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Statistical Analysis of Primary and Random Clusters in 318 GHz Terahertz Channels for Industrial IoT

Siyuan Shao, Peize Zhang, Pekka Kyösti, Trung Q. Duong, Simon L. Cotton

arXiv:2608.25634v1eess.SP

TL;DR

Industrial IIoT requires characterization of THz channels, whose propagation differs from lower-frequency channels and exhibits sparse MPCs with prominent strong reflections. The paper analyzes 318 GHz factory measurements with enhanced clustering and separates primary from random clusters, finding distinct propagation characteristics that support separate modeling.

  • Problem

    Industrial IIoT channel modeling lacks sufficient characterization of sparse, quasi-optical THz propagation and its strong-reflection phenomena.

  • Method

    The paper analyzes 318 GHz factory measurements using MCD-initialized KPowerMeans, an extended Silhouette index, and an FSPL-based threshold to classify primary and random clusters.

  • Results

    Primary and random clusters show significant differences in channel spread characteristics, power decay rates, and angular distributions.

  • Takeaways & Limitations

    The findings support modeling primary and random clusters separately when developing high-fidelity THz stochastic channel models.

Abstract

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The ultra-high data rates enabled by terahertz (THz) communications pave the way for the demanding requirements of industrial Internet of Things (IIoT) applications, making the investigation of THz channels in industrial environments a critical research topic. This paper presents a comprehensive statistical analysis of the propagation channel at 318\,GHz in an industrial environment. In particular, a new clustering scheme is proposed for the sparsity observed in the multipath components (MPCs) of the measured channel. Furthermore, statistical analyses are conducted separately for the group of strong reflections, defined as primary clusters, and other propagation phenomena, defined as random clusters, in a rich-scattering environment. The results demonstrate that the large-scale parameters are predominantly influenced by these strong reflections. This study provides reliable support and guidance for subsequent THz stochastic channel modeling.

I. INTRODUCTION

THz channels in industrial environments differ from lower-frequency indoor channels because of sparsity, strong reflections, and quasi-optical propagation. This paper analyzes 318 GHz factory measurements using clustering methods that separately characterize primary and random clusters.

  • THz communications offer tens of gigahertz of continuous bandwidth for IIoT systems connecting sensors, machinery, and devices.
  • Higher frequencies increase path loss and make THz channel characteristics significantly different from millimetre-wave channels.
  • Sparse clusters and rays in sub-THz channels arise partly from limited measurement coverage, MPC extraction, clustering methods, and attenuation of higher-order reflections.
  • Industrial factory measurements at 142 GHz found 3.4 clusters and 3.9 rays per cluster, indicating richer scattering than typical sparse-channel expectations.
  • The study investigates 318 GHz factory-channel measurements to support THz channel modeling.
  • The proposed analysis extends KPowerMeans and the Silhouette index for sparse MPCs, then classifies clusters as primary or random for separate statistical analysis.

A. THz channel sounder

The channel sounder measures bidirectional angular responses over a 4 GHz band centered at 318 GHz in a factory hall. The processing converts measured frequency responses into refined, denoised PADPs for MPC extraction.

  • The VNA-based sounder uses 220–330 GHz pyramidal horn antennas and measures a 4 GHz bandwidth centered at 318 GHz.
  • 1001 frequency samples provide 0.25 ns delay resolution and a 250 ns maximum excess delay for distinguishing MPCs.
  • Measurements use 11 line-of-sight receiver locations in a factory hall containing machines, lathes, and metal cabinets.
  • The receiver scans 360° in 15° steps, while the transmitter scans 120°–210° in 15° steps to approximate azimuthally omnidirectional radiation.
  • Windowed inverse fast Fourier transformation converts the channel transfer function into a channel impulse response before PADP calculation.
  • Antenna-pattern interpolation improves angular resolution to 1°, sinc interpolation improves delay resolution to 0.025 ns, and denoising identifies MPCs as local peaks.

B. Multipath Component Clustering

The paper combines MCD-based preclustering initialization with KPowerMeans and adapts clustering evaluation for sparse THz MPCs. The procedure uses delay and directional differences, dynamic thresholds, and a modified Silhouette score to evaluate candidate cluster counts.

  • Clustering initialization: MCD-based preclustering initializes KPowerMeans to reduce its sensitivity to random initialization.The procedure is applied before KPowerMeans and uses pairwise MPC distances to form pre-segmented clusters.
  • Distance metric: The MCD measures separation between MPCs using delay differences and differences between transmitter and receiver unit direction vectors.The distance formulation is based on a Mahalanobis metric over delay and directional components.
  • Distance metric: A weighting matrix balances the contributions of delay and direction terms in the MPC distance calculation.The matrix is typically set to diag(ξ2, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25).
  • Clustering initialization: A dynamic threshold uses allowable intra-cluster delay and transmitter–receiver direction deviations to determine MPC grouping.The threshold is defined as Γ = ∥[δτ, δt, δr]∥A, with parameter derivations based on standard deviations across measurements.
  • Clustering initialization: The initialization selects reference MPCs, groups nearby candidates, and samples cluster representatives in descending cluster-power order.If pre-segmented clusters are insufficient, MPCs with the largest minimum MCD supplement the initial points.
  • Cluster validation: The Silhouette score is redefined for single-MPC clusters using a resolution-based residual distance to support evaluation at extreme cluster counts.Γres corresponds to MPCs separated by the temporal and spatial resolutions.

C. Propagation Characteristics Analysis

The channel’s strong reflections follow the FSPL trend and motivate separating primary clusters from random clusters. Comparing DS, ASA, and ASD reveals whether dispersion is dominated by strong reflections, the LoS path alone, or a mixture of propagation phenomena.

