Signals at 318 GHz did not behave as one statistical population in measurements from a factory hall, according to a new preprint. The analysis separated clusters associated with strong reflections from the remaining random clusters and found a clear contrast: primary clusters were fewer, but each contained more rays, while random clusters were more numerous on average and varied much more in number.
That distinction is aimed at engineers building stochastic channel models—mathematical descriptions of the statistical behavior of a radio link—not at showing that a future industrial wireless system will be faster, more reliable or otherwise improved. The authors associate the large-scale patterns primarily with strong reflections and recommend treating the two groups separately in future industrial Internet of Things models. With data from 11 line-of-sight receiver locations in one representative factory hall, the result is best read as a description of that measurement setting.
A rule for separating the signals
The measurements covered 4 GHz of bandwidth using 1,001 frequency points, giving the analysis a delay resolution of 0.25 nanoseconds and a maximum excess delay of 250 ns. Those settings define the time detail available when the measured signal paths are grouped into clusters.
The clustering workflow added an MCD-based pre-clustering initialization before KPowerMeans. The researchers also extended the Silhouette index, a check on how well observations fit their assigned cluster, because conventional cluster-validity measures cannot assess a cluster containing a single multipath component.
Cluster type was then set by an FSPL reference used in the analysis: any cluster no more than 6 dB below the curve was labeled primary, and the rest were labeled random. The two categories are therefore analytical labels created by the study’s threshold.
Fewer clusters, more rays
Across the reported averages, primary clusters numbered 2.0 per measurement, compared with 3.9 random clusters. Random-cluster counts were also more spread out: their standard deviation was 2.9, against 1.2 for primary clusters. Yet primary clusters carried an average of 4.6 rays each, versus 1.8 rays in random clusters. The pattern is a compact strong-reflection core alongside a larger, less predictable set of remaining groupings.
The difference showed up in the reported delay and angular spread regimes as well. The first pair of regimes predominated: either primary clusters were dominant, or no primary clusters existed apart from the line-of-sight cluster. In other words, the strongest reflected structure was usually either the main organized feature or absent, leaving the line-of-sight path and random clusters to describe the rest.
Timing made the split clearer
Timing and power made the separation sharper. The mean interval between primary clusters was 27.4 nanoseconds, compared with 9.8 ns for random clusters. Primary-cluster power declined at −0.173 decibels per nanosecond, versus −0.026 dB/ns for random clusters. Per-cluster shadowing, the reported variation in cluster power, was also lower for primary clusters: 2.87 dB compared with 4.10 dB.
A linear fit of cluster power against delay had a root mean square error, or RMSE, of 2.71 for primary clusters, compared with 4.26 for random clusters. The authors therefore reported a more pronounced and more consistently captured power-delay decline for primary clusters in this dataset. The reported distribution fits all passed the Kolmogorov–Smirnov test at the 5% significance level, although the supplied analysis does not give the test statistics or p-values.
Angles told a less tidy story
For the random group, the angle of arrival, or AoA, had a mean of 18.6° and a standard deviation of 94.8°. The angle of departure, or AoD, averaged −32.9°, with a standard deviation of 35.3°. The reported random-cluster angular summaries were approximately normal, while the primary-cluster angles had no discernible distribution pattern and appeared to depend on environmental conditions.
That angular comparison comes with a built-in measurement constraint: the transmitter azimuth scan was limited to [120°, 210°], and elevation angles were fixed rather than scanned. Those choices bias and truncate the departure-angle statistics, so the angular results should not be treated as a complete three-dimensional picture of the hall.
A useful model, but not yet a universal one
The authors’ broader interpretation is that large-scale channel-parameter patterns are primarily associated with strong reflections. They argue that keeping primary and random clusters as separate components could help represent terahertz channel dynamics and guide stochastic models for industrial IoT. That is a modeling proposal grounded in an observed association, not a causal test or a demonstration of improved throughput, latency or reliability.
The evidence remains narrow: it comes from 11 line-of-sight receiver locations in one representative factory hall. The FSPL boundary and the detected cluster structure may depend on the measurement and clustering choices, so the authors’ interpretation still needs testing in other industrial scenarios.
The manuscript is an arXiv version 1 preprint dated 26 August 2026. Its acknowledgments list support from the UK Engineering and Physical Sciences Research Council, the Research Council of Finland and the 6G Flagship Programme, along with a Keysight Technologies equipment donation.
Paper data and sources
Original title: Statistical Analysis of Primary and Random Clusters in 318 GHz Terahertz Channels for Industrial IoT
Authors: Siyuan Shao, Peize Zhang, Pekka Kyösti et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text