopping malls due to the vast
existence of metallic machines and robotics. Smooth metallic surfaces are more
reflective and less penetrative than common building materials (e.g., drywall)
for wireless signals, especially at sub-THz frequencies. Therefore, extensive
channel measurements and accurate channel models are vital to establishing
future sub-THz wireless networks for manufacturing factories.

Mismatched characteristics of polarization of the transmit antenna,
propagation channel, and receive antenna causes degradation in the received
signal power [7]. Polarization has been widely used at mmWave frequencies as a
degree of freedom other than time, frequency, and space, to support multiple
input multiple output (MIMO) diversity and multiplexing [8, 6, 9]. The sub-THz
channels have been observed to be more sparse than mmWave channels [10, 11].
Thus, the dual-polarized transmit and receive antenna arrays are necessary to
deliver more signal energy and increase channel rank.

The work presents the 142 GHz channel measurements conducted in a factory
building using directional horn antennas with two polarization settings (i.e.,
vertical-to-vertical (V-V) and vertical-to-horizontal (V-H)) at two
transmitter (TX) locations and seven receiver (RX) locations, aiming to
understand the channel characteristics in terms of path loss, delay spread,
angular spread, and polarization effect in the indoor factory (InF) scenario
at sub-THz frequencies. The rest of the paper is organized as follows: Section
II describes the factory environment, measurement settings, and procedure.
Section III presents the omnidirectional and directional path loss using V-V
and V-H antenna polarization and gives the gross cross-polarization
discrimination (XPD) values for the omnidirectional channel and the XPD for
directional paths (e.g., boresight and reflection paths). Section IV derives
the mean and maximum root mean square (RMS) delay spread and RMS angular
spread across all measured locations. Finally, concluding remarks and future
work are provided in Section VI.

##  II 142 GHz InF Channel Measurements

The 142 GHz InF channel measurements were conducted in a factory building in
the Brooklyn Navy Yard, NY, in the fall of 2021. The building ($\sim$110 m
L$\times$ 36 m W $\times$ 25 m H) was initially constructed in 1899 and served
as a machine shop for marine engines and components, and now becomes a hub for
local small manufacturing companies. As shown in Fig. 1, a 6.8 m wide hallway
centers in the building, and the ceiling and truss are made of steel.
Manufacturing labs and conference rooms are located at two sides of the
hallway, covered by large glass windows with metal frames.

Figure 1: An illustration of the measurement setup in the factory environment
(TX1 and RX2).

We used a wideband sliding correlation-based channel sounder generating a 500
MHz pseudorandom sequence. The baseband signal was first mixed with a 7 GHz
intermediate frequency (IF) signal and then up-converted to a center frequency
of 142 GHz with a 1 GHz null-to-null bandwidth. The channel sounder has a two
nanosecond temporal resolution for multipath components and a 152 dB maximum
measurable path loss under a 5 dB signal-to-noise-ratio (SNR) constraint. The
TX and RX were equipped with directional horn antennas of 27 dBi gain and an
8° half-power beamwidth (HPBW). The TX and RX antennas were swept in the
azimuth and elevation planes to search all the multipath components in the
environment. Each azimuth sweep produced 45 directional power delay profiles
(PDPs) using an 8° step size.

Figure 2: TX and RX locations for polarization measurements. Five TX locations
are denoted as orange stars and ten RX locations are denoted as green circles,
resulting in 13 TX-RX location pairs for channel measurements.

The TX was set at 3 m above the ground level emulating an indoor hotspot, and
the RX was set at 1.5 m above the ground level as a mobile user. Five TX
locations and ten RX locations were selected for the polarization measurements
to study the cross-polarization effect, resulting in 11 line-of-sight (LOS)
measurement locations and two non-LOS (NLOS) measurement locations, as shown
in Fig. 2. The TX-RX separation distance ranged from 6.3 m to 39.6 m. At each
measurement location, the best pointing angles with the strongest received
power were first found. A quick RX azimuthal power scan ($\sim$6 s) was
performed for each of 45 AODs (8° apart) to determine the set of AODs that
have detectable powers. Then, 45 8-degree stepped rotations were conducted at
the RX to record directional PDPs for each “good” AOD, which took about three
minutes. Complete azimuth angular statistics of the double-directional
channels were obtained. The vertically polarized antennas were rotated to be
horizontally polarized by applying a waveguide twist between the converter
output waveguide flange and the antenna. A sample power angular delay profile
of TX2 and RX5 is shown in Fig. 3. Two main arriving directions are the
boresight and the reflection from the wall at 90°. The XPD values of these two
directions are 28.3 dB and 22.7 dB, respectively. More details on the XPD will
be elaborated in Section III.