  • Strong NLoS paths and the LoS path closely follow the FSPL power-delay trend, unlike other NLoS paths.This difference indicates distinct propagation characteristics between FSPL-consistent paths and remaining NLoS paths.
  • Clusters within 6 dB of the FSPL curve are defined as primary clusters; all remaining clusters are random clusters.
  • Fig. 3 compares DS, ASA, and ASD across primary clusters, random clusters, and all MPCs at 318 GHz.Random-cluster spread calculations include the LoS cluster to illustrate their contribution.
  • When the overall spread matches random clusters, strong reflections are absent and the primary cluster consists only of the LoS path.
  • When the overall spread matches primary clusters, strong reflections completely dominate channel dispersion; otherwise, primary and random clusters jointly contribute.
  • In practice, the first two cases almost exclusively occur, supporting separate analysis and modeling of primary and random clusters.

IV. STATISTICAL CHARACTERISTICS ANALYSIS

The paper separately analyzes primary and random clusters because distinguishing them is necessary for characterizing THz channels. The comparison targets channel-modeling parameters spanning cluster counts, rays, delay, power, and angular distributions.

  • The statistical analysis treats primary and random clusters separately because their differentiation is necessary for the channel analysis.
  • The analysis covers cluster and ray counts, delay, power, and angular distributions as parameters relevant to THz channel modeling.
  • The comparative analysis is intended to highlight differences between cluster types and provide a reference for THz cluster-based channel modeling.

A. Number of Clusters and Rays

The measured channel contains more total clusters than a prior 142 GHz factory result, but primary clusters are few and comparatively stable. Primary clusters also contain slightly more detectable rays than random clusters because of their higher power.

  • 5.9 average total clusters exceeds the 3.4 average reported at 142 GHz, potentially reflecting methodology or richer factory multipath conditions.
  • 2 average primary clusters have noticeably lower variance than random clusters.
  • Primary clusters tend to contain slightly more rays than random clusters because higher power makes more rays detectable within the sounder’s dynamic range.
  • The observed ray count depends on scattering conditions, measurement angular and delay resolutions, and the MPC extraction algorithm.Therefore, the reported ray counts are primarily intended for comparison analysis.

B. Delay and Power

Primary and random clusters are compared through their arrival timing and power-delay behavior, with primary clusters showing stronger temporal decay and lower shadowing variability.

  • Interarrival time: All primary- and random-cluster interarrival-time fits passed the K–S test at the 5% significance level.Random-cluster mean interarrival time is comparable to the overall mean, whereas primary clusters have a larger mean.
  • Interarrival time: Primary clusters have a larger mean interarrival time than random and overall clusters.The random-cluster mean is comparable to that of all clusters.
  • Power decay with delay: Primary clusters exhibit more severe power decay with delay than random clusters.The linear fit has lower RMSE for primary clusters than random clusters, 2.71 versus 4.26.
  • Power decay with delay: 2.71 versus 4.26: primary-cluster power-delay fits have lower RMSE than random-cluster fits.The reported linear-fit RMSEs are 2.71 for primary clusters and 4.26 for random clusters.
  • Power decay with delay: 2.87 dB versus 4.10 dB: primary clusters have lower per-cluster shadowing than random clusters.The paper relates the difference to more irregular power variations for random clusters.

C. Angular Distribution

The study compares angular distributions of primary and random clusters and finds distinct behavior, while noting that limited transmitter scanning biases and truncates AoD measurements.

  • Angular distribution: Limited Tx-antenna angular scanning biases and truncates the AoD distribution.This measurement limitation affects interpretation of the angular comparison.
  • Angular distribution: Random-cluster AoD approximately follows N(−32.9, 35.32), while random-cluster AoA follows N(18.6, 94.82).These fitted forms are reported despite the AoD scanning limitation.
  • Angular distribution: Primary-cluster AoA and AoD show no discernible distribution pattern and depend considerably on environmental conditions.The paper contrasts this behavior with the approximate normal distributions of random-cluster angles.
  • Angular distribution: The proposed analysis reports significant differences between primary and random clusters in angular distributions and other channel spread characteristics.The conclusion links the comparison to distinct channel behavior for the two cluster classes.

APPENDIX DYNAMIC THRESHOLD IN THE INITIALIZATION PROCESS

The initialization procedure sets dynamic thresholds from cluster-count and distribution assumptions, using delay and angular statistics to support sparse-MPC clustering.

  • Cluster-count assumption: M is set to 5 because clusters are assumed mutually orthogonal with similar intra-cluster characteristics and thresholds should not be too low.Each cluster’s MPC parameter range is constrained to no more than 1/M of the overall range.
  • Delay threshold: The delay threshold is defined at the 20% point of the delay distribution.The procedure derives this threshold from the delay-generation method.
  • Angular thresholds: Azimuth and elevation thresholds at the 20% distribution point are ϕ′ = σϕ/4 and φ′ = σφ/4.5.These thresholds follow the wrapped-Gaussian azimuth and Laplacian elevation models.
  • Angular thresholds: The squared Euclidean distance between unit direction vectors is used to relate azimuth and elevation differences to an angular threshold.The appendix expresses this distance using the azimuth difference ϕ′ and elevation difference φ′.
  • Angular thresholds: Because elevation-domain scanning is not performed, the angular threshold is simplified using an arbitrary elevation angle φ.The appendix identifies I3 as the 3 × 3 identity matrix and φ as an arbitrary elevation angle.
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