Environment-aware indoor LoRaWAN path loss: parametric regression comparisons, shadow fading, and calibrated fade margins

Abstract Indoor long-range wide area network (LoRaWAN) propagation is shaped by structural and time-varying environmental factors, which limit single-slope log-distance models and the standard log-normal shadowing assumption. We propose an environment-conditioned path loss framework that augments a log-distance multi-wall baseline with co-recorded environmental covariates (relative humidity, temperature, carbon dioxide, particulate matter, and barometric pressure) and receiver-reported signal-to-noise, and we validate both the mean and the residual law statistically. The approach is evaluated on a 12-month campaign in an eighth-floor office ( $$240\,\textrm{m}^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>240</mml:mn> <mml:mspace/> <mml:msup> <mml:mtext>m</mml:mtext> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> ) using time-blocked 5-fold cross-validation and a chronological hold-out. Across parametric regressors (regularized multiple linear regression (MLR), conjugate Bayesian linear regression, and a selective quadratic MLR extension on continuous predictors), the selective polynomial mean improves out-of-sample accuracy, reducing cross-validated root mean square error from 8.23 to $$7.38\,\textrm{dB}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>7.38</mml:mn> <mml:mspace/> <mml:mtext>dB</mml:mtext> </mml:mrow> </mml:math> and increasing $$R^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> from 0.81 to 0.84. Out-of-fold (OOF) residuals are distinctly non-Gaussian and are best summarized by a compact 3-component Gaussian mixture with a sharp core and a light, broad tail. Finally, we translate prediction error to reliability by prescribing the fade margin as an upper-tail percentile of OOF errors, attaching moving-block bootstrap uncertainty, and validating the achieved outage on a held-out set. At $$99\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>99</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> reliability, the polynomial model requires $$25.73\,\textrm{dB}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>25.73</mml:mn> <mml:mspace/> <mml:mtext>dB</mml:mtext> </mml:mrow> </mml:math> versus 27.79 to $$28.05\,\textrm{dB}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>28.05</mml:mn> <mml:mspace/> <mml:mtext>dB</mml:mtext> </mml:mrow> </mml:math> for linear baselines, enabling tighter indoor massive Internet of Things link budgets aligned with sixth-generation reliability targets under energy constraints.