Figure 3: The power angular (AOA) delay profile of TX2 and RX5. Two main
arriving directions are the boresight direction and the reflection from the
wall at 90°. The XPD values of these two directions are 28.3 dB and 22.7 dB,
respectively.

##  III Path Loss with Dual Polarization

This section presents the path loss data and the fitting models for both
omnidirectional and directional channels. In addition, the gross XPD values of
omnidirectional channels and the XPD values of different directional channels
are extracted. Due to the dynamic range limit of the channel sounder, the RX3,
RX4, RX8 locations only received negligible power when using the V-H
polarization configuration. Thus, the path loss modeling for cross-
polarization excluded these three locations and used the rest ten locations.

###  III-A CI Path Loss Model

We use the close-in free space reference distance (CI) path loss model with 1
m reference distance [12], as this has been proven to be superior for modeling
path loss over many environments and frequencies [13].
$\mathrm{PL}^{\textup{CI}}$ represents the path loss in dB scale, which is a
function of distance and frequency:

$\begin{split}\mathrm{PL}^{\textup{CI}}(f,d)[\textup{dB}]=&\textup{FSPL}(f,d_{0})+10n\log_{10}\left(\frac{d}{d_{0}}\right)+\chi_{\sigma}^{\textup{CI}}\text{,}\\\
&\text{for}\>d\geq d_{0},\;\;\text{where}\>d_{0}=1\textup{m}\end{split}$ (1)

where $n$ denotes the path loss exponent (PLE), and
$\chi_{\sigma}^{\textup{CI}}$ is the shadow fading that is commonly modeled as
a log-normal random variable with zero mean and $\sigma$ standard deviation in
dB. $d$ is the 3-D T-R separation distance. $d_{0}$ is the reference distance,
and $\textup{FSPL}(f,d_{0})=20\log_{10}(4\pi d_{0}f/c)$. The CI path loss
model uses the FSPL at $d_{0}=1$ m as an anchor point and fits the measured
path loss data with a straight line controlled by a single parameter $n$ (PLE)
obtained via the minimum mean square error (MMSE) method. CI path loss model
can be used for co-polarized or cross-polarized measurement data.

###  III-B CIX Path Loss Model

An extension of the basic CI path loss model for the special case of cross-
polarization propagation is to add a constant attenuation factor known as the
cross-polarization discrimination (XPD) factor, that best fits the measured
data via an MMSE method given by:

$\begin{split}\mathrm{PL}^{\textup{CIX}}(f,d)[\textup{dB}]=&\textup{FSPL}(f,d_{0})+10n_{\textup{(V-V)}}\log_{10}\left(\frac{d}{d_{0}}\right)\\\
&+\textup{XPD}[\textup{dB}]+\chi_{\sigma}^{\textup{CIX}}\end{split}$ (2)

This CI path loss with XPD (CIX) model uses the PLE measured with the co-
polarized (V-V) antenna setting at identical locations and obtains the optimum
XPD value via the MMSE method. As seen from (2), the CIX model uses the
optimum XPD in dB that is added to the CI model to minimize the error between
the estimated and measured cross-polarized path loss.

###  III-C Omnidirectional Path Loss

The omnidirectional path loss data for V-V and V-H polarizations are shown in
Fig. 4. The PLE for the V-V and V-H data are 1.86 and 4.03 using the CI model,
respectively. The standard deviation of the shadow fading are 1.5 dB and 6.0
dB, respectively. The CIX model using the PLE for the V-V polarization leads
to the gross XPD with a mean of 27.7 dB and a standard deviation of 2.6 dB. A
smaller standard deviation of the shadow fading shows that the CIX model
provides a better fit than the CI model to the cross-polarization data.

