# Measurement-Based Modeling of Large-Scale and Time-Varying Small-Scale Fading for LoRa in Indoor Multi-Floor Environments

## TL;DR

This paper studies how LoRa signals behave in multi-floor buildings to help design better IoT networks.

## Contribution

The study introduces new models for LoRa signal propagation, including time-varying small-scale fading and RSSI-SNR relationships.

## Key findings

- A log-distance path loss model with FAF of 5.52 dB per floor was derived.
- Time-varying small-scale fading was modeled using a Markov-modulated process.
- A non-linear RSSI-SNR relationship was modeled with a four-parameter logistic function.

## Abstract

The deployment of robust Internet of Things (IoT) networks within smart buildings requires a thorough understanding of radio propagation in complex indoor environments. Long Range (LoRa) technology is a promising solution for such applications due to its long range and low power consumption. However, its performance in multi-floor structures is heavily influenced by site-specific propagation conditions. This paper presents an empirical characterization of LoRa signal propagation at 433 MHz within a four-story university building. Extensive measurements of Received Signal Strength Indicator (RSSI) and Signal-to-Noise Ratio (SNR) were conducted to model both large-scale and small-scale fading effects. A log-distance path loss model with a Floor Attenuation Factor (FAF) was derived, yielding a path loss exponent of n=2.53, an FAF of 5.52 dB per floor, and a log-normal shadowing standard deviation of σ=6.93 dB. Time-varying small-scale fading was successfully characterized by a Markov-modulated process (Markov Small-Scale Fading). Furthermore, a non-linear relationship between RSSI and SNR was identified and modeled using a four-parameter logistic function, revealing a dynamic range of approximately 30 dB for the transceivers and a minimum measurable RSSI of −125 dBm. The results validate the proposed models and demonstrate that LoRa can provide reliable, building-wide wireless sensor coverage, offering essential guidelines for the planning and deployment of indoor IoT infrastructure in multi-floor environments.