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

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.