Figure 4: Omnidirectional path loss data are fitted by the CI and CIX path
loss models. The gross XPD has a mean of 27.4 dB and a standard deviation of
2.3 dB.

###  III-D Directional Path Loss

The directional path loss data for V-V and V-H polarizations are shown in Fig.
5. Note that all the ten locations that have valid V-H path loss data are in
the LOS scenario. The directions are divided into three sets: boresight (B),
non-boresight best (NBB), and non-boresight (NB). The NB direction set
includes all the directions that can receive a valid signal power. The NBB
direction is the strongest in the NB direction set and then excluded from the
NB direction set. Such classification provides important insight about the
channel condition if a human or robot temporarily blocks the boresight path.
Using the CI model to fit the V-V directional path loss, the resulting PLE of
the B, NBB, and NB directions are 2.08, 2.68, and 4.58, respectively,
indicating the best non-boresight direction is sufficiently strong to support
a communication link if the boresight direction is blocked. However, an
arbitrary non-boresight direction may not be usable.

Figure 5: Directional path loss data are fitted by the CI path loss models.
The NBB direction is the strongest direction in the NB direction set.

The directions that have both valid V-V and V-H received powers are used to
derive the directional XPD. We noticed that all such directions are from
either the boresight path or the first-order reflection path. As shown in Fig.
6, the boresight paths have a mean XPD of 26.2 dB with a standard deviation of
2.7 dB while the reflection paths have a mean XPD of 20.2 dB with a standard
deviation of 4.3 dB, showing that reflection may cause de-polarization.

Figure 6: Empirical cumulative distribution function (CDF) of directional XPD
values of boresight paths and reflection paths.

##  IV Omnidirectional and Directional Delay Spread

Delay spread describes the temporal dispersion of multipath channels, which is
vital for the wireless system design to avoid inter-symbol interference. Note
that the delay spread depends on the threshold used for data denoising. Here
we applied a threshold of 20 and 30 dB below the maximum received power. The
omnidirectional and directional delay spreads are given in Table I.

TABLE I: Omnidirectional and Directional Delay Spread Statistics with 20 dB and 30 dB Threshold: Minimum, Maximum, Mean, Median, and 90 Percentile Delay Spread (ns) | Min | Max | Mean | Median | 90%
---|---|---|---|---|---
Omni RMSDS-20 dB | 0.7 | 43.8 | 11.0 | 6.3 | 33.3
Omni RMSDS-30 dB | 0.7 | 66.0 | 16.0 | 10.4 | 54.4
Omni MDS-20 dB | 4.4 | 372.6 | 74.8 | 56.2 | 163.0
Omni MDS-30 dB | 7.5 | 784.8 | 157.4 | 83.9 | 490.7
Dir RMSDS-20 dB | 0.3 | 292.9 | 3.0 | 0.7 | 4.6
Dir RMSDS-30 dB | 0.3 | 292.9 | 3.0 | 0.7 | 4.6
Dir MDS-20 dB | 1.2 | 706.4 | 10.4 | 3.2 | 14.4
Dir MDS-30 dB | 1.2 | 706.4 | 10.5 | 3.2 | 14.5

We choose the root mean square delay spread (RMSDS) and the maximum delay
spread (MDS) to show the channel dispersion. Omnidirectional delay spreads
with a 20 dB threshold are much smaller than the values with a 30 dB
threshold, while the directional delay spreads do not vary much with different
thresholds since a directional PDP usually contains only one to a few
multipath components. Taking the omnidirectional delay spreads obtained by the
30 dB threshold, the maximum omnidirectional RMSDS and MDS are 66.0 and 784.8
ns, respectively, which shows that multipath components with significant
delays may exist in the factory environment due to the metal building
framework. For the directional delay spread, even though the maximum
directional RMSDS and MDS are 292.9 and 706.4 ns, the 90 percentile of the
directional RMSDS and MDS are only 4.6 and 14.5 ns, suggesting that most
directions have very little time dispersion.

