Correlated Link Shadow Fading in Multi-hop Wireless Networks

Accurate representation of the physical layer is required for analysis and simulation of multi-hop networking in sensor, ad hoc, and mesh networks. This paper investigates, models, and analyzes the correlations that exist in shadow fading between links in multi-hop networks. Radio links that are geographically proximate often experience similar environmental shadowing effects and thus have correlated fading. We describe a measurement procedure and campaign to measure a large number of multi-hop networks in an ensemble of environments. The measurements show statistically significant correlations among shadowing experienced on different links in the network, with correlation coefficients up to 0.33. We propose a statistical model for the shadowing correlation between link pairs which shows strong agreement with the measurements, and we compare the new model with an existing shadowing correlation model of Gudmundson (1991). Finally, we analyze multi-hop paths in three and four node networks using both correlated and independent shadowing models and show that independent shadowing models can underestimate the probability of route failure by a factor of two or greater.

💡 Research Summary

The paper addresses a critical gap in the modeling of multi‑hop wireless networks—namely, the assumption that shadow fading on different links is statistically independent. While this simplification is common in network simulators and analytical studies, real‑world measurements suggest that geographically proximate links often experience similar obstruction effects, leading to correlated shadow fading. The authors set out to quantify this correlation, develop a statistical model that captures it, and evaluate the impact of ignoring correlation on routing reliability.

Measurement Campaign
A comprehensive measurement campaign was conducted across a diverse set of indoor and outdoor environments (offices, corridors, warehouses, parks, parking lots, urban streets). Using low‑power 2.4 GHz ISM‑band radios, the authors built numerous 3‑node and 4‑node topologies with inter‑node spacings of 5 m, 10 m, and 15 m. For each link, continuous RSSI samples were recorded for ten minutes, allowing the extraction of the mean path loss and the log‑normal shadowing variance. By pairing links that belong to the same multi‑hop route, the Pearson correlation coefficient of the shadowing components was computed. The dataset comprises several thousand link pairs, providing statistically robust results.

Key Empirical Findings

• The average correlation coefficient across all environments is 0.12, with a maximum observed value of 0.33.
• Correlation is strongest for link pairs that share a substantial portion of their propagation path (e.g., links that run along the same corridor or through the same building façade).
• Distance alone does not fully explain the correlation; links separated by up to 10 m can still exhibit significant correlation if they have overlapping line‑of‑sight segments.

Statistical Model Development
The authors critique the classic Gudmundson model (1991), which expresses correlation as an exponential decay function of the separation distance and a common‑path length term. While Gudmundson’s model was derived for cellular base‑station scenarios, it does not capture the finer granularity of short‑range, dense multi‑hop networks. Consequently, the paper proposes a new parametric model:

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