Environment-Aware Indoor LoRaWAN Path Loss: Parametric Regression Comparisons, Shadow Fading, and Calibrated Fade Margins

TL;DR

This work tackles indoor LoRaWAN path loss under nonstationary indoor conditions by introducing an environment-aware regression framework that couples a log-distance, multi-wall mean with environmental covariates and a selective second-order polynomial. The approach is evaluated with leakage-safe, time-blocked cross-validation on a $12$-month dataset from an eighth-floor office, demonstrating a reduction in RMSE from $8.07\,\mathrm{dB}$ to $7.09\,\mathrm{dB}$ and an $R^2$ improvement to $0.86$, while revealing multimodal shadow fading captured by a $3$-component Gaussian mixture. Shadow-fading distributions are diagnosed with AIC/BIC, KS tests, Q–Q plots, and KDE, guiding tail modeling for fade-margin calibration, which translates predictive accuracy into reliable, quantile-based margins. At a $99\%$ packet delivery target, the environment-aware polynomial saves about $2\,\mathrm{dB}$ in fade margin versus linear baselines, enabling tighter, state-aware link budgets for indoor IoT. The framework provides a deployment-ready, statistically disciplined workflow aligned with 6G reliability targets and offers a portable blueprint for multi-site validation and real-time ADR integration.

Abstract

Indoor LoRaWAN propagation is shaped by structural and time-varying context factors, which challenge log-distance models and the assumption of log-normal shadowing. We present an environment-aware, statistically disciplined path loss framework evaluated using leakage-safe cross-validation on a 12-month campaign in an eighth-floor office measuring 240 m^2. A log-distance multi-wall mean is augmented with environmental covariates (relative humidity, temperature, carbon dioxide, particulate matter, and barometric pressure), as well as the signal-to-noise ratio. We compare multiple linear regression with regularized variants, Bayesian linear regression, and a selective second-order polynomial applied to continuous drivers. Predictor relevance is established using heteroscedasticity-robust Type II and III analysis of variance and nested partial F tests. Shadow fading is profiled with kernel density estimation and non-parametric families, including Normal, Skew-Normal, Student's t, and Gaussian mixtures. The polynomial mean reduces cross-validated RMSE from 8.07 to 7.09 dB and raises R^2 from 0.81 to 0.86. Out-of-fold residuals are non-Gaussian; a 3-component mixture captures a sharp core with a light, broad tail. We convert accuracy into reliability by prescribing the fade margin as the upper-tail quantile of cross-validated residuals, quantifying uncertainty via a moving-block bootstrap, and validating on a held-out set. At 99% packet delivery ratio, the environment-aware polynomial requires 25.7 dB versus 27.7 to 27.9 dB for linear baselines. This result presents a deployment-ready, interpretable workflow with calibrated reliability control for indoor Internet of Things planning, aligned with 6G targets.

Figures (6)

• Figure 1: Integrated experimental setup and indoor deployment. Floor plan shows the deployment locations of the gateway and the six end devices (ED0–ED5); schematic at the right side summarizes the data path: end devices (EDs) $\rightarrow$ gateway (GW) $\rightarrow$ The Things Network LoRaWAN Server $\rightarrow$ InfluxDB via MQTT. Icons not to scale; 2 m scale bar shown.
• Figure 2: Assembled end devices and the indoor Kerlink Wirnet iFemtoCell gateway used in the deployment.
• Figure 3: Leakage-safe, device-aware modeling pipeline with time-blocked cross-validation and within-fold feature mapping and standardization; residual analysis yields calibrated fade margins.
• Figure 4: Q--Q plots for the second-order polynomial regression residuals under: (a) Normal, (b) Skew--Normal, (c) GMM ($K{=}3$), (d) Cauchy, and (e) Student's $t$. (f) Residual histogram overlaid with fitted probability density functions. The three-component GMM captures a distinct residual structure, modeling two central peaks ($\mu_1$ and $\mu_2$) and extended tails ($\mu_3$), which reflects the multimodal and heterogeneous nature of indoor propagation environments.
• Figure 5: (a) Residual density from KDE overlays at Silverman $h{\approx}0.30$ dB and cross-validation log-likelihood $h{\approx}0.94$ dB. (b) Mode count versus bandwidth on a logarithmic sweep using prominence-based peaks.