<p>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 (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(240\,\textrm{m}^2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>240</mn> <mspace width="0.166667em" /> <msup> <mtext>m</mtext> <mn>2</mn> </msup> </mrow> </math></EquationSource> </InlineEquation>) 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 <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(7.38\,\textrm{dB}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>7.38</mn> <mspace width="0.166667em" /> <mtext>dB</mtext> </mrow> </math></EquationSource> </InlineEquation> and increasing <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(R^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>R</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> 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 <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(99\%\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>99</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> reliability, the polynomial model requires <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(25.73\,\textrm{dB}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>25.73</mn> <mspace width="0.166667em" /> <mtext>dB</mtext> </mrow> </math></EquationSource> </InlineEquation> versus 27.79 to <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(28.05\,\textrm{dB}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>28.05</mn> <mspace width="0.166667em" /> <mtext>dB</mtext> </mrow> </math></EquationSource> </InlineEquation> for linear baselines, enabling tighter indoor massive Internet of Things link budgets aligned with sixth-generation reliability targets under energy constraints.</p>

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

  • Nahshon Mokua Obiri,
  • Kristof Van Laerhoven

摘要

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 ( \(240\,\textrm{m}^2\) 240 m 2 ) 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 \(7.38\,\textrm{dB}\) 7.38 dB and increasing \(R^2\) R 2 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 \(99\%\) 99 % reliability, the polynomial model requires \(25.73\,\textrm{dB}\) 25.73 dB versus 27.79 to \(28.05\,\textrm{dB}\) 28.05 dB for linear baselines, enabling tighter indoor massive Internet of Things link budgets aligned with sixth-generation reliability targets under energy constraints.