##  V AOA and AOD Angular Spread

The root mean square angular spread (RMSAS) describes the spatial dispersion
of multipath channels, which can be computed using Appendix A-1,2 in [6].
Similar to the delay spread, the angular spread varies according to the
threshold. Here we use a 20 or 30 dB threshold below the maximum directional
power over all azimuth angles. In addition, spatial lobes are used to identify
the number of distinct beams for the TX or RX. A spatial lobe represents a
main direction of energy arrival or departure, which may contain multipath
components over a large time window of hundreds of nanoseconds [14]. The
sample AOD and AOA power angular spectrum for TX1 and RX2 are shown in Fig. 7,
which shows five and four AOD and AOA spatial lobes. The number of AOA and AOD
spatial lobes and RMSAS with 20 and 30 dB thresholds are given in Table II.

TABLE II: The number of Spatial Lobes and Angular Spread Statistics with 20 dB and 30 dB Threshold: Minimum, Maximum, Mean, Median, and 90 Percentile Angular Spread (°) | Min | Max | Mean | Median | 90%
---|---|---|---|---|---
# AOA SL-20 dB | 1 | 4 | 2.2 | 2 | 3.2
# AOA SL-30 dB | 1 | 5 | 3.5 | 3 | 5
# AOD SL-20 dB | 1 | 5 | 2.2 | 2 | 3.4
# AOD SL-30 dB | 2 | 7 | 3.5 | 3 | 7
AOA RMSAS-20 dB | 2.9 | 71.1 | 27.0 | 21 | 57.9
AOA RMSAS-30 dB | 3.2 | 72.2 | 28.1 | 22.1 | 58.1
AOD RMSAS-20 dB | 3 | 103.1 | 25.2 | 19 | 55.9
AOD RMSAS-30 dB | 4 | 103.7 | 27.4 | 21.6 | 57.2

(a)

(b)

Figure 7: 2-D AOD and AOA power angular spectrum for TX1 and RX2 with a 30 dB
threshold.

The mean number of AOA spatial lobes using the 20 and 30 dB differs by 1.3,
and the mean number of AOD spatial lobes using the 20 and 30 dB differs by
1.3, showing the threshold level has a notable impact on the number of spatial
lobes. Also, the maximum number of AOD spatial lobes is larger than the
maximum number of AOA spatial lobes. Compared to our previous work at 142 GHz
in an indoor office environment [10], more spatial lobes are observed in the
factory environment, which can be attributed to the surrounding metal
structure and objects. The RMSAS show little difference using the 20 and 30 dB
threshold. The mean AOA and AOD RMSAS are similar (i.e., 28.1° and 27.4° using
a 30 dB threshold) while the maximum AOD RMSAS (103.7°) is much larger than
the maximum AOA RMSAS (72.2°).

##  VI Conclusion and Future Work

This paper presented recent 142 GHz channel measurements in a factory
building. Five TX locations and ten RX locations were selected to investigate
the channel polarization characteristics. The V-V and V-H omnidirectional path
loss data were modeled using the CI and CIX models, giving a gross XPD with a
mean of 27.7 dB and a standard deviation of 2.6 dB. By comparing V-V and V-H
path loss in each direction, the mean XPD of the boresight path and the first-
order reflection path are 26.2 dB and 20.2 dB, respectively. In addition, the
best non-boresight direction produces a PLE of 2.7, which is worse than the
boresight PLE of 2 but sufficient to reliably support a transmission link when
the boresight link is temporarily blocked.

The mean omnidirectional and directional RMSDS are 16.0 and 3.0 ns with a 30
dB threshold, respectively. Moreover, the multipath components with excess
time delays of hundreds of nanoseconds may exist due to the metal framework of
the factory building. On average, a TX and RX location pair may have 3.5
different departing and arriving directions with a 30 dB threshold. These
preliminary measurements show that the channel statistics in the factory
environment are different from those in the office environment. Thus,
extensive channel measurements in various factory buildings are required to
develop a realistic and general channel model for the InF scenario at sub-THz
frequencies, which will facilitate the development of high-accuracy sensing
and positioning techniques and the massive deployment of IIoT for future
intelligent factories in 6G and beyond.

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