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L-Moment-Based LOS and NLOS Channel Characterization via Four-parameter Kappa Distribution for AoA BLE CTE Measurements

Hamed Talebian, Aamir Mahmood, Mikael Gidlund

TL;DR

This work addresses the need for robust, IQ-level LOS/NLOS BLE AoA channel characterization under indoor multipath, where heavy-tailed statistics challenge conventional models. It combines a tightly paired LOS/NLOS BLE CTE dataset with an L-moment based framework that uses L-moment ratios and the four-parameter Kappa distribution to model heavy tails and asymmetry, validated by GoF metrics. The authors demonstrate strong LOS/NLOS separability at the IQ feature level, show that Kappa models yield superior GoF compared to Rayleigh/Rice-like models, and illustrate enhanced ML separability via DBSCAN when using L-moments. The results support using LMR/Kappa descriptors for robust LOS/NLOS detection, realistic channel simulation, and ML preprocessing in BLE AoA systems, with implications for more reliable indoor localization and sensing.

Abstract

Bluetooth Low Energy (BLE) CTE transmissions provide in-phase and quadrature (IQ) samples whose empirical statistics are strongly governed by the propagation regime. in particular, the distributions differ markedly between line-of-sight (LOS) and non-line-of-sight (NLOS) conditions. In NLOS, multipath-induced distortions typically degrade Angle-of-Arrivial (AoA) estimation accuracy. Existing BLE direction finding datasets rarely provide tightly controlled, IQ-level paired LOS and NLOS measurements with rigorous statistical validation, and commonly used flat-fading models can be inadequate for cluttered indoor environments exhibiting heavy-tailed power distributions. To address these limitations, we conduct a paired-geometry BLE AoA measurement campaign using an off-the-shelf module, collecting 132000 labeled CTE packets under matched anchor-tag conditions. A robust preprocessing stage removes anomalous CTEs using combined univariate and multivariate criteria. Feature-wise hypothesis tests on IQ-derived power features confirm strong LOS and NLOS separability. All mean differences are statistically significant; additionally, 92 percent of feature-wise variance differences are significant. We further compute L-moment ratios (LMRs) and analyze them in the L-moment Ratio Diagram (LMRD), showing that NLOS subsets exhibit markedly heavier tails and stronger asymmetry than LOS. Kappa-family distributions fitted from LMRs provide substantially improved dual scored L--moment goodness-of-fit (GoF), Specifically, for NLOS, which is the smallest discrepancy in the LMRD and a near-zero standardized L-kurtosis deviation. As a practice, we apply a self-supervised clustering to L-moment statistics, achieving a more separable representation, compared to product moments.

L-Moment-Based LOS and NLOS Channel Characterization via Four-parameter Kappa Distribution for AoA BLE CTE Measurements

TL;DR

This work addresses the need for robust, IQ-level LOS/NLOS BLE AoA channel characterization under indoor multipath, where heavy-tailed statistics challenge conventional models. It combines a tightly paired LOS/NLOS BLE CTE dataset with an L-moment based framework that uses L-moment ratios and the four-parameter Kappa distribution to model heavy tails and asymmetry, validated by GoF metrics. The authors demonstrate strong LOS/NLOS separability at the IQ feature level, show that Kappa models yield superior GoF compared to Rayleigh/Rice-like models, and illustrate enhanced ML separability via DBSCAN when using L-moments. The results support using LMR/Kappa descriptors for robust LOS/NLOS detection, realistic channel simulation, and ML preprocessing in BLE AoA systems, with implications for more reliable indoor localization and sensing.

Abstract

Bluetooth Low Energy (BLE) CTE transmissions provide in-phase and quadrature (IQ) samples whose empirical statistics are strongly governed by the propagation regime. in particular, the distributions differ markedly between line-of-sight (LOS) and non-line-of-sight (NLOS) conditions. In NLOS, multipath-induced distortions typically degrade Angle-of-Arrivial (AoA) estimation accuracy. Existing BLE direction finding datasets rarely provide tightly controlled, IQ-level paired LOS and NLOS measurements with rigorous statistical validation, and commonly used flat-fading models can be inadequate for cluttered indoor environments exhibiting heavy-tailed power distributions. To address these limitations, we conduct a paired-geometry BLE AoA measurement campaign using an off-the-shelf module, collecting 132000 labeled CTE packets under matched anchor-tag conditions. A robust preprocessing stage removes anomalous CTEs using combined univariate and multivariate criteria. Feature-wise hypothesis tests on IQ-derived power features confirm strong LOS and NLOS separability. All mean differences are statistically significant; additionally, 92 percent of feature-wise variance differences are significant. We further compute L-moment ratios (LMRs) and analyze them in the L-moment Ratio Diagram (LMRD), showing that NLOS subsets exhibit markedly heavier tails and stronger asymmetry than LOS. Kappa-family distributions fitted from LMRs provide substantially improved dual scored L--moment goodness-of-fit (GoF), Specifically, for NLOS, which is the smallest discrepancy in the LMRD and a near-zero standardized L-kurtosis deviation. As a practice, we apply a self-supervised clustering to L-moment statistics, achieving a more separable representation, compared to product moments.
Paper Structure (32 sections, 27 equations, 8 figures, 3 tables)

This paper contains 32 sections, 27 equations, 8 figures, 3 tables.

Table of Contents

  1. Introduction
  2. statistical framework
  3. Outlier Detectors
  4. Statistical Tests for Ordinary Moments
  5. L--Moments Statistics
  6. L--moment Definition
  7. L--moment Ratios
  8. Kappa-family Empirical Distribution
  9. Goodness of Fit (GoF) investigation
  10. Mini-summary
  11. Density-Based Spatial Clustering of Applications with Noise (DBSCAN)
  12. Experimental Framework
  13. Experimental Setup
  14. Measurement Campaign
  15. Experimental results
  16. ...and 17 more sections

Figures (8)

  • Figure 1: Experimental setup. (a) Indoor localization laboratory (b) Area of Interest (AoI) with tag location (TL) and anchor points (AP) (c) LOS blocker stand.
  • Figure 2: Raw feature power moments
  • Figure 3: Sample exemplars based on mean values.
  • Figure 4: Statistical tests of moment equality ($\alpha \le 0.01$).
  • Figure 5: Discordancy diagrams for LOS and NLOS feature sets.
  • ...and 3 more figures