A Statistical Evaluation of Indoor LoRaWAN Environment-Aware Propagation for 6G: MLR, ANOVA, and Residual Distribution Analysis

Modeling path loss in indoor LoRaWAN technology deployments is inherently challenging due to structural obstructions, occupant density and activities, and fluctuating environmental conditions. This study proposes a two-stage approach to capture and analyze these complexities using an extensive dataset of 1,328,334 field measurements collected over six months in a single-floor office at the University of Siegen's Hoelderlinstrasse Campus, Germany. First, we implement a multiple linear regression model that includes traditional propagation metrics (distance, structural walls) and an extension with proposed environmental variables (relative humidity, temperature, carbon dioxide, particulate matter, and barometric pressure). Using analysis of variance, we demonstrate that adding these environmental factors can reduce unexplained variance by 42.32 percent. Secondly, we examine residual distributions by fitting five candidate probability distributions: Normal, Skew-Normal, Cauchy, Student's t, and Gaussian Mixture Models with one to five components. Our results show that a four-component Gaussian Mixture Model captures the residual heterogeneity of indoor signal propagation most accurately, significantly outperforming single-distribution approaches. Given the push toward ultra-reliable, context-aware communications in 6G networks, our analysis shows that environment-aware modeling can substantially improve LoRaWAN network design in dynamic indoor IoT deployments.