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During the last few years, there is a growing interest on the usage of Wi-Fi signals for human activity detection. A large number of Wi-Fi based sensing systems have been developed, including respiration detection, gesture classification, identity recognition, etc. However, the usability and robustness of such systems are still limited, due to the complexity of practical environments. Various pioneering approaches have been proposed to solve this problem, among which the model-based approach is attracting more and more attention, due to the advantage that it does not require a huge dataset for model training. Existing models are usually developed for Line-of-Sight (LoS) scenarios, and can not be applied to facilitating the design of wireless sensing systems in Non-Line-of-Sight (NLoS) scenarios (e.g., through-wall sensing). To fill this gap, we propose a through-wall wireless sensing model, aiming to characterize the propagation laws and sensing mechanisms of Wi-Fi signals in through-wall scenarios. Specifically, based on the insight that Wi-Fi signals will be refracted while there is a wall between the transceivers, we develop a refraction-aware Fresnel model, and prove theoretically that the original Fresnel model can be seen as a special case of the proposed model. We find that the presence of a wall will change the distribution of Fresnel zones, which we called the "squeeze effect" of Fresnel zones. Moreover, our theoretical analysis indicates that the "squeeze effect" can help improve the sensing capability (i.e., spatial resolution) of Wi-Fi signals. To validate the proposed model, we implement a through-wall respiration sensing system with a pair of transceivers. Extensive experiments in typical through-wall environments show that the respiration detection error is lower than 0.5 bpm, while the subject's vertical distance to the connection line of the transceivers is less than 200 cm. To the best of our knowledge, this is the first theoretical model that reveals the Wi-Fi based wireless sensing mechanism in through-wall scenarios.

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